2.8.

2.9.

2.10.

2.11.

2.12.

2.13.

2.14.

2.15.

2.16.

2.17.

2.18.

March 2003

Calibration results with the units of measurement in tabular or other convenient form.
(When an instrument has been repaired or adjusted the calibration results before and
after repair or adjustment, if available, are reported.)

Identify standards used and their traceability to national standards.

Conditions (e.g., environmental) under which the calibrations were made that have an
influence on the measurement results.

Where relevant, a statement of compliance/non-compliance with requirements and/or
specifications. Compliance refers to all criteria, both specifications and tolerances, of a
referenced standard and not just portions (e.g., compliance to tolerance only).

A statement of the estimated measurement uncertainty, components that were
considered and included, a rationale for their inclusion, and the coverage factor and
estimated confidence interval.

Where appropriate and needed, opinions and interpretations.

Additional information which may be required by specific methods, clients or groups of
clients.

Name, title, and signature of person authoring the report or certificate. Other signatures
may be required, at the discretion of the laboratory director. Each signer accepts
his/her share of responsibility for the contents of the report.

Where relevant, a statement to the effect that the results relate only to the items tested
or calibrated.

Hard copies of test reports should also include the page number and total number of
pages.

A statement specifying that the test report or calibration certificate shall not be
reproduced except in full, without written approval of the laboratory.

3. Recording

3.1.

3.2.

SOP 1

File all test reports in a systematic manner for ease of retrieval, as necessary.
Retain copies of all test reports for a minimum period of five years, until superseded by

a subsequent report, or as stated in the laboratory quality manual, or until deemed by
the laboratory director as having no future value.

Page 2 of 6


SOP 8

2.6.

2.5.2.

2.5.3.

2.5.4,

2.5.5.
2.5.6.

2.5.7.

2.5.8.

2.5.9.

December 2003

Add a sensitivity weight equal to approximately one-quarter full scale
reading and record reading as O>.

Calculate the value of a scale division using the equation in 3.2. If the
sensitivity is within + 2 % of nominal value (usual case) of the scale
division, the nominal value of a division may be used.

Remove the sensitivity weight and re-adjust the optical scale to obtain a
midscale indication, if the indication has changed from that set in 2.5.1.

Remove the Standard.

Place the weight to be tested on the balance pan, read the optical scale and
record the indication as X,. The error in the weight is the amount by
which the indication deviates from the mid-scale reading. If the weight
indication is more than the mid-scale value, the weight is heavier than the
standard by the indicated difference; if the indication is less than the mid-
scale value, the weight is lighter than the standard.

After several weights have been tested (no more than 10 without
rechecking the standard) put the standard on the balance pan and record
the reading. The difference between this indication and the previous one
for the standard indicates a balance drift. This drift will normally be very
small. If the drift exceeds 10 % of the tolerance applicable to the weights
under test or affects a measurement result to the extent that a weight may
be out of tolerance, the measurement should be repeated and more
frequent checks of the standard should be made or a more appropriate
procedure should be used.

Readjust the optical scale at any time that a significant difference is
observed when rechecking a standard.

Calculate the correction of the unknown using the equation

Cy = Cs + (Xn-Oy).

Procedure - Option B

Use of Full Electronic Balance

2.6.1.

2.6.2.

2.6.3.

Select a reference standard of the same nominal value as the weight under
test. Place the standard on the pan. Zero the balance and record reading
as O}.

Add a calibrated sensitivity weight (sw > 2 times the tolerance but not
exceeding 1 % of the balance capacity) and record the reading as Op.
Verify whether the nominal scale division is within + 2 % of nominal
value of the scale division using the equation in 3.2. If so, the nominal
value of the scale division may be used.

Remove sensitivity weight and zero the balance so weight differences, d,
can be read directly from the balance indications.

Page 4 of 12


March 2003

near the balance where a temperature gradient of 2 °C was present (when the uncertainty was less
than 0.1 mg).

The balance must be installed in an area free from air currents. Balances should be installed
away from heating/cooling vents. It is not adequate to merely close vents when weighing
because disrupting the temperature control system may result in temperature changes near the
balances.

Handling Weights

The masses of standard weights or objects weighed can be affected significantly by the manner in
which they are handled. Human contact can leave grease or oily films that affect the mass at the
time of measurement and can even cause permanent damage due to corrosion.

Small weights should never be touched by hand, but handled using forceps, clean gloves, or
swatches of cloth. In the latter case, the cloth must be lint free. Instructions for cleaning weights
and for removing adhering foreign material are described in GMP 5.

Large weights of lower tolerance classes (NIST Class F) may be handled by bare hands. Large
weights are a source of special problems. Fork lifts, portable cranes, hoists, or even overhead
cranes may have to be used to move the weights within the laboratory and on or off the balances.
Laboratory personnel must become expert in using such equipment, as necessary, to avoid
damage to the laboratory facilities, to the balances used, and even to the weights themselves.
Special hoist/crane hydraulics or multi-speed systems are available to gently set large weights in
place on large comparators to avoid damage. The problem of temperature equilibrium for large
weights is qualitatively the same as for small weights and needs consideration on an individual
basis.

Large weights must be clean at the time of use, but cleaning may be a problem. Minimally, they
should be inspected to ensure that foreign material is not present. Cleaning is addressed further
in GMP 5.

Operation

Analytical balances are high precision instruments and should be operated carefully. Excessive
shock can damage a balance. Avoid shock loading the balance. Gently place all weights in the
center of the weighing pan/platform. The dials on mechanical balances should be turned slowly
and gently. Careful balance operation will improve the repeatability of measurements.

Mechanical analytical balances are provided with partial and full release positions. The partial
release position is used when determining if an unknown load will provide an on-scale reading.
The balance beam has limited movement in this position. The partial release position provides
some protection to the balance when the dialed-in weights are not close to the actual mass placed
on the pan. It is good practice to arrest the pan each time a dial is being changed to protect the
balance from shock loading. It is acceptable to change the dial representing the smallest built-in

GMP 10 Page 2 of 6


December 2003

calibrated using a calibration standard other than the
calibration standard(s) it will be controlling.

2.5.2. Establish Control Measurements for Reference Limits

2.5.2.1. Control measurements to establish initial reference limits may
be made at any time to verify current measurement process
performance. But to achieve control of calibration standards
accuracy and measurement instrument capability, the control
measurements should be made just after calibration of the
calibration standards and servicing of the measurement
instrument. Any significant change in the calibration status
can then be detected by the performance change in the
reference limits data.

2.5.2.2. Make the control measurement by duplicating the calibration
process with the check standard substituted for the calibrated
item. Make an observation of the check standard (S,) and
determine its measured value by completing calculations as
described in the calibration SOP.

2.5.2.3. Record the measured value (S,) and plot it on the control chart
and evaluate it with reference to the accepted value of the
check standard. Record date, time, and information tags with
data.

2.5.2.4. Evaluate the bias (difference) between the mean of the
measured S, values and the accepted value for S, from its
calibration report.

Bias (deviation) of check standard = Observed mean of S, - Accepted S,

2.5.2.5 Repeat the control measurement at various intervals to sample
environmental change and other factors than can affect
measurement performance. Although a control chart and
some statistical control can be established with as few as
seven to 12 measurements, a minimum of twenty-five is
recommended for estimates and control of uncertainties

2.5.3 Create and Prepare Control Charts

2.5.3.1 Construct a graph with the deviation of the check standard
measurements on the y-axis and chronological date and time
(or observation number) on the x-axis. The accepted value of
the check standard (S,) is identified near the center of the
chart. The y-axis of the control chart should extend plus and

SOP 30 Page 5 of 9




SELECTED LABORATORY

AND MEASUREMENT

PRACTICES, AND PROCEDURES
TO SUPPORT BASIC MASS

CALIBRATIONS

Editor:

Georgia L. Harris

NIST Weights and Measures Division
Gaithersburg, MD 20899

Jose A. Torres
NIST Weights and Measures Division
(contract)

U.S. Department of Commerce
Donald L. Evans, Secretary

Technology Administration
Phillip J. Bond, Under
Secretary of Commerce

for Technology

National Institute of Standards

and Technology
Arden L. Bement, Jr., Director

NISTIR 6969

2003




March 2003

4. — Assignment of Uncertainty

The uncertainty in determining the air buoyancy correction is usually negligible relative to
the precision of the measurement process itself. Consequently, the uncertainty for the
measurement is based upon the uncertainty for the measurement process used. The
uncertainty in the air density equation as given in numerous periodicals is 0.0012 mg/cm?
(or about 0.1 % of normal air density.)

Table 3. Tolerances for measurements related to air density estimation

Uncertainty of air density values in % of air density
Variable +01 % of air + 1.0 % of air density Recommended
density (Section 2.2)
Air pressure (Pa) +101 +1010 + 66.5
Air pressure (mm Hg) + 0.76 £7.6 +0.5
Air temperature (°C) + 0.29 +2.9 +01
Relative Humidity (%) £13 | eeeeeeeee +10

SOP 2 Page 5 of 22


December 2003

2.3, Apparatus/Equipment Required

2.4.

2.3.2. A calibration process that meets the requirements of the standard
operating procedure (SOP).

2.3.3. A check standard that has been selected to evaluate the established
objectives of: the 1) measurement process uncertainty; 2) the
calibration standards; or 3) both the process and the standards.

2.3.4. A data input, statistical calculating, and control charting system to
provide analysis of measurement control data. (i.e., special software

package or spreadsheet)
Table 1. Symbols description

Symbol Description
Sc Control measurement of check standard
Scs Accepted value of check standard
U Expanded Uncertainty (of the process)
Ue Combined standard uncertainty
Us Standard uncertainty of the standard
Uo Standard uncertainty of other factors
Ug Standard uncertainty of differences
Sp Standard deviation of the process
k Coverage factor

2.5. Procedure

SOP 30

2.5.1. Preliminary Procedure

2.5.1.1.

Model the Calibration Process

Set objectives for the PMAP application. These objectives
will establish the value of the check standard, the check
standard measurement procedure, and influence the frequency
of control measurements of the check standard. Objectives
may be: 1) Determine the standard deviation of the process
(sp); 2) Determine the Expanded Uncertainty (U); 3) Measure
the value of the calibration standard uncertainty (u,). The
model may allow any one objective or a combination of the
objectives to be established with a single PMAP application
and PMAP control chart.

Diagram the process to clarify the measurement steps and
determine the approach that will achieve the established
objectives. When determining and controlling the expanded
uncertainty (U), evaluate the range of use of the process to

Page 3 of 9


March 2003

CM, (12x10 - p, (2 - +) (8)
Ps Pp

It is a requirement for manufacture that the actual density of standard weights be near
enough to the assumed density of the apparent mass scale to which they are adjusted that
the magnitude of (8) will always be small under normal conditions in laboratories near sea
level.

The fact that there are two apparent mass scales widely used - one based on density
8.0 g/cm? and an older one based on 8.4 g/cm? - means that some caution is required on the
part of the user. Conventional mass is generally preferred and reported for all calibrations
where mass standards will be used to calibrate weighing instruments. For the most accurate
work, the apparent mass scale should be abandoned in favor of substitution weighing with
standards of known mass and volume.

The user must decide the accuracy required of the particular mass measurement and choose
a buoyancy correction technique commensurate with that accuracy.

The same considerations, which apply to the accuracy of buoyancy corrections in weighing
by substitution, are easily extended to the other types of weighing indicated above.

There are many factors, which affect the accuracy of a mass measurement. The above has
dealt only with those arising from problems of buoyancy.

Appendix SOP 2 Page 16 of 22


March 2003

4, When two or more figures are to the right of the last figure to be retained, consider
them as a group in rounding decisions. Thus, in 2.4(501), the group (501) is
considered to be greater than 5 while for 2.5(499), (499) is considered to be less
than 5.

Several examples to illustrate the proper method of reporting corrections and uncertainties
follow.

Example 1

Suppose the correction for a weight is computed to be 1.3578 mg and the uncertainty is 0.5775
mg. First, round the uncertainty to two significant figures, that is, 0.58 mg. Then state the
correction as 1.36 mg. Notice that the uncertainty and the correction express the same number of
decimal places. Report the correction as 1.36 mg + 0.58 mg.

Example 2

The volume of a given flask is computed to be 2000.714431 mL and the uncertainty is 0.084024
mL. First, round the uncertainty to two significant figures, that is, 0.084 mL. (Do not count the
first zero after the decimal point.) Round the calculated volume to the same number of decimal
places as the uncertainty statement, that is, 2000.714 mL. Report the volume as 2000.714 mL +
0.084 mL.

Example 3

The correction for a weight is computed to be 4.3415 mg and the uncertainty is 2.0478 mg. First,
round the uncertainty to two significant figures, that is, 2.0 mg. (Notice that two significant
figures are shown. The zero is a significant figure since it follows a non-zero number.) Then,
round the correction to the same number of decimal places as the uncertainty statement, that is,
4.3 mg. Report the correction as 4.3 mg + 2.0 mg.

Example 4

The correction for a weight is computed to be 285.41 mg and the uncertainty is 102.98 mg.
Because this uncertainty is a large number, we first convert both values to the next larger
commonly reported unit (i.e., 0.28541 g and 0.10298 g respectively). First, round the uncertainty
to 0.10 g. (The first nonzero digit (1) is the first significant figure and the remaining digits are
rounded to the nearest number following the first nonzero digit.) Then, round the correction to
the point where the rounding occurred in the uncertainty statement. Round the correction to
0.29 g. Report the correction as 0.29 g + 0.10 g.

Example 5

The correction for a weight is computed to be 285.41 mg and the uncertainty is 33.4875 mg.
First, round the uncertainty to two significant figures, that is 33 mg. Then, round the correction

GLP 9 Page 2 of 3


December 2003

5.4. The expanded uncertainty, U, must be < 1/3 of the tolerance applicable as per
ASTM E617-97 and OIML R111.

6. Report

Report results as described in SOP No. 1, Preparation of Calibration/Test Reports.

SOP 8 Page 9 of 12


December 2003

and warning limits that represent probabilistic limits for the distribution of
results around the central line. These parameters are evaluated on the basis
of a reasonable number of initial measurements and updated as additional
measurement data are accumulated.

3.3.2. Make at least seven (minimum number) and preferably 12 or more,
independent measurements of the check standard under the same conditions
that will be used to make routine measurements. No two measurements
should be made on the same day. This is necessary to estimate the long-term
standard deviation to the extent feasible. To make statistically valid
decisions or calculate uncertainties based on this data, 25 to 30 points are
necessary.

Calculate the mean, x and the estimate of the standard deviation, s in the
conventional manner.

Establish the control chart parameters as follows:

Central Line =x
Upper Control/Action Limit =xt+3s
Upper Warning Limit =x+2s
Lower Warning Limit =x-2s
Lower Control/Action Limit = x -3s

Control chart parameters for Echelon III (Class F or other) may be completed
as follows to track practical limits:

Central Line =x

Upper Control/Action Limit =x + 1/4 tolerance

Upper Warning Limit = x + 1/10 tolerance
Lower Warning Limit - 1/10 tolerance
Lower Control/Action Limit = x - 1/4 tolerance

SOP 9 Page 3 of 5


Table 9.6 Factors for Two-sided Tolerance Intervals

for the Normal Distribution

December 2003

y_ =0.95 Y =0.99

0.75 | 0.90 0.95 | 099 | 0999 } 0.75 0.90 | 0.95 | 0.99 0.999
n
2 | 22.858 | 32.019 | 37.674 | 48.430 | 60.573 114.363 [160.193 [188.491 |242.300 |303.054
3 5.922 | 8.380 | 9.916 | 12.861 | 16.208 } 13.378 | 18.930 | 22.401 | 29.055 | 36.616
4 3.779 | 5.369 | 6.370 | 8.299 | 10.502 | 6.614 | 9.398 | 11.150 | 14.527 | 18.383
5 3.002 | 4.275 | 5.079 | 6.634 | 8.415 | 4.643 | 6.612 | 7.855 | 10.260 | 13.015
6 2.604 | 3.712 | 4.414 | 5.775 | 7.337 | 3.743 | 5.337 | 6345 | 8.301 | 10.548
7 2361 | 3.369 | 4.007 | 5.248 | 6.676 | 3.233 | 4.613 | 5.488 | 7.187 | 9.142
8 2.197 | 3.136 | 3.732 | 4.891 | 6.226 | 2905 | 4.147 | 4.936 | 6.468 | 8.234
9 2.078 | 2.967 | 3.532 | 4.631 | 5.899 | 2.677 | 3.822 | 4.550 | 5.966 | 7.600
10 1.987 | 2.839 | 3.379 | 4.433 | 5.649 f 2.508 | 3.582 | 4.265 | 5.594 | 7.129
i 1.916 | 2.737 | 3.259 | 4.277 | 5.452 ]| 2.378 | 3.397 | 4.045 | 5.308 | 6.766
12 1.858 | 2.655 | 3.162 | 4.150 | 5.291 | 2.274 | 3.250 | 3.870 | 5.079 | 6.477
13 1.810 | 2.587 | 3.081 | 4.044 | 5.158 | 2.190 | 3.130 | 3.727 | 4.893 | 6.240
14 1.770 | 2.529 | 3.012 | 3.955 | 5.045 | 2.120 | 3.029 | 3.608 | 4.737 | 6.043
15 1.735 | 2.480 | 2.954 | 3.878 | 4.949 | 2.060 | 2.945 | 3.507 | 4.605 | 5.876
16 1.705 | 2.437 | 2.903 | 3.812 | 4.865 | 2.009 | 2.872 | 3.421 | 4.492 | 5.732
17 1.679 | 2.400 | 2858 | 3.754 | 4.791 | 1.965 | 2.808 | 3.345 | 4.393 }] 5.607
18 1.655 | 2.366 | 2.819 | 3.702 | 4.725 } 1.926 | 2.753 | 3.279 | 4.307 | 5.497
19 1.635 | 2.337 | 2.784 | 3.656 | 4.667 | 1.891 | 2.703 | 3.221 | 4.230 | 5.399
20 1.616 | 2310 | 2.752 | 3.612 | 4.614 | 1.860 | 2.659 | 3.168 | 4.161 | 5.312
21 1.599 | 2.286 | 2.723 | 3.577.] 4.567 } 1.833 | 2.620 | 3.121 | 4.100 | 5.234
22 1.584 | 2.264 | 2.697 | 3.543 | 4.523 | 1.808 | 2.584 | 3.078 | 4.044 | 5.163
23 1.570 | 2.244 | 2.673 | 3.512 | 4.484 |] 1.785 | 2.551 | 3.040 | 3.993 | 5.098
24 1.557 | 2.225 | 2.651 | 3.483 | 4.447 || 1.764 | 2.522 | 3.004 | 3.947 | 5.039
25 1.545 [| 2.208 | 2.631 | 3.457 | 4.413 | 1.745 | 2.494 | 2.972 | 3.904 | 4.985
26 1.534 | 2.193 | 2612 | 3.432 | 4.382 | 1.727 | 2.469 | 2.941 | 3.865 | 4.935
27 1.523 | 2.178 | 2.595 | 3.409 | 4.353 f| 1.711 | 2.446 | 2914 | 3.828 | 4.888

From: NBS Handbook 91, p T-11

Reference Tables

Page 7 of 13



March 2003

8.2. Air density, Option B — Preferred

The density of air should be calculated with the following formula.°

— PM, (, _
2 = Te (1 - 0.3780 x, )

x, = (h/100) f 22
P

2
Z=1- Pla, + at + at? +(b + bt)x, +(e + et )xy | + Pp (a + ex,’ )

Table A-4. Variables for CIPM air density equation

Variable Description

Ma molar mass of the air within laboratory 28.963 5 x 10° kg/mol
Pp ambient barometric pressure in Pascal

T ambient temperature in Kelvin

R universal gas constant: 8.314 510 J mol! KTM
h relative humidity in %

ft 1,000 62 + (3.14 x 10°) p+ (5.6.x 10)”

t ambient temperature in degrees Celsius
Pow 1 Pascal x exp (AT’ + BT + C + D/T)

A 1.237 884 7 x 10° K*

B -1.912 131 6x 10° KTM

C 33.937 110 47

D -6.343 164 5x 10°K

ao 1.581 23 x 10°K Pa"

ay -2.933 1x 10° PaTM

a 1.1043 x 107K” Pa?

bo 5.107 x 10° K Pa"

by -2.051 x 10% Pa"

co 1.989 8 x 10% K Pa"

ci -2.376 x 10° Pa"

d 1.83 x 107" K? Pa

e -0.765 x 10° K? Pa”

Calculate the density of air at the balance during the weighing. Then determine the
mass of the unknown, M,, as follows:

® CIPM References: Giacomo, P. Metrologia 18: 33-40 (1982), Davis, R.S., Metrologia 29: 67-70 (1992).

Appendix SOP 2 Page 11 of 22


GMP 11

March 2003
Length Critical Parameters

Length Comparison Performance

The measurement performance of each length calibration is evaluated with a
check standard (when performing tape-to-tape comparison).

Initial Length Intervals
Length standards are dynamic with use. Wear, contamination and other factors
can cause drift from accepted values. The following intervals have been set due

to these factors:

Table 2. Calibration intervals for length standards

Item Initial Cal Interval (months) Source
100 ft Tape #1 60 NIST
100 ft Tape #2 60 NIST
25 ft or 7 m Tape 60 NIST
18 in Steel Rule 120 NIST
Length Bench 24 (if used or moved) Lab

Volume Critical Parameters (Example shown corresponds to Option A for
volume calibration in GMP 13.)

Volume Comparison Performance

The measurement performance of a volume transfer calibration is evaluated in
each use with a repeatability check. Use of check standards is the preferred
method for evaluating the measurement process over time. Traceability for
volume standards may be established through gravimetric calibrations using
traceable mass standards.

Initial Volume Intervals

Volume standards are dynamic with use. Wear, contamination and other factors
can cause drift from accepted values. Calibration intervals are as follows:

Page 3 of 6


December 2003

Use equation 3.1.2 for optional sequence B (XSSX) with NO buoyancy corrections4:

C, = C, + CM, -CM, + ae} = 22] CMe | 4 yn,
2 a 2 0,- 0;

Note: be careful to combine like units only!

]+2 - Itoz

C, =0.407 mg + 1.1003596g- 0 + [ (20.93 -17.21) + (7081-68) [ 49.916 mg

2 67.08 - 17.21
C, =0.407mg + 1.1003596g - 0 + 3.7284359mg + 30g - 31.1034768g
Cy = 1 104.495 036 mg — 1.103 47688

C, = 1.018 236 mg

Calculate the uncertainty for the calibration:

U=u,*2

The uncertainty for the standard, U, must be divided by the k factor for the standard and the tare
weight to determine each u,. The additional uncertainty for not performing the air buoyancy
correction can be determined using the magnitude of the air buoyancy correction from SOP 2.

u, = ¥(0.007 33)? + (0.0021)? + (0.018)? + (0.0016)

Ue = 0.019 617 15 mg

U = 0.019 61715 * 2 = 0.039 234 mg

The conventional mass correction and uncertainty would be reported as follows:
C, = 1.018 mg + 0.039 mg

OR

Cx = 0.000 032 7 t oz + 0.000 001 3 t oz

4 Keep in mind that these equations may be truncated for the purpose of this example and minor differences
may be seen in the ending decimal places due to the use of calculators or spreadsheets.

SOP 4 Page 18 of 18


March 2003

Parameter Process Recommended SOP
Measurement Assurance
Length SOP 10, 11, 12, 23 Redundancy built into procedures
Volume SOP 13, 14, 15, 16, 18, | SOP 17, laboratory check standards OR
19, 21, 26 SOP 20, range charts
Temperature SOP 25 Use of check standards in procedure
Uncertainty
All parameters All SOPs SOP 29, Calculation of Uncertainty

GMP 12

Page 4 of 4



December 2003

8.5 "Within" and "Between" Standard Deviation

Estimation of the within-series, sy, and between-series, sp standard deviation, (also referred to as
short-term and long-term standard deviations in the applications described here) is an important
way to characterize a measurement process. The former provides guidance as to how many
repetitions of a measurement are required to obtain a result on a single occasion with a given
precision, while the latter is a better estimate of the precision of replication (reproducibility) of a
result on various occasions and is a more realistic evaluation of measurement variability.

To estimate these standard deviations, sets of measurements may be made on several occasions.
To simplify the calculations, each set should consist of the same number of measurements. For
most measurements, it is recommended that duplicate measurements be made on at least 12
separate occasions when estimating sy and sp.

Given k sets of duplicate measurements made on k occasions the following table and calculation
can be made.

Table 8.1
Occasion Measured Values Range Mean
Tex
1 x xf Ri (+x) x)
2
, , X,+x3)
2 x, xy Ro (+3) Diz,
3 x, xt Rs (+21)
2
k Xy x Rx G+) +3)

path tytn R)
k

1. Calculate
2. Calculate s,,=s,->

d,
Note: One may use the procedure of 8.2 to calculate s,, if preferred.

Statistical Techniques Page 3 of 10


1,

2.

SOP 2

March 2003

SOP 2

Recommended Standard Operations Procedure
for
Applying Air Buoyancy Corrections

Introduction

1.1.

Purpose

If uncorrected, the effect of air buoyancy on the objects being compared is frequently
the largest source of error in mass measurement. This SOP provides the equations to
be used to correct for the buoyant effect of air. The significance of the air buoyancy
correction depends upon the accuracy required for the measurement, the magnitude
of the air buoyancy correction relative to other sources of error in the overall
measurement process, and the precision of the mass measurement. An air buoyancy
correction should be made in all high accuracy mass determinations. The gravimetric
volume procedure uses a high accuracy mass determination with the corresponding
buoyancy corrections. The Appendix to this SOP provides a brief theoretical
discussion of this subject.

1.2. Prerequisites

1.2.1. Verify that (true) mass values or corrections are available for the standards used
in the measurement process. The calibration values for the mass standards
must be traceable to NIST.

1.2.2. Verify that the thermometer, barometer, and hygrometer used have been
calibrated and are in good operating condition as verified by periodic tests or
cross-checks with other standards.

Methodology
2.1. Scope, Precision, Accuracy

This procedure is applicable to all weighings using a comparison of mass standards.
The precision will depend upon the accuracy of the thermometer, barometer, and
hygrometer used to determine the air density. When the calculations for the air
density and air buoyancy corrections are made, a sufficient number of decimal places
must be carried so the error due to the rounding of numbers is negligible relative to
the error in the measurement process. Typically, carrying six to eight decimal places
is sufficient, but depends upon the precision of the measurement.

Page | of 22


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sumone ee on puinoyy = sonyea pouodas pue qe ut sonyea |_| 40 Ajureooun yuawidinbs - fi ypoy 10 aBuex Woy) uowomseou| |
MOUs Bisp Wiqos Punoy pearasqo Uaaayag UoNBIASp ~ E ‘uf Jo UoNeIAAp prepueys - sunouyur, pure
juawomseay 0} payejaquy s10yoe{ SPIEPUBIS 21 JO YUP - OuHUOA ALE] HDI | ss9001g Jo Aumey99u; cn sprepuryg yoo “uoneIqlTeD WIM
°n vd Jo ReHsouN Prepuels Pareloossy Ajureyeoun) prepucrs
S1OgYO SNBUIAISKS [UTNA, .
0} ang Ajureysoun) prepueys
Th
| i |
es i " oom ag
quowioinseayy Jo Ajurep9oUp) prepueg paulquod
*n
age pees pena a
(= Aqyensn) y x on
Aqureyaouy) uoneiqyeD popuedxg
UNIO A 1OJ J.B D MOLT
Ayayey1090)

£007 YORI


GMP 11

March 2003
3.2. Adjustment of Intervals

3.2.1. Intervals will be adjusted when determined to be necessary by the laboratory’s
Technical Manager.

3.2.2. The intervals will be adjusted by taking the following factors into consideration
as appropriate:

calibration history;

measurement assurance data;

data for the population of similar equipment;
NIST recommendations;

statistical analysis methods; and
manufacturer's recommendations.

Assignment of Uncertainty
The uncertainty associated with the establishment of calibration intervals is not included as a

part of the uncertainties associated with the respective measurement SOPs. See SOP 29 for
calculating uncertainties for standards and the instruments.

Page 6 of 6


March 2003

Table 2. Variables not previously defined

Variable Description of Variable
d jmeasured difference between X and the reference standard, S, using one of
[the weighing designs given in other SOPs
M, [true] mass of the reference standard
M,, [true] mass of the tare weights carried with S
M,, [true] mass of the tare weights carried with X
Ps \density of the reference standard, S
Pa \density of the unknown standard, X
Pr, \density of the tare weights carried with S
Pu, density of the tare weights carried with X

3.2. If reporting the conventional mass’, CM,, compute it using the following.

uf _ a

cM, = —\—__* /
7p — 2.0012 )
8.0
3.3. If reporting the apparent mass, 4M,, versus brass, compute it using the following.
M, [ 1 20012
Px
AM, =e Tt
x vs brass (v _ 0.0012 |
8.3909

3.4. The conventional and apparent mass values are related by the following:

AM satan 1 90002)
CM, = U ~ 0.0012
8.0

? Conventional Mass: “The conventional value of the result of weighing a body in air is equal to the mass of a
standard, of conventionally chosen density, at a conventionally chosen temperature, which balances this body at this
reference temperature in air of conventionally chosen density.” The conventions are: reference density 8.0 g/om?;
reference temperature 20 °C; normal air density 0.0012 g/em3. Conventional mass was formerly called “Apparent
Mass versus 8.0 g/cmTM” in the United States. See OIML IR 33 (1973, 1979), under revision.

SOP 2 Page 4 of 22


1.0

SOP 7

December 2003

SOP No.7

Recommended Standard Operations Procedure
for
Weighing by Single Substitution

Using a Single-Pan Mechanical Balance, a Full Electronic Balance, or a
Balance with Digital Indications and Built-In Weights

Introduction

11.

Purpose

In the single substitution procedure a standard and an unknown weight are
intercompared once to determine the difference in weights. Errors in any built-in
weights or in the balance indications are eliminated by using the balance only as a
comparator and by calibrating the balance indications over the range of use for the
measurement with a sensitivity weight. This procedure is suitable for calibration
when moderate accuracy is required and as a single substitution, does not
eliminate errors due to drift. The procedure does not incorporate measurement
control steps to ensure the validity of the standards and the measurement process;
additional precautions must be taken.

1.2.
1.2.1.

1.2.2.

1.2.3.

1.2.4.

1.2.5.

Prerequisites

Verify that valid calibration certificates are available for the standards
used in the test.

Verify that the standards to be used have sufficiently small standard
uncertainties for the intended level of calibration. Primary standards
should not be used at this level.

Verify that the balance that is used is in good operating condition with
sufficiently small process standard deviation as verified by a valid control
chart or preliminary experiments to ascertain its performance quality when
a new balance is put into service.

Verify that the operator is experienced in precision weighing techniques
and has had specific training in SOP 2, SOP 7, SOP 29, GMP 4, and GMP
10.

Verify that the laboratory facilities meet the following minimum
conditions to meet the expected uncertainty possible with this procedure.

Page 1 of 15


December 2003

8.8 Statistical Tolerance Intervals

Statistical tolerance intervals define the bounds within which a percentage of the population is
expected to lie with a given level of confidence. For example, one may wish to define the limits
within which 95 % of measurements would be expected to lie with a 95 % confidence of being
correct. The interval is symmetrical and is computed using the expression

xX + ks
where k depends on three things
Variable Description
Pp the proportion or percentage of the individual measurements to be
included
y the confidence coefficient to be associated with the interval
n the number of measurements on which the estimate, s, is based

Table 9.6 may be used to obtain values for k for frequently desired values of y and p. A more
extensive table is Table A-6 found in NBS Handbook 91 [19].

8.9 Comparing Estimates of a Standard Deviation
(F Test)

The F-test may be used to decide whether there is sufficient reason to believe that two estimates
of a standard deviation differ significantly. The ratio of the variances (square of the standard
deviation) is calculated and compared with tabulated values. Unless the computed ratio is larger
than the tabulated value, there is no reason to believe that the observed standard deviations are
significantly different.

The F ratio is calculated using the equation

Fez

lee

where s, is the numerically larger value and ss is the smaller value of the two estimates under
consideration.

The critical value of F depends on the sigriificance level chosen for the decision (test) and the
number of degrees of freedom associated with s,, and ss, respectively.

Table 9.4 contains critical values for F at the 95 % level of confidence. The tabulated values of
F are not expected to be exceeded with 95 % confidence on the basis of chance alone. As an
example, if both the numerator and the denominator values for s were each based on 9 degrees of
freedom, an F value no larger than 4.03 is expected with 95 % confidence, due to the
uncertainties of the s values, themselves. Table A-5 of NBS Handbook 91 [19] contains values
for F for other confidence levels.

Statistical Techniques Page 6 of 10


December 2003

Table 2. Example of Weighing Sequence
Measurement No. Weights on Pan Observation
1 Ss O;
2 St+sw Op
3 S O3
4 XxX) Og
5 X2 Os
6 XG Os
7 Xy O7
8 Xs Os
9 XG Oo
10 X7 Ojo
11 Xs On
12 Xo O;,
13 5, O73
14 s On
3. Calculations
3.1. Air buoyancy corrections are generally not made with the modified substitution.

3.2.

3.3.

SOP 8

Calculate the conventional mass correction, C,, for the test weight as follows,
according to the optional sequence used. In each case, the conventional mass
corrections for the standard weight(s) are included.

Table 3. Symbols used
Symbol Description
CM; conventional mass of weight i
N; nominal value of S
Ny nominal value of X

Evaluate the sensitivity of the balance:

CM.

sensitivity = (0,-0,)

If the sensitivity error is less than 2 % of the nominal value of a division on the
optical scale or the electronic range of operation, proceed with the modified
substitution. If the sensitivity error is greater, SOP 7, Single Substitution may be
acceptable.

Calculate the mass correction of each unknown weight as follows if the correction
for the standard IS NOT used in setting a reference point on the balance:

C= Co+d
C= Cs + (Xn- On)

Page 7 of 12


GMP 13

Mass - Option C

NIST

Accredited

Metric/Avdp

Laboratory Field
Level Working
Standards

Client
Echelon Ill
Calibration
Workload

Page 6 of 11

March 2003


December 2003

Table 1. Environmental conditions
. Relative Humidity
Echelon Temperature (percent)
Il 20 °C to 23 °C, a set point + 2 °C, maximum change 1.0 °C/h 40 to 60+ 10/4h
Il 18 °C to 27 °C, maximum change 2.0 °C/h 40 to 60+ 20/4h

2. Methodology

2.1.

2.2.

2.3.

SOP 4

Scope, Precision, Accuracy

This method is applicable to all weighings utilizing a mass comparator, a
single-pan mechanical balance, a full electronic balance, or a balance that
combines digital indications with the use of built-in weights (combination
balance). The precision will depend upon the sensitivity of the balance and the
care exercised to make the required weighings. The accuracy achievable with this
procedure depends on the accuracy of the calibration of the working standards and
the precision of the intercomparison.

Summary

The balance is adjusted if necessary, to obtain balance indications for all
measurements that will be within the range of the optical scale or digital
indications of the balance without changing the dial settings for the built-in
weights, if present. The standard and the test weight are each weighed. A small,
calibrated weight, called a sensitivity weight, is added to the test weight and these
are weighed. The standard and the same sensitivity weight are then weighed. The
latter two weighings provide both second weighings of the standard and the test
weight as well as a determination of the sensitivity of the balance under the load
conditions at the time of the intercomparison. All weighings are made at regularly
spaced time intervals to average out any effects due to instrument drift.

The double substitution procedure is the same for all of the balances mentioned
above, but the adjustment of the balance to prepare for the intercomparison and
the selection of the sensitivity weight differs slightly depending upon the balance
used. When steps specific to a particular balance are required, they are given in
subsections of the procedure identified by a, b, and c along with the balance type.

Apparatus/Equipment Required

2.3.1. Precision balance with sufficient capacity and sensitivity for the
calibrations planned.

2.3.2. Calibrated working standard and sensitivity weights with recent
calibration values that are traceable to NIST.

Page 2 of 18



Good Laboratory Practices


IR 6969 Revisions

Section 8, Statistical Techniques

Section 8.6

The Greek letter sigma (c) replaced the incorrect variable “s” in the table as the known standard
deviation. NBS replaced NIST in the references to Handbook 91 because this reference was
originally published by NBS.

Section 9, Reference Tables

Table 9.1

An infinity symbol has been inserted in place of the number “4” which printed in the first
column, last row. Formatting of the d} notation was edited. The Greek letter nu (UV) was
inserted in the text below the table where it was inadvertently omitted. The formatting of the ©
symbol was corrected.

Table 9.2

The values for the confidence levels noted for 100 should be 99.999 to the level noted in the
original. E.g., 100 — 10° is: 99.999 999 99. A comma was used in IR 6969 instead of the minus
sign. This has been corrected.

Table 9.3

A space was inserted between the number and percent symbol in the first row according to NIST
SP 811. NBS replaced NIST in the references because these references were originally
published by NBS. An infinity symbol was inserted in the first column, last row where it was
missing.

Table 9.4

The nl value was moved to the right side of the diagonal slash mark to indicate the degrees of
freedom for the numerator. All numbers in the column for 20 degrees of freedom from 4 degrees
of freedom in the denominator to infinity were incorrectly referencing the same values in the
column for 8 degrees of freedom. All values have been corrected.

Table 9.6
The Greek letter gamma (y ) was missing in the first row heading before the equal sign. NBS

replaced NIST in the reference because this reference was originally published by NBS.

Table 9.7

NBS replaced NIST in the reference because this reference was originally published by NBS.
The font for the Greek letter alpha on p. 9 of 13 (Table 9.7, Part 2) was increased to match the
other font sizes.

Table 9.8

The density for 16.9 °C was corrected from 0.997 890 g/em? to 0.998 790 g/cm?. The sentence:
‘Reference equations for Air-Saturated distilled water may be used.’ was changed to: ‘Reference
equations for Air-Saturated or Air-Free distilled water may be used but reference source should
be noted.’

Page 2 of 3


December 2003

SOP 30

Recommended Standard Operating Procedure
fora
Process Measurement Assurance Program

1. Introduction

1.1. Purpose

The Process Measurement Assurance Program (PMAP) is used for the control
and surveillance of measurement performance using check standards in
measurement and calibration procedures. Incorporation of these measurement
control steps ensures the validity of the measurement process and the standards
used. The variables used in calculation and assignment of uncertainty can be
determined and controlled by the use of this Standard Operating Procedure
(SOP).

1.2. Prerequisites

1.2.1. A Standard Operating Procedure that describes and provides rigor and
consistency in the calibration process.

1.2.2. _ Check standards that represent the items to be calibrated. These check
standards should be stable and their values should be established with
accuracy, since they will be used to control the uncertainty in the
calibration process. Check standard values are to be determined by
NIST or inside the laboratory with a procedure one level higher than
the calibration process to be controlled.

1.2.3. | The operator must be experienced in the calibration process and the
standard operating procedure for the calibration to which this method
is applied. The operator should also have had specific training on
SOP 29 (uncertainty identification and calculations).

1.2.4. A calculating system for statistical control that performs standard
deviations, control limits, “F” and “t” tests, root-sum-of-the-squares
(RSS), and control charting. It is recommended that a computer
program be used for efficiency, consistency, and uniformity.

SOP 30 Page | of 9


March 2003

1.4 — Safety
No outstanding safety concerns
2. Methodology
2.1 Summary
Traceability is maintained through comparison to appropriate standards with suitable
procedures and measurement uncertainties. Procedures are outlined in SOPs and
GMPs. Examples of possible hierarchies of the standards leading to the traceability
of a calibration are provided in this document.
2.2 Procedure
The charts in this GMP show examples of the traceability hierarchy for mass, length,
volume, and temperature measurement disciplines. Each laboratory must define the
exact traceability system in their operating quality manual. (A worksheet is included
as an Appendix to help in the definition of the traceability system.)
3. Calculations
There are no calculations in this GMP.

4, Assignment of Uncertainty

The uncertainty associated with reported calibration values is included within the uncertainty
analysis for each SOP and in SOP 29, Calculating and Reporting Uncertainties.

GMP 13 Page 3 of 11




March 2003

7. Procedure
Weigh the unknown object as directed by the balance manufacturer or in accordance with
accepted procedure. Record the temperature, pressure and relative humidity of the air in
the balance at the time of weighing. Do not correct the barometric pressure to sea level.

8. Calculation
8.1 Air density, Option A (Option B is preferred)

The density of air, in g/cm’, can be approximated for lesser accuracy from the
following formula:°

p= { 0.464 60[ P - (0.0037960 U e, M} xia? ()

(273.15 +1)

Table A-3. Variables for air density equation

Variable Description
Pa density of air, g/cm?
P barometric pressure, mm Hg
U % relative humidity, entered as a whole number
t temperature, °C
e 1.314 6x 10x qe SNF TBI

Note: e; can be written as follows in a spreadsheet and in some calculators:
1.3146E9* @EXP(-5315.56/(t+273.15))

Small errors (of order 0.01 %) in this equation occur for locations well above sea level or
under conditions in which the concentration of carbon dioxide differs greatly from the
global average. See the references for a more general formulation of the equation.

SJones, F.E., "The Air Density Equation and the Transfer of the Mass Unit," Journal of Research, National Institute
of Standards and Technology, Vol. 83, 1978, p. 419.

Appendix SOP 2 Page 10 of 22


March 2003

which is within 100 jg of the answer found in Example 1.

Example 3:

Another piece of silicon is measured on a single-pan microbalance. The balance weights were
adjusted by the manufacturer to the conventional mass scale. The sensitivity of the balance has
been determined to be exactly 1.000. This particular laboratory is well above sea level. At the
time of the weighing, the following measurements were recorded:

P = 612.3 mm Hg

t=23.4°C

U = 23 % relative humidity

The balance reading was 15.00 g on the built-in weights and 0.000 358 g on the optical screen.
What is the mass of the silicon?

Answer:

First, calculate e, and pa:
és = 21.59 mm Hg

Pa = 0.956 x 10° g/em?

Then, use Eq. 5:

-3
(15.00 + 0.000358 1 - esos |

M, =
1 — 0.956 x107
2.3291

M, = 15.004 724 g

Example 4:

The built-in weights in Example 3 are actually stainless steel of density 7.78 g/cm? at 20 °C.
What is the approximate error caused by using the apparent mass scale?

Appendix SOP 2 Page 19 of 22


NUST

National Institute of
Standards and Technology
Technology Administration
US. Department of Commerce

SELECTED LABORATORY
AND MEASUREMENT

NISTIR 6969

2003



SOP 7

2.5.1.3.

2.5.1.4.

2.5.1.5.

December 2003

If a sensitivity weight will be used, select one that is (See GMP
14, Table 2):

a. Single-pan balance - between 4 and 4 the range of the
optical scale, and at least 4 times the mass difference
between X and S.

b. Full electronic balance - at least 4 times the mass difference
between X and S but not exceeding 1 % of the balance

capacity.

c. Combination balance - between % and % the range of the
digital indications, and at least 4 times the mass difference
between X and S.

Determine whether optional sequence A or B will be used.
Optional sequence A uses the standard on the balance for the
first observation and the unknown on the balance for the second
and third observations; this is often called the “SXX” sequence.
Optional sequence B starts with the unknown on the balance
first and with the standard on the balance for the second and
third observations; this is often called the “SS” sequence.

Adjust the single pan balance or the combination balance so the
first two readings of the single substitution fall in the first
quarter of the optical scale or digital indications. The zero
adjustment and tare adjustment may be used. Small weights
may be placed on the balance pan to reach the desired reading
range. These weights remain on the pan throughout the single
substitution. Once the balance has been adjusted to the desired
position, neither the balance dials, the zero and tare adjustments,
nor the small weights placed on the balance pan are to be
changed during the measurement.

If the balance is equipped with a pan arrestment mechanism,
arrest the pan between each observation.

2.5.2. Measurement Procedure, Optional Sequence A (SXX)

Table 3. Optional Sequence A
Measurement No. Weights on Pan Observation
1 Stts oO,
2 Xt+t Oz
3 X+ t+ sw O3

All observations should be recorded on suitable data sheets, such as those
in the appendix. Record the laboratory ambient temperature, barometric

pressure, and relative humidity.

Page 5 of 15



December 2003
Table 9.9 Density of Air, g/cm’, as Function of Temperature and Air Pressure’

Barometric Pressure

Temperature, °C

kPa mbar | mm Hg 18 20 22 24 26 28
77.33 773 580 | 0.00092 | 0.00092 |0.00091 | 0.00091 |0.00090 |0.000 90
79.99 800 600 | 0.00095 | 0.00095 |0.000 94 |0.00093 | 0.00093 |0.000 92
82.66 827 620 | 0.00099 {0.000 98 |0.00097 10.000 96 {0.00096 {0.000 95
85.33 853 640 | 0.00102 |0.001 01 | 0.001 00 | 0.00100 |0.000 99 |0.000 98
87.99 880 660 | 0.00105 |0.001 04 {0.001 03 {0.001 03 | 0.00102 {0.001 01
90.66 907 680 | 0.001 08 }0.001 07 [0.001 07 {0.00106 |0.001 05 |0.001 04
93.33 933 700 | 0.001 11 }0.001 10 {0.001 10 |0.00109 |0.001 08 |0.001 07
95.99 960 720 | 0.001 14 |0.00] 14 {0.001 13 |0.001 12 |0.001 12 ]0.001 10
98.66 987 740 | 0.00118 |0.001 17 |0.001 16 |0.001 15 |0.001 14 {0.001 13
101.32 1013 760 | 0.00121 | 0.00120 |0.001 19 {0.00118 | 0.001 17 |0.001 17
103.99 1040 780 | 0.001 24 |0.001 23 |0.001 22 {0.001 21 |0.001 21 |0.001 20
106.66 1067 800 | 0.00127 |0,001 26 }0.001 25 | 0.001 24 |0.001 24 |0.001 23

Computed for air at 50 % relative humidity

*Equations to compute the density of air at any pressure, temperature, and relative humidity are
given in Section 8 of the Appendix to SOP No. 2 and are preferred for all precision mass and

volume calibrations.

Reference Tables

Page 11 of 13



December 2003

Sensitivity guidelines indicate a sensitivity weight, greater than or equal to 2 times the tolerance
(460 mg) but not exceeding 1 % of the balance capacity (23 g). For a 5 lb load, the Class F
tolerance is 230 mg so a 5.g weight was selected.

A 2 % sensitivity error in a 5 gram range would allow readings between 4.900 g and 5.100 g in
the sensitivity test. Calculate the sensitivity:

5.000 002 g

—°.=1.000 200 4 g/div
4.999 div

sensitivity =

which deviates less than 2 % of the nominal value of a division.

The drift observed was 3 mg and is less than 1/10 of the tolerance and 23 mg could be allowed,
so the error for each nominal weight may be calculated as follows.

C,, =7.5 mg + (205 mg - 0) = 212.5 mg
Cy, =7.5 mg +(104mg-0)=111.5mg
C,, =7.5mg + (-89mg-0)=-81.5 mg
Cy, =7.5mg+( -Smg -0)= 2.5mg

Calculate the uncertainty for the calibration:

U=u, *2

The uncertainty for the standard must be divided by the k factor for the standard and the tare
weight to determine each u;. The additional uncertainty for not performing the air buoyancy
correction can be determined using the magnitude of the air buoyancy correction from SOP 2.
Since the working standard was previously calibrated with buoyancy corrections and is the same
density as the unknown weights, the uncertainty for the buoyancy correction drops out of the
equation.

u, = J (0.1672 + (0.85 7

Uc = 0.866 19 mg
U = 0.866 19 * 2 = 1.732 38 mg

The expanded uncertainty is less than 1/3 of the tolerance (76 mg) so the unknown weights can
either be reported as “within tolerance” or the values and uncertainties can be reported. The
value plus the uncertainty for the first unknown X; is within 25 % of the Class F tolerance,
therefore it is desirable to adjust the weight closer to nominal value, although based on the
tolerances and uncertainties, and it can be claimed as “within tolerance.”

SOP 8 Page 12 of 12




IR 6969 Revisions

IR 6969 Revisions Since March 2003 Publication

NOTE: GMP 14 was provided on the original CD-ROM, in Word and Adobe PDF on the
website in March 2003, but was missing in the original printed version provided in March 2003.
Subsequent printed versions that have been used in seminars have included the printed version of
GMP 14.

Revisions July 2003

SOP 4

An error was corrected in the example on p. 15 to 16. The negative sign for 0.126 mg and

0.126 49 mg was missing in the March version. The calculated C, value should be -0.126 49 mg
and the rounded value -0.126 mg.

SOP 8

The wording was clarified in sections 2.4.3, 2.5.3, 2.6.2, 3.2, to clarify that the “sensitivity error”
refers to the error in the nominal mass of a division. In section, 2.5.7, the following underlined
clause was inserted: no more than 10 without rechecking the standard.

Revisions December 2003

GLP 4
The reference to NIST Handbook 130 was corrected from section 6 to section 12 (2004 version).

SOP 4

Table I, Echelon III was updated to reflect environmental criteria given in NIST Handbook 143,
Program Handbook, 2003. (Temperature range was extended to 27 °C, maximum change per
hour was increased to 2 °C, and relative humidity limits were changed to allow + 20 %/ 4h.

SOP 7

Table I, Echelon III was updated to reflect environmental criteria given in NIST Handbook 143,
Program Handbook, 2003. (Temperature range was extended to 27 °C, maximum change per
hour was increased to 2 °C, and relative humidity limits were changed to allow + 20 %/ 4h.
Subscripts for the tare weights on the check standard on the datasheets were changed from t, to
tc.

SOP 8

Table I, Echelon III was updated to reflect environmental criteria given in NIST Handbook 143,
Program Handbook, 2003. (Temperature range was extended to 27 °C, maximum change per
hour was increased to 2 °C, and relative humidity limits were changed to allow + 20 %/ 4h.

SOP 30
A space was added to the first sentence in section 1.2.2., between the words be calibrated.

Page 1 of 3


SOP 7°

December 2003

2.5.1.1. Observation 1. Place the standard weight(s), S, along with ¢, on

— 2.5.1.2.

the balance pan. If equipped with a pan arrestment mechanism,
release the balance pan. When the pan is released, start the
stop-watch and record observation O, once the balance indication
has stabilized.

Observation 2. Remove weight(s) S and ¢, and replace with test
weight X and its tare weight, 4. Release the pan, time the
interval, and record observation O2.

2.5.1.3. Observation 3. Add the sensitivity weight, sw, to the weights of

2.5.1.4.

observation 2. Release the pan, time the interval, and record
observation O3.

If repeated single substitutions are performed, the values between
successive trials should not differ from one another by more than
+ 2 sd of the balance. If this difference is exceeded, reject the
data and take a new series of measurements that will so agree.

2.5.3. Measurement Procedure, Optional Sequence B (XSS)

Table 4. Optional Sequence B
Measurement No. Weights on Pan Observation
1 X+k 0;
2 Stts Or
3 St+t,+sw O3

Measurements for Option B are made as described in Option A except that

X, S, ty, and t, are interchanged.

Page 6 of 15



March 2003

GMP 11

Good Measurement Practice
for

Assignment and Adjustment of Calibration Intervals for Laboratory Standards

1.

GMP 11

Introduction

1.1.

1.2.

1.3.

Purpose

Measurement processes are dynamic systems and often deteriorate with time or use.
The design of a calibration system would be incomplete without some established
means of determining how often to calibrate instruments and standards. A
calibration performed only once establishes a one-time reference of uncertainty.
Recalibration detects uncertainty growth and serves to reset values while keeping a
bound on the limits of errors. A properly selected interval assures that an item will
receive recalibration at the proper time. Proper calibration intervals allow
specified confidence intervals to be selected and they support measurement
traceability. The following practice establishes calibration intervals for standards
and instrumentation used in measurement processes.

Prerequisites

1.2.1. Calibration history for laboratory standards
1.2.2. Expected tolerance limits if applicable
Safety

1.3.1. No outstanding safety concerns

Methodology

2.1.

2.2.

Summary

Recommended calibration intervals are based on various examples of traceability as
described in GMP 13. As data is collected and evaluated, the laboratory technical
manager may adjust the calibration intervals to ensure that measurement results are
not invalidated by the intervals selected.

Apparatus

None.

Page 1 of 6


December 2003

Symbol

Description

Pn

density of normal air (1.2 kg/m’)

Pp

density of masses; subscripts s, x, fs, 4, sw are used to identify the weight.

2.5.

SOP 4

Procedure
2.5.1. Preliminary Procedure
2.5.1.1. Place the test weight and standards in the balance chamber or
near the balance overnight to permit the weights and the balance
to attain thermal equilibrium.
2.5.1.2. Conduct preliminary measurements to obtain an approximate

value for the difference between the standard and the unknown,
to determine where the readings occur on the balance, to
determine if tare weights are required, to determine the
sensitivity weight that must be used, and to determine the time
interval required for the balance indication to stabilize.

Tare weights are rarely needed for high precision mass
standards. If tare weights are required, carry tare weights, ¢, and
t,, with the standard and the unknown, S and_X, respectively.
The tare weights must be calibrated standards with valid
uncertainties that are evaluated in the process of determining
calibration uncertainties. The standard and its tare weight, S + t,,
should be "nearly the same mass" as the unknown with its tare
weight, X + t,. "Nearly the same mass" depends upon the
balance used (See GMP 14, Table 1). Select ¢, and ¢, such that
the difference in mass between S'+ /, and X + f, is:

a. Single-pan mechanical balance - less than ao the range

of the optical scale.

b. Full electronic balance - less than 0.05 percent of the
balance capacity.

c. Combination balance - less than = the range of the

digital indications.
d. Mass comparator — less than a digital range

A sensitivity weight must be used on equal-arm balances, and is
normally used on single-pan mechanical and electronic

Page 4 of 18


March 2003

Table B-1. | Example of calibration report data
Mass Uncertainty Vol at 20 °C Coefficient of

(g) (g) (cm?) _ Expansion
100.00094070 0.00002535 12.67439 0.000045
50.00046277 0.00001550 6.33719 0.000045
30.00029259 0.00001361 3.80232 0.000045
20.00015779 0.00001113 2.53487 0.000045
10.00012644 0.00001330 1.26744 0.000045
5.00004198 0.00000688 0.63372 0.000045
3.00004588 0.00000459 0.38023 0.000045
2.00000627 0.00000333 0.25349 0.000045
1.00001438 0.00000300 0.12674 0.000045
0.49995376 0.00000160 0.03012 0.000020
0.29996145 0.00000115 0.01807 0.000020
0.19994984 0.00000087 0.01205 0.000020
0.09996378 0.00000091 0.00602 0.000020
0.04998659 0.00000072 0.00301 0.000020
0.02999100 0.00000077 0.00181 0.000020
0.02000570 0.00000066 0.00741 0.000069
0.01000277 0.00000086 0.00370 0.000069
0.00499706 0.00000070 0.00185 0.000069
0.00300299 0.00000076 0.00111 0.000069
0.00200197 0.00000066 0.00074 0.000069
0.00100083 0.00000086 0.00037 0.000069

Appendix SOP 2

Page 21 of 22


December 2003

GLP 4

Good Laboratory Practice
for
Periodic Recalibration of State Standards

A number of States have provisions in their weights and measures laws that require the periodic
submission of their State standards to NIST for calibration. Those provisions are based on an
early version of the Model Law (1911), which was considered appropriate for the circumstances
that prevailed prior to the establishment of the New State Standards Program by NIST. Periodic
calibration is necessary on a regular, periodic basis, and also when measurement control results
from internal control charts or external round robins indicate questionable data.

Standards of mass, volume, and length, fabricated from modern materials, kept in the controlled
environment of a State metrology laboratory under the custody of trained metrologists, are
generally stable and not subject to change. Moreover, the cooperative NIST-State audit
programs often identify changes in ample time for corrective action in the unlikely event that
such a change should occur. These same programs provide the necessary evidence of the ability
to provide traceable measurement results at a level of confidence sufficient for the need.

Moreover, the process of packing, shipping, and unpacking exposes the standards to unnecessary"
hazards that could result in damage, compromising their integrity. The return and re-calibration
could take several months causing an unavailability of State services that would be disruptive to
the performance of the mission of the State laboratories.

In order to develop a policy for the guidance of and implementation by all 50 States regarding
this subject, the following actions are recommended:

1. All States should recognize the fact that periodic return of their State
standards to NIST for re-calibration is essential to comply with ISO/IEC
17025, GMP 11, and when: 1) data regarding traceability is unavailable;
2) charted measurement results indicate that the standards are out of
control; 3) measurement results on round robins or performance tests are
suspect; or 4) NIST advises the State of the need.

3. References to the periodic re-calibration of State standards in the law such
as,

"He (the director) shall maintain the State standards in good order and
shall submit them, at least once in ten years, to the National Institute of
Standards and Technology for calibration,"

should be followed if present and may be amended to reflect a regular

interval, plus identified needs. In lieu thereof, the wording of Sections 3
and 12 of the present Uniform Law may be substituted:

GLP 4 Page 1 of 2


March 2003

Table 1.Maximum allowed difference between X and S

Balance (X-S)
Equal arm balance each other within
one division on the scale
Mechanical 1/10 optical scale
Combination 1/10 digital range
Fully electronic 0.05 % capacity
Comparator 1/10 digital range

2.3.4. Select tare weights, if necessary, making sure that the difference
between X and S, with the appropriate tare weights, do not exceed the
values shown in Table 1.

2.3.5. Select a sensitivity weight according to Table 2.

Table 2. Selection of Sensitivity Weight

Balance Procedure Sensitivity Weight
Equal Arm SOP 3, 5, 6, 7, 8, 28 change turning points by 20 %
SOP 4, 5, 7, 28 >4 times (X— S); < % optical
Mechanical SOP 8 scale
= % optical scale
Combination SOP 4, 5, 7, 8, 28 >4 times (X- S); < % digital
Electro-mechanical Range
: SOP 4, 5, 7, 28 <1% capacity
Fully Electronic SOP 8 2 times the applicable tolerance
7 SD. SIP diol
Comparator* SOP 4, 5, 7, 8, 28 24 times (X¥—S); < 4 digital
range

*A sensitivity weight is not required if the electronic mass comparator that is used has been
tested (with supporting data available) to determine that the balance has sufficient accuracy,
resolution, repeatability, and stability so that no advantage is gained using a sensitivity
weight. For example, any possible errors must be less than the last digit retained in the
expanded uncertainty. When a mass comparator is used without a sensitivity weight, the
sensitivity must be periodically verified and documented (e.g., prior to each use).

24. Use of sensitivity weight

The sensitivity weight is used to ensure that the mass differences determined
with the optical scale, or electronic range, have valid accuracy and traceability.
The sensitivity weight calibrates the range of use of the balance used for
making the mass determinations. Using a sensitivity weight provides us with a
sensitivity value in terms of mass units per division.

mass units M,,

sensitivity = ——— =
divisions deflection

GMP 14 Page 3 of 4


December 2003

ignore it and proceed until a valid match is encountered. This becomes the first item in the
sequence. Continuing in the same manner, items are selected in the sequence in which their
serial numbers are encountered ignoring the repetition of previously identified items. The
procedure is continued until all items have been randomly selected.

As an example, select 10 specimens (numbered 01 to 10) in random order. Start from a
randomly selected place, say column 2, row 5 of Table 9.11. Proceed from this point along the
table as one would read a book. The starting number is 14, which is not usable. The first useful
number encountered is 08, the next 03, and so on. Using the procedure described above, the
following random order was found:

Specimen No.
os { 03 | o9 [| 05 [ 06 | o2 | 07 [ 10 | 04 | o1
Order
1 2 3 4 5 6 7 8 9 10

Statistical Techniques Page 10 of 10


December 2003

Appendix
Double Substitution Data Sheet
(Optional Sequence A)

SXXS
Laboratory data and conditions:
Operator
Date Temperature
Balance Pressure
Nominal Load Relative Humidity
Standard deviation of the process, from control chart, sp

Mass standard(s) data:

+ + Expanded Une: Une: Density
*
ID. Nominal Mass Correction’ From cal. report k factor g/cm?
Ss
xX

bs

*Mass Correction = True Mass if using buoyancy correction. Mass Correction = Conventional Mass if NOT using
buoyancy correction. Density is used only with buoyancy corrections.

Observations:
Observation No. Weights Balance Observations, Units
Time:
1() Sth,
2 (02) Xtk
3 (03) X+t + sw
4 (0) S+ tt sw
Time:

Measurement Assurance (Duplication of the Process):

Observation No. Weights Balance Observations, Units
Time:
1(0) Sth i
2 (O,) Set bse
3 (03) So + tye + Sw
4 (O,) S+ tt sw
Time:

Note: dotted line represents decimal point

SOP 4 Page 11 of 18


December 2003

Case Il

Confirming (or assuming) that s, and s, are significantly different, their individual values are
used to calculate U, as outlined below.

Step 1. Choose a , the level of significance for the test.
Step 2. Calculate the respective variances of the means.
2 2
s Ss
v,=— and v, =—%
ny Ns

Step 3. Calculate the uncertainty of |X, -X,|=A
U,=t' (V,49,)
using a value for t’ based on $ and f , the effective number of degrees of

freedom calculated as described in Step 4.

Step 4. Calculate f, the effective number of degrees of freedom as follows:
2
pa] atte ay,
V; + Vs

n+l n,+1

Step 5. Compare U, with A.
If U, 2A, there is no reason to believe that A is significant at the level of
confidence chosen.

8.12 Use of Random Numbers

Conducting operations in random sequences can avert problems of bias that might stem from a
particular order of operations. For example, in the measurement of a series of items, it might be
difficult to determine whether systematic trends in the measured values were due to differences
in the items or to measurement system drift unless the items were measured in random order.

Use of tables of random numbers is a convenient means for randomizing measurement
operations. The operations, test objects, and other matters requiring randomization may be
assigned serial numbers. The order of selection is then determined by use of a random number
table, as described below. When the number of operations or test items is less than 100, a table
such as Table 9.11, reproduced from NBS Handbook 91 [19], may be used conveniently. One
may start from any arbitrarily selected position in the table and proceed from it in any
pre-determined arbitrary manner. If the first number encountered is not that of one of any item,

Statistical Techniques Page 9 of 10


March 2003

8.3. Ifa two-pan balance is used:

M, =M, + p,(V, ~V,) + sensitivity AM,,, (3a)

or

M, [! - | + sensitivity AM,
M, = Ps (3b)

(2)

or

M, — p,V, + sensitivity AM,
vr, = Maz Babs + sensitivity Moy 60)

CF)
Px

Table A-5. Variables not previously defined

Variable Description
M, mass of the unknown object
M, mass of the standard weights
Ds density of the standard weights, ue
Ss
AMonr off-balance indication read on the optical scale
V; volume of the unknown object
Vs volume of the standard weights
M
Dx density of the unknown object, —*
. V,

Volumes and densities are, in general, a function of temperature. The thermal
coefficients of volumetric expansion of the unknown object and the standard may be
significant in very accurate work.” The coefficient of volumetric expansion is usually
estimated as three times the linear coefficient of expansion of the weight material.

In general, V(t) = V2o [1 + B(t - 20 °C)] where t is the temperature of the weight, V29 is the volume at 20 °C, and B is
the coefficient of volumetric expansion.

Appendix SOP 2 Page 12 of 22


March 2003

GMP 12

Good Measurement Practice
on
Standard Operating Procedure Selection

Good laboratory practices, use of proper standards and equipment, and selection of standard
operating procedures are essential for providing calibration results with accurate and traceable values
with appropriate and suitable uncertainties. The following matrix recommends SOPs based on the
parameter, type of test items, and level of uncertainty needed.

Parameter Test Item Recommended SOP
Mass
Railroad test cars SOP 27, Railroad Test Cars using a Master
Track Scale
Weight carts SOP 33, Calibration of Weight Carts
(References SOP 4 and SOP 7)
HB 105-1, Class F Class F SOP 8, Modified Substitution - may be used if
ASTM, OIML Class 5, 6,7 expanded uncertainty is less than 1/3 of the
Class M1, M2, M3 tolerance
e.g., 10 kg to 250 kg SOP 7, Single Substitution - to be used, as a
(2500 Ib) cast iron minimum, if conditions given for SOP 8 cannot
1 mg to 5 kg be met
(1 plb to 10 Ib) NOTE: Balances and standards must be
stainless steel selected properly for these conditions to be met.
ASTM, OIML Class 3, 4 (P) SOP 7, Single Substitution - may be used if
Class Fl, F2 expanded uncertainty is less than 1/3 of the
e.g., 1 kg kit, 100 g kit | tolerance. If uncertainty is greater than 1/3 of
the tolerance, then use SOP 4.
SOP 4, Double Substitution - to be used for
buoyancy corrections and if expanded
uncertainty is less than 1/3 of the tolerance
Modified SOP 4/5, to be used to incorporate
measurement control into SOP 4
NOTE: Balances and standards must be
selected properly for these conditions to be met.
GMP 12 Page | of 4



December 2003
Table 9.8 Density of Air-free Water in g/cm? asa
Function of Celsius Temperature

tT | oor | orc | o2ec | 03°C | 04ec | 05°C | 06°C | 07°C | 08°C | 09°C
0.0 | 0.999840 | 0,999 846 | 0.999.853 0.999859 0.999 865 | 0.999 871 | 0.999 877 | 0.999 883 | 0.999 888 | 0.999 893
1.0 | 0.999899 | 0.999 903 | 0.999 908 | 0.999 913 | 0.999917 | 0.999 921 | 0.999 925 | 0.999 929 | 0.999 933 ] 0.999 937
2.0 0.999940 0.99 0,999 946 | 0.999949 | 0.999952 0.999 954 | 0.999 956 | 0.999 959 | 0.999 961 | 0.999 963
3.0 | 0.999.964 | 0.999 966 | 0.999967 | 0.999 968 | 0.999 969 | 0.999 970 | 0.999971 | 0.999971 | 0.999 972 | 0

40 0.999972 0.999.972 0.999971 | 0.999971 | 0.999 970 | 0.999 969 | 0.999 968 0.999 967 | 0.999 965
50 99 962 | 0.999 960 | 0.999 958 | 0.999 956 | 0.999 954 | 0.999951 | 0.999 949 | 0.999 946 | 0.999 943
0.999 940 0.999 933 | 0.999.930 | 0.999926 0.999922 | 0.999918 | 0.999914 | 0.999 910 | 0.999 9
0.999 901 (0.999 892 | 0.99 [0.999 876 | 0.999 871 | 0.999 865 | 0.999 860 | 0.999 854
0.999 848, 0.999835 , 0.999 829 | 0.999822 0.999 816 0.999 809 0.999 802 0.999 795 0.999 787
. 0.999 780 0.999 765 | 0.999 757 i 0.999 749 j 0.999 ml 0.999 733 | 0.999 725 | 0.999 716 | 0.999 707 1
10.0 0.999 699 0.999 681 | 0.999 672 0,999 662 0.999 653 | 0.999 643 | 0.999 634 | 0.999 624 | 0.999 614
110 | 0.999.604 0.999 583 | 0.999.573 | 0.999 562 | 0.999 552 | 0.999 sa1 | 0.999 530 | 0.999 519 | 0.999 507

12.0 0.999.496 | 0.999.485 0.999.473 | 0.999.461 0.999 449 0.999437 0.999425 | 0.999 413 | 0.999 401 | 0.999 388
13.0 | 0.999 376 | 0.999 363 | 0.999 350 | 0.999337 | 0.999 324 | 0.999 311 | 0.999297 | 0.999284 | 0,999 270 | 0.999 256
14.0 0.999243 | 0.999229 0.999215 | 0.999200 | 0.999 186 | 0.999 172 | 0.999 157 | 0.99 142 | 0.999 128 | 0.999113
15.0 | 0.999 098 | 0.999 083 | 0.999 067 | 0.999 052 | 0.999 036 | 0.999.021 | 0.999 005 | 0.998 989 | 0.998 973 | 0.998 957

16.0 0.998 941 | 0.998 925 | 0.998 908 | 0.998 892 0.998 875 | 0.998 858 | 0.998 841 | 0.998 824 | 0.998 807 | 0.998 790

17.0 | 0.998.773 | 0.998.755 | 0.998 738 | 0.998 720 | 0.998 702 | 0.998 684 | 0.998 666 | 0.998 648 | 0.998 630 | 0.998 612
18.0 | 0.998 593 0.998 575 | 0.98 556 | 0.998 537 | 0.998 519 | 0.998 500 | 0.998 480 | 0.998 461 | 0.998 442 | 0.998 422
19.0 | 0.998 403 | 0.998 383 | 0.998 364 | 0.998 344 | 0.998 324 | 0.998 304 | 0.998 284 | 0.998 263 | 0.998 243 | 0.998 222
20.0 | 0.998 202 | 0.998 181 | 0.998 160 0.998 139 0.998 118 0.998 097 | 0.998 076 | 0.998 055 | 0.998.033 | 0.998 012
21.0 | 0.997 990 | 0.997 968 | 0.997 947 | 0.997 925 | 0.997 903 | 0.997 881 | 0.997 858 | 0.997 836 | 0.997814 | 0.997 791

22.0 | 0.997768 | 0.997 746 | 0.997 723 | 0.997 700 | 0.997 677 | 0.997 654 | 0.997 630 | 0.997 607 | 0.997 584 | 0.997 560
23.0 0.997 536 | 0.997513 | 0.997 489 | 0.997465 0.997 441 _ 0.997 417 | 0.997 392 | 0.997 368 | 0.997 344 | 0.997 319

24.0 | 0.997294 | 0.97270 | 0.997 245 | 0.997220 0.997 195 | 0.997 170 | 0.997 145 | 0.997 119 | 0.997 094 | 0.997 068
25.0 0.997 043 | 0.997017 | 0.996.991 0.996966 0.996 940 0.996 913 | 0.996 887 | 0.996 861 | 0.996 835 | 0.996 808
26.0 | 0.996 782 | 0.996 755 | 0.996 728 | 0.996 702 | 0.996 675 | 0.996 648 | 0.996 621 | 0.996 593 | 0.996 566 | 0.996 539
27.0 | 0.996 511 | 0.996 484 | 0.996 456 | 0.996 428 0.996 401 0.996 373 | 0.996 345 | 0.996 316 | 0.996 288 | 0.996 260
28.0 | 0.996 232 | 0.996203 | 0.996 175 | 0.996 146 | 0.996 117 | 0.996 088 | 0.996 060 | 0.996 031 | 0.996.001 | 0.995 972
29.0 0.995 943 | 0.995914 | 0.995 884 | 0.995 855 | 0.995 825, 0.995 795 “0.995 765 | 0.995 736 ; 0.995 706 0.995 676

30.0 0.995 645 | 0.995 615 | 0.995 585 | 0.995 554 | 0.995 524 | 0.995 493 | 0.995 463 | 0.995 432 | 0.995 401 | 0.995 370

31.0 0.995 339 . 0.995 308 : 0.995 277 | 0.995 246 - 0.995 214 . 0.995 183 | 0.995 151 | 0.995 120 | 0.995 088 | 0.995 056

32.0 _| 0.995 024 | 0.994 992 | 0.994 960 | 0.994 928 | 0.994 896 | 0.994 864 | 0.994 831 | 0.994 799 | 0.994 766 | 0.994 734

33.0 0.994 701 | 0.994 668 . 0.994 635 | 0.994 602 _ 0.994 569 | 0.994 536 | 0.994 503 | 0.994 470 | 0.994 436 _ 0.994 403
34.0 0.994 369 Toss 336 | 0.994 302 | 0.994 268 | 0.994 234 | 0.994 201 | 0.994 167 | 0.994 132 | 0.994 098 | 0.994 064

35.0 0.994 030 | 0.993 995 | 0.993 961 0.993 926 | 0.993 891 0.993 857 | 0.993 822 0.993 787 | 0.993 752

36.0 0.993 682 | 0.993 647 | 0.993 611 ! 0.993 576 | 0.993 541 | 0.993 505 | 0.993 469 | 0.993 434 | 0.993 398

37.0 0.993326 | 0.993290 | 0.993 254 | 0.993218 | 0.993 182 | 0.993 146 | 0.93 109 | 0.93 073 | 0.993 036
38.0 0.992 963 | 0.992 926 : 0.992 889 | 0.992 852 | 0.992 815 | 0.992 778 | 0.992 741 | 0.992 704 | 0.992 667
39.0 0,992 592 | 0.992 554 | 0.992 517 | 0.992 479 | 0,992 442 | 0.992 404 | 0.992 366 | 0.992 328 | 0.992 290 | 0.992 252

*Based on the work of H. Wagenbreth and W. Blanke, PTB - Mitteilingen 6-71.
Reference equations for Air-Saturated or Air-Free distilled water may be used but reference source should be noted.

Reference Tables Page 10 of 13


March 2003

Length
NIST
18" Rigid Rule 25' Tape 100 ' Tape
Primary Standard Primary Standard Primary Standard

Client
Calibration won eee
Workload °
Client
Calibration
Workload

GMP 13 Page 9 of 11


December 2003
Calculation of Conventional Mass 3
Use equation 3.1.1 for optional sequence A (SXX) without buoyancy corrections :

Since no tare weights were used and equal nominal values were used, the equation may be
simplifies as follows:

5]

C,=C,+ (0, -0,)| oe

C, = 0.255mg + (12.51 - 12.62) 49.916mg |

(62.37- 12.51)
Cy = 0.255mg + (-0.110 124) mg

C, = 0.144 876 mg

Calculation of Uncertainty

Calculate the uncertainty for the calibration:

U=u, *2

The uncertainty for the standard from the calibration report (or data sheet) must be divided by
the k factor to determine the u;. Refer to SOP 29 for the use of multiple standards. An additional
uncertainty for not performing the air buoyancy correction can be determined using the
magnitude of the air buoyancy correction from SOP 2.

u,=¥ (0.011 ? +( 0.018 ? +( 0.0010
ue = 0.021 330 7 mg
U = 0.021 3307*2 = 0.042 661 5mg

Uncertainty Statement

The uncertainty reported is the root sum square of the standard uncertainty of the standard, the
standard deviation of the process, and an uncorrected systematic error for lack of buoyancy
corrections, multiplied by a coverage factor of 2 (k=2) for an approximate 95 % confidence
interval. Factors not considered in the evaluation: magnetism (weights are considered to meet
magnetism specifications unless measurement aberrations are noted), balance eccentricity and

3 Keep in mind that these equations may be truncated for the purpose of this example and minor differences
may be seen in the ending decimal places due to the use of calculators or spreadsheets.

SOP7 Page 14 of 15


GMP 14

Methodology

2.1.

2.2.

2.3.

March 2003

Summary

A sensitivity weight is selected to calibrate the balance over the range to be
used in the measurement procedure. Minimizing the difference in mass values
between X and S is critical when choosing an appropriate sensitivity weight.
Therefore, tare weights may be necessary whenever the difference in mass
values is significant. Minimizing the difference between X and S works to our
benefit since the range of the measurements is minimized and reduces potential
errors that can be introduced by nonlinearity of the balance.

Apparatus

2.2.1. Sensitivity weights with accurate and traceable calibration values.
2.2.2. Tare weights with accurate and traceable calibration values.

2.2.3. Clean forceps to handle the weights, or gloves to be worn if the

weights are to be moved by hand.

Procedure for selection

2.3.1.

2.3.2.

2.3.3.

Conduct preliminary measurements to determine the approximate
mass value for the difference between the standard and the unknown

(X-S).

Define the range of use for the balance to be used:
2.3.2.1. Equal arm — number of scale divisions
2.3.2.2. Mechanical — optical scale

2.3.2.3. Combination — digital indications
2.3.2.4. Fully electronic — capacity

2.3.2.5. Comparators — digital indications

Determine the need for tare weights if the difference between X and S
exceeds the values shown in Table 1.

Page 2 of 4


March 2003

SOP No. 29

Standard Operating Procedure
for the
Assignment of Uncertainty

1. Introduction

1.1. Purpose
Laboratories performing calibrations that meet ISO/IEC Guide 25, ISO/IEC

17025, or ANSI/NCSL Z 540-1-1994 must report uncertainties in conformance
with the 1993 ISO Guide to the Expression of Uncertainty in Measurement
(hereafter called the GUM). This SOP provides instruction for the laboratory to
meet this requirement.

1.2. Prerequisites

1.2.1. Calibration certificates with valid uncertainties must be available for all
standards.

1.2.2. Statistical data regarding the calibration measurement process must be
available; preferably from measurement control programs within the
laboratory.

1.2.3. Knowledge of the technical basis for the measurement is critical for
completeness in uncertainty evaluation. This can be obtained through
brainstorming, experimentation, interlaboratory comparisons, cause and
effect diagrams and the like. Flow charts at the end of this SOP show a
number of common factors affecting measurements in the areas of mass,
length, and volume.

2. Methodology
2.1. Scope, Precision, Accuracy
Each measurement made in a laboratory has a corresponding uncertainty assigned
to the calibration value. The uncertainty is directly related to the measurement
parameter (scope), range of the measurement, the equipment or measurement

process being used (affecting precision), and the standards available with
associated uncertainties.

SOP 29 Page 1 of 11


GMP 13

Temperature
NIST
SPRT Liquid-in-Glass Laboratory Fixed
Primary Standard Primary Standard Points
Laboratory

Working Standards

Client
Calibration
Workload

Page 10 of 11

March 2003


March 2003

Precision

The contribution of the random error of the evaluation of air density to the precision of
mass measurement may be estimated as follows:

For mechanical balances, or electronic balances used in weighing by substitution, the
contribution is:

&p,(V, -V,)

Table A-10. Variables for above equation

Variable Description

Oa random error of evaluation of py

V volume of standards, if weighing by substitution
‘ V, = Mp/ Da, if using the built-in weights on a single pan balance.

V volume of object weighed

10.

The quantity, dp, will have contributions from the measurements of temperature, pressure
and relative humidity which are required for the calculation of p,. Equation (1) may be
used to estimate the effects of imprecision in measurements of P, t, and U. It is unrealistic
to expect 5p,/pa ever to be less than 0.05 % even using the best techniques available.

Accuracy

Inattention to problems of buoyancy most often results in systematic errors. For a
substitution weighing, for example, the buoyancy correction is of the order of p,(V, - V,).
While this quantity may be significant to a measurement, day-to-day variation in py
(usually no more than 3 %) may not be noticeable and hence need not be measured. For
the most accurate work, not only must p, be accurately determined, but the volumes of the
unknown and standard may have to be measured to better than 0.05 % - the minimum
systematic uncertainty attainable in the calculation of py.

If the standards have been calibrated in terms of conventional mass, complete neglect of
buoyancy corrections will produce an error in the measured result M, of order:

cu] (rao ~ »,( 2-2) «(Ae J 2.)] ”
Ps Pp Ps Px

This error is often unacceptably large.

Use of equation (4), on the other hand, introduces only an error of approximately

Appendix SOP 2 Page 15 of 22


December 2003
2.3.3. Calibrated small standard weights with recent calibration certificates and
values traceable to NIST to be used as tare weights.

2.3.4. Uncalibrated weights to be used to adjust the balance to the desired
reading range.

2.3.5. Forceps to handle the weights, or gloves to be worn if the weights are
moved by hand. :

2.3.6. Stop watch or other timing device to observe the time of each
measurement.

2.3.7. Calibrated barometer accurate to + 66.5 Pa (0.5 mm Hg) with recent
calibration values traceable to NIST to determine air pressure.

2.3.8. Calibrated thermometer accurate to + 0.10 °C with recent calibration
values traceable to NIST to determine air temperature.

2.3.9. Calibrated hygrometer accurate to + 10 percent with recent calibration
values traceable to NIST to determine relative humidity."

2.4. Symbols
Table 2. Symbols used in this procedure
Symbol Description
Ss standard reference weight

xX weight to be calibrated

small calibrated tare weight, A subscript s or x is used to indicate the larger
weight with which it is associated

sw small calibrated weight used to evaluate the sensitivity of the balance

the mass (true mass) of a specific weight. Subscripts s, x, t, sw are used to

M identify the weight (equals Nominal plus Correction)
N the nominal value of a specific weight. Subscripts s, x, are used to identify the
weight.
Cc the correction for a specific weight. Subscripts s, x, are used to identify the
weight.
the conventional mass of a specific weight. Subscripts s, x, t, sw are used to
CM |... i
identify the weight.
Pa density of air at time of calibration

'The barometer, thermometer, and hygrometer are used to determine the air density at the time of the measurement.
The air density is used to make an air buoyancy correction. The accuracies specified are recommended for high
precision calibration. Less accurate equipment can be used with only a small degradation in the overall accuracy of
the measurement.

SOP 4 Page 3 of 18


GMP 13

Mass - Option A

NIST

W 1-kg. C 1-kg.
wl W 1-kg.. a C 1-kg..
W 100 g. C 100g.
W 100 g.. C 100 g..
v
Remaining Client
Laboratory Echelon |, Il
Standards Calibration
Metric/Avdp Workload
Laboratory Field
Level Working
Standards
Client
Echelon Ill
Calibration
Workload
Page 4 of 11

March 2003


Laboratory data and conditions:

Appendix

Modified Substitution Data Sheet

December 2003

Operator
Date Temperature
Balance Pressure
Load Relative Humidity

Standard deviation of the process, from control chart, sp

Mass standard(s) data:

. + Expanded Une: Une: Density
*
ID Nominal Mass Correction’ From cal. Report k factor g/em’
Ss
sw

*Mass Correction = True Mass if using buoyancy correction. Mass Correction = Conventional Mass if NOT using
buoyancy correction. Density is used only with buoyancy corrections.

Observations:
Observation No. Weights Balance Observations, Units
[Time:
1(0)) Ss
2 (02) S+sw
Error < 2 % of optical scale or electronic range? Yes No
3 (03) Ss
4(0) x;
5 (Os) xX)
6 (Os) x3
7(O,) Se
8 (Os) Ss
[Time: Drift < 1/10 Tol. ?: Yes Nol

Up to 10 unknown weights may be checked with this procedure if the drift is less than 1/10 of the tolerance.

SOP 8

Page 10 of 12


December 2003

6. Report

Report results as described in SOP No. 1, Preparation of Calibration/Test Reports.

SOP 7 Page 10 of 15


SOP 8

2.5.

2.4.2.

2.43.

2.4.4.

245.
2.4.6.

2.4.7.

2.4.8.

2.4.9.

December 2003

tare weights and the balance’s coarse and fine Zero controls. This setting
must not be altered during a measurement sequence. Record the reading
as O};.

Add a sensitivity weight equal to approximately one-quarter full scale
reading and record reading as O2.

Calculate the value of a scale division using the equation in 3.2. If it is
within + 2 % of nominal value (usual case) the nominal value of a division
can be used for tolerance testing.

Remove the sensitivity weight and adjust the optical scale to account for
corrected value of standard used.

Example: Suppose that the nominal range of the optical scale is 100
mg and that the reference standard has a correction of -2.5 mg. The optical
scale is adjusted to read 47.5 mg when the standard is on the pan. Under
this condition, the reading 50.0 mg represents the nominal mass of the
reference standard.

Remove the Standard.

Place the weight to be tested on the balance pan, read the optical scale and
record reading as X,,. The error in the weight is the amount by which the
indication deviates from the mid-scale reading. If the weight indication is
more than the mid-scale value, the weight is heavy by the indicated
difference; if the indication is less than the mid-scale value, the weight is
light.

Afier several weights have been tested (no more than 10), put the standard
on the balance pan and record the reading. The difference between this
indication and the previous one for the standard indicates a balance drift.
This drift will normally be very small. If the drift exceeds 10 % of the
tolerance applicable to the weights under test or affects a measurement
result to the extent that a weight may be out of tolerance, the measurement
should be repeated and more frequent checks of the standard should be
made or a more appropriate procedure should be used.

Readjust the optical scale at any time that a significant difference is
observed when rechecking a standard.

Calculate the mass correction for the unknown weights using the
appropriate equation in Section 3.

Procedure - Option A;

2.5.1.

Use of Single-Pan Balance

Select a reference standard of the same nominal value as the weight under
test. Place the standard on the balance pan. Adjust the optical scale
reading (See GMP No. 4) to midscale using uncalibrated tare weights and
the balance’s coarse and fine Zero controls. This setting must not be
altered during a measurement sequence. Record the reading as O).

Page 3 of 12


SOP 8

3.4.

3.5.

December 2003

Note: If an electronic balance is used and zeroed with the standard on the
balance, O; is “O" and d becomes the X,, balance reading.

Calculate the mass correction of each unknown weight as follows if the correction
for the standard IS used in setting a nominal reference point on the balance:

Cx = (X batance reading — Nnominal reference point )

Note: In this case the standard and its correction are used to artificially set a
perfect nominal reference point for use in comparing the unknown weights.

If tare weights and unequal nominal values are used, use the following equation
for modifying section 3.3:

G.= Cs + CM, ~ CM + (Xn — 07) + Ns - Ne

Measurement Assurance

4.1. Duplicate the process with a suitable check standard (See GLP 1, SOP 9, SOP 30,
and Sec. 7.4)

4.2. Plot the check standard value and verify that it is within established limits; a t-test
may be incorporated to check observed value against accepted value.

4.3. The mean of the check standard is used to evaluate bias and drift over time.

4.4. Check standard observations are used to calculate the standard deviation of the
measurement process, Sp.

Assignment of Uncertainty

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of
the mass standards used, u;, estimates of the standard deviation of the measurement
process, sp, and estimates of the effect of other components associated with this
procedure, up», These estimates should be combined using the root-sum-squared method
(RSS), and the expanded uncertainty, U, reported with a coverage factor of two (k=2), to
give us an approximate 95 % level of confidence. See SOP 29 for the complete standard
operating procedure for calculating the uncertainty.

5.1.

5.2.

5.3.

The expanded uncertainty for the standard, U, is obtained from the calibration
report. The combined standard uncertainty, u,, is used and not the expanded
uncertainty, U, therefore the reported uncertainty for the standard will usually
need to be divided by the coverage factor k.

Standard deviation of the measurement process from control chart performance
(See SOP No. 9.) The value for sp is obtained from the control chart data for
check standards using modified substitution measurements.

Other standard uncertainties usually included at this calibration level include
uncertainties associated with lack of performing buoyancy corrections and can be
determined using the equation given in SOP 2 for the magnitude of the air
buoyancy correction. Buoyancy corrections are not generally needed at the
uncertainty level this procedure is designed for.

Page 8 of 12


December 2003

2. Methodology

24.

2.2.

SOP 30

Scope, Precision, Accuracy

This method can be used on any measurement or calibration process where a
check standard can be substituted for, or measured as, the item being
calibrated. The method duplicates the standard operating procedure with the
check standard serving as a surrogate for the item being calibrated. The results
of these check standard measurements are recorded, charted, and analyzed to
establish the measurement capability and to set process control limits, called
reference limits. The reference limits are used to establish process uncertainties
and to control future measurement performance.

Summary

Process Measurement Assurance Program (PMAP) is used for determining and
controlling the measurement process uncertainty as the calibration is
performed. The uncertainty includes effects of the measurement instrument,
the operator, the procedure, the standards, and the environment. Each
application is modeled to meet the following objective for determining and
controlling uncertainties 1) in the measurement process; 2) in the calibration
standards; or 3) in both the process and the standards.

The check standard is selected to evaluate the standard deviation of the process
(sp), other process uncertainties (u)) such as material density or air density
accuracy, and possible bias (wa) of the process (see SOP 29). Reference
measurements for the check standard are performed after calibrating the
calibration standards and after the servicing of the measurement instrument.

Control measurements of the check standard are graphed for visual
examination of process performance and are evaluated against control
reference limits.

Statistical tools, ‘F’ and ‘t’ tests, determine if there are process changes in
variability and bias (systematic error). These tests are used when process
performance is questionable; when current data is evaluated to establish new
reference control limits; and when evaluating uncertainty statements.

Page 2 of 9


SOP 30

2.5.3.2

December 2003

minus three standard deviations from the mean(x) of the

control measurements. All control measurements are charted
as deviation from the accepted value of the check standard

(Sc)

Establish control chart parameters by calculating the mean
and the estimate of the standard deviation (sp) of the check
standard reference measurements (S,).

Control chart parameters are as follows :
Reference Line = Accepted S,

Mean Line = X of Observed S: data

3s Action Limits = X +3(s,)

2s Warning Limits = x + 2(s,)

Process Bias = Mean of Observed Sc - Accepted Sc

2.5.4 Establish Reference Limits and Process Uncertainty

2.5.4.1

2.5.4.2

Establish reference control limits (as described in 2.5.3.2) by
calculating control limits and process bias using the control
measurements obtained when calibration standards and
measurement instruments are calibrated. These limits are to
be stored and used as a reference for future control
measurements. Future control measurements should be
control-charted and tested against these limits for “in” or
“out” of control status. This reference data will also be
Statistically used to periodically evaluate process and
calibration standard performance for change from the
calibrated reference status.

Establish the Expanded Uncertainty (U) by using the
reference data, calibration standard uncertainty (u,), and any
other uncertainty (uo) not covered by the reference data.

4. = (sp) +@) +,)° + (Ua)?

U=k*u,

According to the PMAP model, sp, uo, and ug are evaluated by
comparison with the reference data. The uncertainty for the
standard, us, and, in some situations, additional uy are included
in PMAP calculation of the process expanded uncertainty (U).

Page 6 of 9


This page is CODEN page on back of title page or Blank.

ii


3.6.

3.7.

3.8.

SOP 29

March 2003

Step 6. Calculate the expanded uncertainty

The combined standard uncertainty is then multiplied by a coverage factor, k, equal to 2
or 3, as chosen by the laboratory, to provide a level of confidence of approximately 95 %
or 99 %, respectively. This procedure is based on the Central Limit Theorem and in
most cases allows the use of 2 or 3 to provide an approximate 95 % or 99 % level of
confidence. The equation used to determine the expanded uncertainty is as follows:

U=u,*k
where k= 2 or k=3.

Step 7. Evaluate the expanded uncertainty

The expanded uncertainty may be evaluated against established criteria such as tolerance
limits. For mass standards, the specifications clearly state that the expanded uncertainty
must be less than 1/3 of the tolerance.

Step 8. Report the uncertainty
Once the uncertainty has been calculated, a statement such as the following is reported:

The combined standard uncertainty includes the standard uncertainty reported for the
standard, for the measurement process, and for any observed deviations from reference
(e.g., NIST) values, which are less than surveillance limits. The combined standard
uncertainty is multiplied by k, a coverage factor of (2, 3) to give the expanded
uncertainty (which defines an interval with an approximate (95, 99) % level of
confidence).

Page 8 of 11


December 2003

2.3.6. Stop watch or other timing device to observe the time of each
measurement.
2.3.7. Calibrated barometer accurate to + 66.5 Pa (0.5 mm Hg) with recent
calibration values that are traceable to NIST to determine air pressure.
2.3.8. Calibrated thermometer accurate to + 0.10° C with recent calibration
values that are traceable to NIST to determine air temperature.
2.3.9. Calibrated hygrometer accurate to + 10 % with recent calibration values
that are traceable to NIST to determine relative humidity."
2.4. Symbols
Table 2. Symbols used in this procedure
Symbol Description
Ss standard weight
xX weight calibrated
t small calibrated tare weight, A subscript s or x is used to indicate the larger
weight with which it is associated
sw small calibrated weight used to evaluate the sensitivity of the balance
M the mass (true mass) of a specific weight. Subscripts s, x, t, sw are used to
identify the weight (equals Nominal plus Correction)
the nominal value of a specific weight. Subscripts s, x, are used to identify
the weight.
Cc the correction for a specific weight. Subscripts s, x, are used to identify the
weight.
the conventional mass of a specific weight. Subscripts s, x, t, sw are used to
CM : . :
identify the weight.
Pa density of air at time of calibration
Pn density of normal air (1.2 kg/m*)
p density of masses; subscripts s, x, t;, ,, sw are used to identify the weight

SOP7

The barometer, thermometer, and hygrometer are used to determine the air density at the time of
the measurement. The air density is used to make an air buoyancy correction. The accuracies
specified are recommended for high precision calibration. Less accurate equipment can be used
with only a small degradation in the overall accuracy of the measurement.

Page 3 of 15


March 2003

2.4. Procedure

2.4.1.Record the temperature, pressure, and relative humidity at the start and at the
end of the measurement process as near the location of the measurement as
necessary and practical. If these parameters change significantly during the
measurement process, it may be necessary to wait for more stable operating
conditions or to use average values to compute the air density. Use of the
average environmental values may influence the uncertainty of the
measurement result and must be evaluated for significance.

2.4.2. Determine the air density using the equation given in Section 8 of the Appendix
to this SOP.

3. Calculations

3.1. Calculate the mass, M@,, of the unknown weight, X, using the following equation,
where d represents the “difference” obtained with buoyancy corrections applied to the
sensitivity weight.

u [1-2 \ea
M =—<—/4

CF)
Py

If tare weights were carried with X and/or S, use the following equation:

u{1- 2) «dem, 1 - £ -M, p— fa
M.= Ps ‘ Py . Pr,

(-z
Px

SOP 2 Page 3 of 22


GMP 14

March 2003

GMP 14

Good Measurement Practice
for the
Selection and Use of Sensitivity Weights in Weighing Procedures

Introduction

Mass calibration procedures are based on comparing the unknown mass, X, to a standard
mass, S, utilizing the balance as a comparator. This comparison relies on the accuracy
of balance indications. Most balance indications are not accurate enough for precision
mass calibrations, and they tend to drift with time. Drift can often be assumed to be
linear over a short period. Concerns over balance inaccuracy and drift result in two
possible causes of errors in mass determination procedures. Inaccuracy of the balance
indications can be corrected by incorporating a sensitivity weight in the procedure that
calibrates the range of use of the optical scale (mechanical balances) or of the digital
indications (electronic balances). Errors due to drift can be minimized by using the
correct comparison method, selecting a suitable sensitivity weight, and by consistent
timing within the procedure. The proper selection of procedures (GMP 12), the
adherence to those procedures, and equal time intervals between weighing operations
will allow the measured difference between X and S to be corrected for inaccuracy of the
balance indications and for balance drift.

11. Purpose

The following practice will guide you through the process of selecting and
using a correct sensitivity weight for mass determination procedures.

1.2. Prerequisites

1.2.1. Verify that valid calibration certificates are available for the masses to
be used as standards, sensitivity weights, and tare weights.

1.2.2. Verify that weight-handling equipment is available and in good
operational condition.

1.2.3. Verify that the operator is familiar with the design and the operation of
the balances and familiar with weighing procedures.

1.3. Safety

1.3.1. Handling of large or small weights can represent a hazard to either the
weights or personnel if the weights are dropped.

Page 1 of 4


December 2003
Table 9.1 Use of Range to Estimate Standard Deviation

Number of | pactor Number of Replicates in a Set
Sets of Degrees of
Replicates Freedom 2 3 4 5 6
I d 1.41 1.91 2.24 2.48 2.67
D 1.00 1.98 2.93 3.83 4.68
3 d; 1.23 1.77 2.12 2.38 2.58
D 2.83 5.86 8.44 11.1 13.6
5 d; 1.19 1.74 2.10 2.36 2.56
D 4.59 9.31 13.9 18.4 22.6
10 d 1.16 1.72 2.08 2.34 2.55
D 8.99 18.4 27.6 36.5 44.9
15 d 1.15 1.71 2.07 2.34 2.54
v 13.4 27.5 41.3 54.6 67.2
20 d; 1.14 1.70 2.07 2.33 2.54
i) 17.8 36.5 55.0 72.7 89.6
co d, 1.13 1.69 2.06 2.33 2.53
yt *
Rid, > 0

Intermediate values for d. ; and U may be obtained by interpolation, or from the reference from which this
table was adapted.

Example: If 10 sets of measurements were made. and each set consisted of two measurements (duplicates),
the value for d) is 1.16; if 15 sets of measurements were made and each set consisted of three measurements

(triplicates) the value for d} is 1.71.

Adapted from Lloyd S. Nelson, J. Qual. Tech. 7 No. 1, January 1975.
© 1975 American Society for Quality Control, Reprinted by permission.

Reference Tables Page 2 of 13



December 2003

Compliance Evaluation

We have to evaluate the correction with its expanded uncertainty to determine if the weight is in
tolerance or not. The magnitude of the expanded uncertainty has to be less than 1/3 of the
tolerance to be able to perform that evaluation, according to ASTM E617-97 and OIML R111.

Load = 10g
ASTM E617 OIML R111
Class Tolerance (mg) Class Tolerance (mg)
0 0.025 Ei 0.020
1 0.050 E, 0.060
2 0.054 F 0.20

If we look at three times the uncertainty: 0.011 mg x 3 = 0.033 mg, we realize that the
uncertainty complies with the 1/3 rule for ASTM classes 1, 2, and OIML classes Ep, F).

Next, we look at the correction with the uncertainty: - 0.126 mg + 0.011 mg.
We can see that the absolute value of the correction is within: 0.1/5 $C, < 0.137, therefore, it
only complies with OIML class Fj.

Reporting
The conventional mass correction and uncertainty would be reported as follows:

Cy = - 0.126 mg + 0.011 mg

SOP 4 Page 16 of 18



March 2003

weights when in the partial release position because the small weight changes should not result in
shock loading of the balance.

When releasing the pan to either the full or partial release position, the action should be done
slowly and carefully. The objective is to minimize disturbances to the balance as much as
possible.

Similarly, all loads should be placed on the balance pan carefully and centered on the pan.

When a mechanical balance is released, the beam goes through a series of oscillations. The
frequency of these oscillations diminishes as time passes until they are almost imperceptible to
the naked eye. At this point, optimal stabilization is achieved. This stabilization of the balance
typically lasts for a very short period of time, after which the balance reading will usually drift.
A similar situation occurs when a mass is placed on the pan of an electronic balance. Therefore
readings should be taken at the precise moment of achieving balance stability. This interval
between the releasing of a pan on a mechanical balance, or the placing of a mass on an electronic
balance, and the reading of the observation, varies from balance to balance. Stabilization time
differs for all balances, even among those of the same type and model. Knowledge of the
instrument is critical to correctly establish this time interval. Although manufacturers will
usually state this value, it is necessary for the metrologist to verify its reliability. Many electronic
balances have a stability signal incorporated into the design, but this also must be verified. All
measurements in a calibration should be performed at the same time interval, and within the
shortest time possible.

All balances should be exercised before taking readings. A load equal to the load to be measured
should be placed on the balance, a reading taken, and the pan arrested, if appropriate, or the
weight removed from electronic balances. This operation should be repeated several times
before readings are taken for measurement purposes. Once the balance has been "warmed-up",
better repeatability will be achieved. Balances can be very accurate even when used without
being exercised first, but improved results can be obtained by going through a "warm-up"
procedure. If the larger variation present in initial weighings on a balance that has not been
exercised is not significant to the measurement, the warm-up procedure may be minimized.

To determine the repeatability of measurements when a balance has not been exercised versus its
performance after being exercised, and to determine how much warm-up time is required, begin
measurements starting with the unexercised balance and record the readings. Repeat a series of
measurements until you have obtained several measurements after the balance has been
exercised. This test can be repeated over several days using the same objects and the results
compared. The readings obtained when using an unexercised balance are likely to show a
slightly larger variation than those obtained after the balance has been exercised. Balance drift is
likely to be larger initially and then reach a steady state when the balance has been "warmed-up".

GMP 10 Page 3 of 6


March 2003

GMP 1

Good Measurement Practice
for
Reading Turning Points on an Equal-Arm Balance

The damping of the beam oscillations of an equal-arm balance is generally very slow.
Consequently, it is practical to read the turning points (the highest and lowest value of the beam
oscillation) on the graduated scale and use the sum of the turning points as the observation value
rather than wait for the beam to come to rest. This GMP requires that the graduated scale be
numbered such that adding weights to the left arm increases the readings.

Suppose the graduated scale has 20 graduations that are numbered from 0 to 20. The loads on
the balance arms should be adjusted so that the sum of the turning points is approximately twice
the midscale reading. In this example, the sum of the turning points should be within one
division of twenty. Turning points should be estimated to at least 0.1 division in this example,
which is typical of the Russell balance. This means that the final rest point is approximately 10,
the midscale reading. Motion should be induced to the beam so that the turning points can be
read easily. Care should be taken so that the beam does not hit limiting stops during its normal
oscillation while turning points are being read. The amount of the beam oscillation is not critical
although a span of from three to ten divisions is adequate.

Once motion has been induced for the beam oscillation, wait for at least one complete oscillation
cycle for the beam motion to stabilize. After this time, the turning points can be read. The
readings may begin with either the high or low turning point. The turning points for at least two
consecutive oscillation cycles should be recorded. The turning points should reveal a consistent
pattern of slow damping; that is, the turning points should gradually converge to the eventual rest
point. For example, if the Jast high turning point was greater than the previous high turning point
(assuming that the readings normally drop on successive readings), this would indicate that
something has interfered with beam oscillation, hence the last reading was not valid with respect
to the previous readings. Under these circumstances, turning points should continue to be read
until a consistent damping pattern has been obtained. In some cases, the balance oscillation will
dampen so slowly that the same readings may be obtained for several oscillations before a
decrease is observed. These readings are valid and may be used to compute the sum of the
turning points.

When at least four satisfactory turning points have been obtained (two high and two low turning
points), all but the last three readings should be discarded. This will leave two high and one low
turning point or vice versa. The two readings for the high or low turning points, as the case may
be, should be averaged and added to the single turning point to obtain the sum of the turning
points. The sum should be carried out to two decimal places if the second decimal place digit is
nonzero. As an example, the following readings were obtained: 15.5, 4.3, 15.4, 4.4. The sum of

the turning points is computed as (A*4) +15.4=19.75.

GMP | Page | of 1


December 2003

Table 1. Environmental conditions
Echelon Temperature ares inicity
I 20 °C to 23 °C, a set point + 2 °C, maximum change 1.0°C/h | 40to60+10/4h
Tl 18 °C to 27 °C, maximum change 2.0 °C/h 40 to 60+ 20/4h
2. Methodology
2.1. Scope, Precision, Accuracy

SOP7

This method is applicable to all weighings utilizing a single-pan mechanical balance, a
full electronic balance, or a balance that combines digital indications with the use of
built-in weights (combination balance). The precision depends upon the sensitivity of the
balance and the care exercised in making the required weighings. The accuracy
achievable with this procedure depends on the accuracy of the calibration of the working
standards and the precision of the intercomparison.

2.3.

2.2. Summary

The balance is adjusted, if necessary, to obtain balance indications for all
measurements that will be within the range of the optical scale or digital
indications of the balance without changing the dial settings for the built-in
weights, if present. The standard and the test weight are each weighed. A small,
calibrated weight, called a sensitivity weight, is added to the test weight and these
are weighed

The single substitution procedure is the same for all of the balances mentioned
above, but the adjustment of the balance to prepare for the intercomparison and
the selection of the sensitivity weight differ slightly depending upon the balance
used. When steps specific to a particular balance are required, they are given in
subsections of the procedure identified by a, b, and c along with the balance type.

Apparatus/Equipment Required

2.3.1. Precision balance with sufficient capacity and sensitivity for the
calibrations planned.

2.3.2. Calibrated working standard and sensitivity weights with recent
calibration values that are traceable to NIST.

2.3.3. Calibrated small standard weights with recent calibration values that are
traceable to NIST to be used as tare weights.

2.3.4. Uncalibrated weights to be used to adjust the balance to the desired
reading range.

2.3.5. Forceps to handle the weights, or gloves to be worn if the weights are
moved by hand.

Page 2 of 15



December 2003

8. STATISTICAL TECHNIQUES

Statistics are used in metrology to summarize experimental data, to provide the basis for
assessing its quality, and to provide a basis for making probabilistic decisions in its use. The
essential basic statistical information for describing a simple data set is:

The mean of the set, x
The standard deviation of the set, s
The number of individuals in the set, n

If the set is a random sample of the population from which it was derived, if the measurement
process is in statistical control, and if all of the observations are independent of one another, then
s is an estimate of the population standard deviation, O, and ¥ is an unbiased estimate of the
mean, HH.

The population consists of all possible measurements that could have been made under the test
conditions for a stable test sample. In this regard, the metrologist must be aware that any
changes in the measurement system (known or unknown) could possibly result in significant
changes in its operational characteristics, and, hence the values of the mean and standard
deviation. Whenever there is doubt, statistical tests should be made to determine the significance
of any apparent differences before statistics are combined.

The following discussion reviews some useful statistical techniques for interpreting
measurement data. In presenting this information, it is assumed that the reader is already
familiar with basic statistical concepts. For a detailed discussion of the following techniques and
others not presented here, it is recommended that the reader consult NBS Handbook 91 -
Experimental Statistics, by Mary G. Natrella [19]. That handbook also contains comprehensive
statistical tables from which the tables contained in Chapter 9 of this publication were taken.

8.1 Estimation of Standard Deviation from a Series
of Measurements on a Given Object

Given n measurements x1, X2, X3, .-.... oXn

G@, +x, +x, +..+x,)
n

Mean, x =

Standard deviation estimate, s =

The estimate, s, is based on n-1 degrees of freedom

Statistical Techniques Page 1 of 10


December 2003

3. Calculate s, as follows:

Note that s, is an estimate of the long term component of the standard deviation of a single
measurement. The long term standard deviation of the mean of n measurements taken at a single
occasion is estimated by:

2

~ 2 Sy
84%) = 5 ——

Important note: Do not use this approach for handling within-series and between-time standard
deviations with the Mass Code. Separate formulas are available for that application.

8.6 Confidence Interval for the Mean

The estimation of the confidence interval for the mean of n measurements is one of the most
frequently used statistical calculations. The formula used will depend on whether the population
standard deviation,c, is known or whether it is estimated on the basis of measurements of a
sample(s) of the population.

Using Population Standard Deviation, ©

Strictly speaking, o, is never known for a measurement process. However, the formula for use in
such a case is:

x4 72
dn
Variable Description
x sample mean
So known standard deviation
n number of measurements of sample
Zz standard normal variate, depending on the confidence level desired

For 95 % confidence z = 1.960; for 99.7 % confidence z = 3.0.
For other confidence levels, see Table 9.2

Statistical Techniques Page 4 of 10


December 2003

Confirming (or assuming) that s, and s, are not significantly different, they are pooled, as

already described (but repeated here for convenience) and used to calculate a confidence interval
for the difference of the means. If this is larger than the observed difference, there is no reason
to believe that the means differ. The steps to follow when making the calculation described
above are:

Step 1. Choose a , the level of significance for the test

Step 2. Calculate the pooled estimate of the standard deviation, sp

Sp will be estimated with na + ng - 2 degrees of freedom

Step 3. Calculate the respective variances of the means
2 2
s s
v,=— and vy, =
nN4 Np

Step 4. Calculate the uncertainty of [x a7 X,[=A
U, =t/V,47,)
using a value for ¢ based on S and vb = n,+n,-2.
Step 5. Compare U, with A

If U, >A, there is no reason to believe that A is significant at the level of
confidence chosen.

Statistical Techniques Page 8 of 10


3.

GMP 11

Calculations

3.1.

March 2003
Mass and Gravimetric Volume Secondary Parameters

Environmental Measurement Equipment

Table 5. Calibration intervals for environmental equipment

Item Initial Calibration Interval Source
(months)

Barometer 12 NIST

Hygrometer 24 NIST

Thermometer 12 Lab

Length Secondary Parameters - No secondary parameters.
Volume Secondary Parameters
Water Temperature Measuring Device

Table 6. Calibration intervals for volume secondary parameters

Item Initial Cal Interval (months) Source

Thermometer 12 Lab

Temperature Secondary Parameters - No secondary parameters.

Initial Intervals

3.1.1.

3.1.2.

Assignment of Initial Intervals

Assignment of initial intervals is based on these recommendations. Subsequent
intervals may be adjusted based on analysis of Check standard data that is
recorded on control charts. The initial interval is equivalent to the amount of
time that passes before a metrologist makes the first observation of a result lying
outside the warning limits of the chart when the investigation yields no apparent
correctable cause. Warning limits are established at + 2 standard deviations of
the measurement process around the accepted value of the check standard.

Absence of Control Charts
Ifno control charts are available, the laboratory’s Technical Manager will assign

the initial interval based on engineering evidence, manufacturer's specifications,
NIST recommendations, and experience.

Page 5 of 6


Table 9.3 Student t-Variate

December 2003

* 80% 90 % 95 % 98 % 99 % 99.73 %
df tos0 toss toors too» to995 tosses
1 3.078 6.314 12.706 31.821 63.657 235.80
2 1.886 2.920 4.303 6.965 9.925 19.207
3 1.638 2.353 3.182 4.541 5.841 9.219
4 1.533 2.132 2.716 3.747 4.604 6.620
5 1.476 2.015 2.571 3.365 4.032 5.507
6 1.440 1.943 2.447 3.143 3.707 4,904
7 1.415 1,895 2.365 2.998 3.499 4.530
8 1.397 1.860 2.306 2.896 3.355 4.277
9 1,383 1,833 2.262 2.821 3.250 4.094
10 1.372 1.812 2.228 2.764 3.169 3.957
aa 1.363 1.796 2.201 2.718 3.106 3.850
12 1.356 1.782 2.179 2.681 3.055 3.764
13 1.350 1.771 2.160 2.650 3.012 3.694
14 1.345 1.761 2.145 2.624 2.977 3.636
15 1,341 1.753 2.131 2.602 2.947 3.586
16 1.337 1.746 2.120 2.583 2.921 3.544
17 1,333 1,740 2.110 2.567 2.898 3.507
18 1.330 1.734 2.101 2.552 2.878 3.475
19 1,328 1.729 2.093 2.539 2.861 3.447
20 1.325 1.725 2.086 2.528 2.845 3.422
25 1.316 1.708 2.060 2.485 2.787 3.330
30 1.310 1.697 2.042 2.457 2.750 3.270
40 1.303 1.684 2.021 2.423 2.704 3.199
60 1,296 1.671 2.000 2.390 2.660 3.130
~o 1.282 1.645 1.960 2.326 2.576 3.00

* Columns to be used in calculating corresponding two-sided confidence interval. From: NBS Handbook 91
p. T-5; Last column from B.J. Joiner, J. Research NBS.

Reference Tables

Page 4 of 13



December 2003

Appendix
Single Substitution Data Sheet
(Optional Sequence B)

XSS
Laboratory data and conditions:
Operator
Date Temperature
Balance Pressure
Load Relative Humidity
Standard deviation of the process, from control chart, sp

Mass standard(s) data:

Mass Une: Une: Density

iD Nominal Correction _| From cal. report | _k factor g/m’

x
Ss
sw
ts
by

Mass Correction = True Mass if using buoyancy correction. Mass Correction = Conventional Mass if
NOT using buoyancy correction. Density is used only with buoyancy corrections.

Observations:
Measurement # Weights Balance Observations, Units
Time:
1 (0) Xt tk }
2 (0) Stt, i
3 (03) St+ts+sw i
Time:

Measurement Assurance (Duplication of the Process):

Measurement # Weights Balance Observations, Units
Time:
1 (0) S+t, i
2 (02) Set tse :
3 (O3) So + tse + sw :
Time:

Note: dotted line represents decimal point.

SOP7 Page 12 of 15


SOP 9

December 2003

If a plotted point is outside the warning limits but within the control limits,
investigate the presence of calculation errors. Ifnone were made, re-measure
the check standard. The re-measured value must be within the warning limits
to merit the decision of "in control". If the results are not within limits,
consider the measurement process "out of control". Reject all data obtained
since last "in-control" measurement and take corrective action (hence
“action” limit). Accept no further data until the system is demonstrated to be
in-control as indicated by at least two successive measurements of the check
standard within the warning limits.

Ifa plotted point is outside the control limits and arithmetically correct, the
system is considered to be out of control. Data are rejected, corrective
actions must be taken and re-attainment of statistical control demonstrated, as
above, before data may be accepted.

4.2. Transfer of Measurement Statistics

4.2.1.

4.2.2.

Absence of a significant difference between the central line and the accepted
value for the check standard may be considered as evidence of insignificant
bias at the level of confidence of the statistical test used. This conclusion is
valid, as long as the system remains in control. On occasion, small
differences (less than 1 s) from unknown sources will be obvious over time
and the value observed for the bias should be incorporated into the
uncertainty per SOP 29.

The estimate of the standard deviation of the process, sp, used to establish the
control limits may be used to calculate confidence intervals for all pertinent
measurements made while the system is in control. However, see SOP 29 for
calculation of measurement uncertainty using the process variability, s,. The
value of the test weight is said to be within the limits

ytU
where y represents the mean of the measurements on the test weight and

U=k*Jju2 +52 +12, , with the value of k determined by the confidence level
required for the interval.

Note:. For n 230, k > z.

Page 5 of 5


U, = degrees of freedom for numerator

Table 9.5 Critical values for the F-Test, Fo.99
UD, = degrees of freedom for denominator

December 2003

v .
1 2 3 4 5 6 7 8 9 10
v2

10 10.04 7.56 6.55 5.99 5.64 5.39 35.20 5.06 4.94 4.85
ll 9.65 721 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 439 4.30
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10
14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94
15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80
16 8.53 6.23 5.29 4T7 4.44 4.20 4.03 3.89 3.78 3.69
17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51
19 8.18 5.93 5.01 4.50 417 3.94 3.77 3.63 3.52 3.43
~ 20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37
22 7.95 5.72 4.82 431 3.99 3.76 3.59 3.45 3.35 3.26
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17
26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09
28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98
35 742 5.27 4.40 3.91 3.59 3.37 3.20 3.07 2.96 2.88
40 731 5.18 431 3.83 3.51 3.29 3.12 2.99 2.89 2.80
45 7.23 5.11 4.25 3.77 3.45 3.23 3.07 2.94 2.83 2.74
50 TAT 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.78 2.70
55 712 5.01 4.16 3.68 3.37 3.15 2.98 2.85 2.75 2.66
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63
65 7.04 4.95 4.10 3.62 3.31 3.09 2.93 2.80 2.69 2.61
70 7.01 4.92 4.07 3.60 3.29 3.07 2.91 2.78 2.67 2.59
78 6.99 4.90 4.05 3.58 3.27 3.05 2.89 2.76 2.65 2.57
80 6.96 4.88 4.04 3.56 3.25 3.04 2.87 2.74 2.64 2.55
85 6.94 4.86 4.02 3.55 3.24 3.02 2.86 2.73 2.62 2.54
90 6.93 4.85 4.01 3.53 3.23 3.01 2.84 2.72 2.61 2.52
95 6.91 4.84 3.99 3.52 3.22 3.00 2.83 2.70 2.60 2.51
100 6.90 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.59 2.50
105 6.88 4.81 3.97 3.50 3.20 2.98 2.81 2.69 2.58 2.49
110 6.87 4.80 3.96 3.49 3.19 2.97 2.81 2.68 2.57 2.49
115 6.86 4.79 3.96 3.49 3.18 2.96 2.80 2.67 2.57 2.48
120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47
ca 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 2.32

For use for a one-tailed test of equality of standard deviation estimate at 2.5 % level of confidence, or for a
two-tailed test at 2 % level of confidence.

Reference Tables

Page 6 of 13



March 2003

SOP 1

Recommended Standard Operations Procedures
for
Preparation of Test/Calibration Reports

1. Introduction

1.1.

1.2.

1.3.

Test/calibration reports are the visible outputs of the testing laboratory. They should be
prepared with utmost care to ensure that they accurately convey all information
pertaining to the testing so that reports may be used with maximum benefit by all
concerned. Carefully prepared test reports will contain or refer to all information
necessary to justify the test results.

The test report may consist of filling in the blanks in a form in the case of a routine
measurement. A more detailed report, including narrative information, may be required
for special calibrations or tests.

Regardless of the final form, the test report must contain the basic information
described in the following sections.

2. Content

2.1.

2.2.

2.3.

2.4.

2.5.

2.6.

2.7.

SOP 1

Title (e.g., “Test Report” or “Report of Calibration”).
Name and address of the laboratory, or location at which tests were performed.

Unique identification of the test report or calibration certificate, and on each page an
identification in order to ensure that the page is recognized as part of the test report or
calibration certificate, and a clear identification of the end of the report or certificate.

Name and address of the client.

Method used — Describe how test was made by reference to SOP(s). In the absence of
SOP’s, brief but informative descriptions of the methodology should be included.
Information describing deviations from previously agreed upon procedure must also be
included.

Description of, the condition of, and unambiguous identification of the item calibrated.
A laboratory number should be assigned and attached to each test item at the time of its
acceptance for testing. The use of the laboratory number will facilitate the internal
control of test items during the testing process.

Date of receipt of calibration item where this is critical to the validity and application of
the results, and the date of performance of calibration.

Page | of 6


SOP7

December 2003

3.2.5.1. Apparent mass versus brass
Ms 7 nm
AM = Sl

x vs brass 1 - Pr )
8.3909

Measurement Assurance

4.1. Duplicate the process with a suitable check standard (See GLP 1, SOP 9, SOP 30,
and Sec. 7.4)

4.2. Plot the check standard value and verify that it is within established limits; a t-test
may be incorporated to check observed value against accepted value.

4.3. The mean of the check standard is used to evaluate bias and drift over time.

4.4. Check standard observations are used to calculate the standard deviation of the
measurement process, sp.

Assignment of Uncertainty

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of
the mass standards used, us, estimates of the standard deviation of the measurement
process, sp, and estimates of the effect of other components associated with this
procedure, u,. These estimates should be combined using the root-sum-squared method
(RSS), and the expanded uncertainty, U, reported with a coverage factor of two (k=2), to
give us an approximate 95 % level of confidence. See SOP 29 for the complete standard
operating procedure for calculating the uncertainty.

5.1.

5.2.

5.3.

5.4.

The expanded uncertainty for the standard, U, is obtained from the calibration
report. The combined standard uncertainty, u., is used and not the expanded
uncertainty, U, therefore the reported uncertainty for the standard will usually
need to be divided by the coverage factor k.

The value for sp is obtained from the control chart data for check standards using
single substitution measurements. (See SOP No. 9.)

Other standard uncertainties usually included at this calibration level include
uncertainties associated with calculation of air density and standard uncertainties
associated with the density of the standards used.

Evaluation of compliance. The expanded uncertainty, U, must be < 1/3 of the
tolerance applicable as per ASTM E 617-97 and OIML R 111 if compliance
statements are used

Page 9 of 15


March 2003

The error in M, incurred by ignoring the buoyancy correction is p, (V; - V3). To
estimate quickly whether such an error is of consequence in a_ particular
measurement, (assume py = 1.2 x 10 3 g/cm’).

If the mass and volumes of the standards have been adjusted to a conventional mass
scale, then

cM, [: - 2) + sensitivity AM ,,,
Mix Ps @)

[|
Px

Table A-6. Variables not previously defined
Variable Description

CM, conventional mass of the standard
The symbol ~ signifies an approximation

8.4 Ifa single-pan balance with built-in weights is used, it is probable that the built-in
weights have been adjusted on an apparent mass or conventional mass scale’.
Determine which apparent mass scale has been used and calculate the mass of the
unknown from the equation

al _ a + sensitivity M,,

Pp

M, » (6)
[ - -
Px
Table A-7. Variables not previously defined
Variable Description
Mp mass indicated by dial or digital readings
Mopt mass indicated on the optical scale when present

If the balance has been used only as a comparator, that is, to compare the mass of the
unknown object with that of some external standard, then:

Schoonover, R. M. and Jones, F. E., "Air Buoyancy in High-Accuracy Weighing on Analytical Balances," Anal.
Chem., 53, 1981, p. 900.

Appendix SOP 2 Page 13 of 22


March 2003

Comparison Weighing - Electronic Balance

Measurements made on a full electronic balance are simplified because there are no built-in
weights to consider. Although many electronic balances are equipped with a built-in calibration
weight, the weight is not involved in the comparison weighing.

The principles for comparison weighing on a full electronic balance are the same as when using a
single pan mechanical balance. The balance indications are used to measure the mass difference
between the standard and the unknown, and a sensitivity weight is used to establish the mass
value for a digital division on the balance. Since there are no built-in weights in the full
electronic balance, the entire range of the digital indications can be considered for "optical scale"
of the balance.

For comparison weighing the standard and the unknown should be "nearly the same mass."
Since a full electronic balance has a much larger range for indicating mass values, the masses do
not have to be as close together as when a mechanical balance is being used. When using an
electronic balance, the difference in mass between the standard and unknown should be less than
0.05 % of the balance capacity. Tare weights that are known standards should be used if the
masses are not sufficiently close together. The sensitivity weight used to determine the mass per
digital division should have a mass that is at least 10 to 20 times the mass difference between the
standard and the unknown but not exceeding 1 % of the balance capacity. For high precision
weighing, air buoyancy corrections must be made for all objects used in the intercomparison.

Magnetic and Electrostatic Fields

Care must be taken when weighing magnets or objects having electrostatic charges. A magnetic
field will likely affect results of a mass measurement. A magnet is attracted to ferromagnetic
materials in the balance and balance chamber. The magnetic field may also affect the magnetic
field generated in an electronic balance that utilizes the principle of magnetic force restoration as
its method of measurement.

Weights made of ferromagnetic material can become magnetized during manufacture or during
use if they are placed in a strong magnetic field. Magnetized weights can result in measurement
errors that may go undetected. If a measurement problem is suspected, the weights should be
checked for magnetism and may have to be rejected if excessively magnetized.

If magnets or magnetized material must be weighed, the material should be placed in a
magnetically shielded container to prevent the magnetic field from generating measurement
errors. If balance design and conditions permit, an alternative is to position the magnetized
material a relatively large distance from the balance pan using a non-ferromagnetic object on the
pan to serve as a platform for the magnetic. Since the strength of the magnetic field drops off at
arate of the cube of the distance from the magnetic, it may be possible to effectively isolate the
magnet from other ferromagnetic material in the balance.

GMP 10 Page 5 of 6


December 2003

3.2.4. Calculate the conventional mass? of X, CM,. It is recommended that the
conventional mass be reported.

3.2.4.1. Conventional mass

M, [) - ee)
CM, = —~—24
(35)
8.0
3.2.5. If requested, the apparent mass versus the reference density of brass may

be calculated. This value should only be used when calibrating
mechanical balances that have been adjusted to this reference density.

3.2.5.1. Apparent mass versus brass

u, [1-4]
—\ Px J

AM 5 55 brass =
[ 7 2 }
8.3909

4, Measurement Assurance

4.1. Duplicate the process with a suitable check standard (See GLP 1, SOP 9, SOP 30,
and Sec. 7.4)

4.2. Plot the check standard value and verify that it is within established limits; a t-test
may be incorporated to check observed value against accepted value.

4.3. The mean of the check standard is used to evaluate bias and drift over time.

4.4. Check standard observations are used to calculate the standard deviation of the
measurement process, Sp.

5. Assignment of Uncertainty

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of
the mass standards used, u;, estimates of the standard deviation of the measurement
process, sp, and estimates of the effect of other components associated with this
procedure, u%, These estimates should be combined using the root-sum-squared method

2 Conventional Mass: “The conventional value of the result of weighing a body in air is equal to the mass of a
standard, of conventionally chosen density, at a conventionally chosen temperature, which balances this body at this
reference temperature in air of conventionally chosen density.” The conventions are: reference density 8.0 g/cm’;
reference temperature 20 °C; normal air density 0.0012 g/cm3. Conventional mass was formerly called “Apparent
Mass versus 8.0 g/cm” in the United States. See OIML IR 33 (1973, 1979), under revision.

SOP 4 Page 9 of 18




March 2003

M, = M, + p,(V, -V,) + sensitivity AM’,
Table A-8. Variable not previously defined
Variable Description

difference in optical scale reading between observations of the
standard and the unknown

AM ‘opt

For some balances, operation requires that the user restore the balance to null by
means of a manually controlled dial. The portion of the mass reading controlled by
this dial should be treated, for purposes of buoyancy corrections, as an optical scale.

8.5 Ifa single-pan balance with full-range electronic control is used, the following should
be noted. As part of its calibration, the electronic gain has been adjusted by means of
a weight of known mass. For example, if the range of electronic control is 100 g, the
electronics have been adjusted so that a 100-g standard weight produces an indication
of precisely 100 g. This procedure effectively builds an apparent mass calibration
into the balance. The reference density of the apparent mass scale is the density of
the standard mass used for the calibration and the reference air density is the air
density at the time of calibration.

The mass of an unknown object weighed on the balance is then

H(r-8
M, = Pe ©

(3
Px

Table A-9. Variables not previously defined

Variable Description
Mp readout displayed on the balance
La density of air at the time of balance calibration
density of the standard used to calibrate the balance (or pg if the
Pe apparent [conventional] mass of the standard was used instead of the
true mass

If the balance includes both an electronic control system and built-in weights, the
buoyancy considerations for the built-in weights are as described in section 8.2 and
the considerations for the electronically determined mass are those given directly
above.

8.6 Top-loading balances may be considered a form of single-pan balance and the
appropriate procedure for buoyancy correction followed.

Appendix SOP 2 Page 14 of 22


March 2003

Answer:

Using (7), the error is approximately

I 1

15 ¢(0.2x10° g/cm’ )|) ————- - ——___.
a( * grem i 7.78 gicm’ 8.0 g/cm?

)= 14

This discrepancy, though larger than the precision of the best analytical balances, is actually well
within the tolerance of Class 1 weights.

Appendix SOP 2 Page 20 of 22


This page is blank.

iv


December 2003

3.2.2.2. Optional Sequence B (XSS)

3.2.3. Calculate the mass correction C,, as follows:

Cy = My - Nx

where N, is the nominal value for X.

3.2.4. Calculate the conventional mass? of X, CM,. It is recommended that the
conventional mass be reported.

3.2.4.1. Conventional mass

(3)
8.0
3.2.5. If requested, the apparent mass versus the reference density of brass may

be calculated. This value should only be used when calibrating
mechanical balances that have been adjusted to this reference density.

2 Conventional Mass: “The conventional value of the result of weighing a body in air is equal to the mass of a
standard, of conventionally chosen density, at a conventionally chosen temperature, which balances this body at this
reference temperature in air of conventionally chosen density.” The conventions are: reference density 8.0 g/cm’;
reference temperature 20 °C; normal air density 0.0012 g/cem3. Conventional mass was formerly called “Apparent
Mass versus 8.0 g/emTM in the United States. See OIML IR 33 (1973, 1979), under revision.

SOP 7 Page 8 of 15


March 2003

Calculate the sensitivity:

0.010003 g - (0.00370 )(1.172 x10" )

tivity =
sensitivity 103
sensitivity = (0.009999) = 0.000 971 g/division = 0.971 mg/division
vy, ~ {13.000172 ~ (1.647 )(1.172 x10 )] + [(0.971.x10% )(- 3.5)]
. _ 1.172.x10°
2.3291

M, = 13.001 385 g¢

Note that the thermal expansion is insignificant in this example.

Example 2:

Let us again consider the weighing performed in Example 1. This time, all we know about our
weight set is that it has been adjusted to the 8.4 apparent mass scale at the best available

commercial tolerance.

Using Eq. (4),
5 ,
Ec - ume" | + [oor - mae” ) | 33)
8.3909 8.3909 103
M, =
1 — L172 x10"
2.3291

M,= 13.001 329 g

For routine weighing, it is sometimes satisfactory to assume that the temperature is 20 °C and the
density of air is 1.2 x 103 g/cm’, Had this been done, the computed value for the silicon would

be
a ayy.
13.00{ 1 - 22220" )) 4] oo1ol 1 - E2220" 35)
8.3909 8.3909 J |\ 103
M, =
) _ 12x07
2.3291

My = 13.001 442 g

Appendix SOP 2 Page 18 of 22


SOP 7

2.5. Procedure

December 2003

2.5.1. Preliminary Procedure

2.5.1.1.

2.5.1.2.

Place the test weight and standards in the balance chamber or
near the balance overnight to permit the weights and the balance
to attain thermal equilibrium.

Conduct preliminary measurements to obtain an approximate
value for the difference between the standard and the unknown,
to determine where the readings occur on the balance, to
determine if tare weights are required, to determine the
sensitivity weight that must be used, and to determine the time
interval required for the balance indication to stabilize.

Tare weights are rarely needed for high precision mass
standards. If tare weights are required, carry tare weights, t, and
t,, with the standard and the unknown, S and_X, respectively.
The tare weights must be calibrated standards with valid
uncertainties that are evaluated in the process of determining
calibration uncertainties. The standard and its tare weight, S + t,,
should be "nearly the same mass" as the unknown with its tare
weight, X + t,. "Nearly the same mass" depends upon the
balance used (See GMP 14, Table 1). Select ¢, and ¢, such that
the difference in mass between S + t, and X + t, is:

a. Single-pan mechanical balance - less than = the range of

the optical scale.

b. Full electronic balance - less than 0.05 % of the balance
capacity.

c. Combination balance - less than = the range of the digital
indications.

A sensitivity weight must be used on equal-arm balances, and is
normally used on single-pan mechanical and_ electronic
balances, to ensure that the differences determined through the
use of the optical scale or electronic range have valid accuracy
and traceability. (e.g., The optical scale is calibrated each time
the procedure is used through the use of a sensitivity weight).
The uncertainty of the sensitivity weight does not need to be
included in calculations of uncertainty since the uncertainty
value is distributed across the range of use.

Page 4 of 15


December 2003

measurements. Investigate possible causes of excess variability
if measurements do not agree within these limits.

2.5.2.6. If repeated double substitutions are performed, the values
between successive trials should not differ from one another by
more than + 2 standard deviations of the balance for this process
and load. If this difference is exceeded, reject the data and take
a new series of measurements that do so agree.

2.5.3. Measurement Procedure, Optional Sequence B (XSSX)

Table 4. Optional Sequence B
Measurement No. | Weights on Pan Observation
1 X+h Or
2 S+s O2
3 Stt.+sw O3
4 X+t+ sw On

Measurements for Option B are made as described in Option A except that X, S,
t,, and f, are interchanged.

3. Calculations

3.1. No air buoyancy correction. Calculate the conventional mass correction, C,, for
the test weight as follows, according to the optional sequence used. In each case,
the conventional mass corrections for the standard weight(s), C,, the conventional
mass of the tare weights,CM, andCM, , and the conventional mass of the

sensitivity weight, CM,,, are included. The symbols N, and N, refer to the
nominal values of S and_X, respectively. If no tare weights, and equal nominal
values are used, those terms may all be deleted from the equations.

3.1.1. Optional Sequence A (SXXS)

C,=C,+CM, - CM, [82 Lene.)) Ms bn -N,
; . 2 0,- 0,

SOP 4 Page 7 of 18


December 2003

Table 9.7 Factors for Computing Two-sided Confidence Limits for a (Part 2)

Degrees of

Freedom a =0.05 a= 0.01 a= 0,001
Sv Si Su SL Su SL
26 1.351 0.7783 1.504 0.7253 1.719 0.7130
27 1.343 0.7817 1.491 0.7293 1.698 0.6758
28 1.335 0.7849 1.479 0.7331 1.679 0.6800
29 1.327 0.7880 1.467 0.7367 1.661 0.6841
30 1,321 0.7909 1.457 0.7401 1.645 0.6880
31 1,314 0.7937 1.447 0.7434 1.629 0.6917
32 1.308 0.7964 1.437 0.7467 1.615 0.6953
33 1,302 0.7990 1.428 0.7497 1.601 0.6987
34 1.296 0.8015 1.420 0.7526 1,588 0.7020
35 1.291 0.8089 1.412 0.7554 1.576 0.7052
36 1.286 0.8062 1.404 0.7582 1.564 0.7083
37 1.281 0.8085 1.397 0.7608 1.553 0.7113
38 1.277 0.8106 1,390 0.7633 1.543 0.7141
39 1.272 0.8126 1.383 0.7658 1.533 0.7169
40 1.268 0.8146 1.377 0.7681 1,523 0.7197
4) 1.264 0.8166 1.371 0.7705 1.515 0.7223
42 1.260 0.8184 1.365 0.7727 1,506 0.7248
43 1.257 0.8202 1.360 0.7748 1.498 0.7273
44 1.253 0.8220 1.355 0.7769 1.490 0.7297
45 1.249 0.8237 1,349 0.7789 1.482 0.7320
46 1.246 0.8253 1.345 0.7809 1.475 0.7342
47 1.243 0.8269 1.340 0.7828 1.468 0.7364
48 1,240 0.8285 1.335 0.7847 1.462 0.7386
49 1.237 0.8300 1.331 0.7864 1.455 0.7407
50 1.234 0.8314 1.327 0.7882 1.449 0.7427

From: NBS Handbook 91, p. T-34

Reference Tables

Page 9 of 13



December 2003

Table 9.10 Density and Coefficient of Expansion

Material Density Coefficient of Expansion
g/em? Linear (/°C) Cubical (/°C) Cubical (/°F)
0.000 038
Aluminum 2.7 0.000 024 0.000 069 (not suitable for
provers)
8.4 at0°C
Brass 8.390 9 at 20 °C 0.000 019 0.000 054
Cast iron 1 0.000 010 0.000 030
Copper 0.000 017 0.000 050
Diamond 0.000 001 18 0.000 003 5
Fused silica (quartz) 0.000 000 5 0.000 001 6
Glass, borosilicate (T1CA) 0.000 010
Glass, borosilicate (T1CB) 0.000 015
Glass, soda-lime 0.000 025
Gold 18.0 0.000 043
Invar 0.000 000 4 0.000 001 2
Lead 11.34 0.000 029 0.000 087
Length bench 0.000 010 6
Mercury 0.000 018
Nichrome 8.39 0.000 039
Nichrome V 8.5 0.000 039
Platinum 0.000 011 0.000 027
Polycarbonate plastic 0.000 45
Polypropylene plastic 0.000 24
Polystyrene plastic 0.000 21
Steel, stainless (mass) 7.84, 7.95, 8.0 0.000 045
Steel, stainless (provers) 0.000 018 0.000 047 7 0.000 026 5
Steel, tape, mild 0.000 0116 0.000 033 5
Steth pressure vessel, low 0.000 016
Steel, prover, low carbon 0.000 012 0.000 033 5 0.000 018 6
Steel, terne plate 0.000 012 0.000 035 0.000 019 5
Tantalum 16.6 0.000 020
Water (20 °C) 0.000 21

Reference values for cubical coefficient of expansion given in per °F are provided as reference for prover calibrations
used for petroleum products where the reference temperature is 60 °F.

Reference Tables

Page 12 of 13



March 2003

APPENDIX A - Sample Format

Recommended Format for Report of Test

Report of Test
Issued by
Name of Testing Laboratory
Laboratory Report No.
Test Item(s)/Lab No(s):
Submitted by:
Date:
Purpose of Test:
Test Results*:
As Found After Adjustment

Reference Information:

Test Method:

Traceability:

Uncertainty Statement:

Conditions of Test:

Data
Reference:

Test Results Approved by (name, title, date):

*Report, as appropriate

The results stated on this report relate only to the items specifically identified.
This test report or calibration certificate shall not be reproduced except in full, without written approval of the laboratory.

SOP 1 Page 3 of 6


Standard Operating Procedures


March 2003

GLP 11

Good Laboratory Practice
for
Painting Cast Iron Weights

Large cast iron or steel weights should be painted both for their protection and to preserve their
mass integrity. Unprotected weights are subject to corrosion. Furthermore, when corrosion is
present, the extent and any changes resulting from it may be difficult to estimate.

Thin even coats of aluminum paint are recommended for this purpose. Spray applications are
best if large weights or a number of small weights are to be painted. In preparation for painting,
a weight should be cleaned and loose scale should be removed using a wire brush (DO NOT
remove old paint and corrosion by means of sand blasting or pressure washing. Severe damage
may result.). The painting should be done before the weights are calibrated or tolerance tested,
unless arrangements are made to obtain "as found" values. If “as found” values are desired, two
tests may be required.

Painting should be done in an area reserved for this purpose, or at least in a place which is
removed from laboratory measurement operations. Painting operations must be in compliance
with applicable safety standards. The weights should be protected from dust or dirt
contamination while the coating is drying.

GLP 11 Page | of 1


GMP 13

Volume - Option B

NIST
Volume Group
Volume Standards Volume Standards
5 gal, 25 gal, Glassware
100 gal Standards
Client Volume Client Volume

Transfer Transfer
Calibration Calibration

Workload Workload
(5 gal or larger) (Glassware)

Page 8 of 11

March 2003




March 2003

Appendix B
Examples

Example 1:
The weight set of Table B-1 is used with an equal-arm balance to find the mass of a piece of
single-crystal silicon. The following weights were used to balance the silicon: 10 g, 3 g. The
balance pointer showed the silicon side to be light by 3.5 divisions. The 10 mg weight of Table 1
was used to find the sensitivity of the balance. When the weight was added, the pointer moved
10.3 divisions. At the time of the weighing, the following measurements were taken:
P = 748.1 mm Hg
t=223 TC
U = 37 % relative humidity
What is the mass of the silicon?

Answer:

From Eq. 1, or Table B-2, calculate

5315.56

e, = 1.3146x10° x las) = 20.194 mm Hg

__ | 0.464 60[ 748.1 — (0.003 796 0 )( 37 )( 20.2 ) ] 10?
Po (273.15 + 22.3)

Pa = 1.171 94x 10? g/om?

The density of silicon at 20 °C is 2.329 1 g/cm? and its coefficient of linear expansion is
0.000 002 6 /°C.

Make use of Eq. 3c and Table B-1.

M, = 10.0001264 + 3.0000459 = 13.000172g

V, = (1.267 + 0.380 ) = 1.647cm*

Appendix SOP 2 Page 17 of 22


SOP 29

3.2.5.1.

3.2.5.2.

March 2003

Identifying cause.

If the cause can be identified, it is usually corrected or applied to the
measurement equation. In some cases, it is not possible to unarguably
define the cause without exhaustive studies that provide little benefit. In
those cases, the significance level must be evaluated.

Significance level.

When there is little to be gained from exhaustive studies on the
measurement process to identify bias or potential errors, a test of
significance may be conducted to determine alternative approaches for
incorporating the bias into the uncertainty calculations.

In deciding whether a known bias can reasonably be included in the
uncertainty, the following approach may be followed:

3.2.5.2.1. Estimate the combined uncertainty without considering the
relevant bias.

3.2.5.2.2. Evaluate whether or not the bias is less than two times the

combined uncertainty (i.e., bias <2,u2+s,+u2 ).

3.2.5.2.3. Ifthe bias is less than twice the combined uncertainty, it may
be included in the uncertainty using one of several
approaches that must clearly be communicated in the report.

3.2.5.2.4. If the bias is larger than twice the combined uncertainty, the
error must be investigated further prior to providing
calibration data.

If the deviations show that a standard is out of control, it
should not be used for calibration until corrective action has
been taken and the value for the standard is verified as being
within criteria limits.

criteria limit | Xap ~ Xref | <2u,

If these differences are smaller than the criteria limits,
investigation and corrective action may be unrealistic. If the
deviations are less than the surveillance limits shown above,
and corrective action is not taken, the deviations may be
included in the uncertainty statement following one of

Page 5 of 11


4.

SOP 9

3.4.

December 2003

3.3.3. Upgrading Contro! Chart Parameters

Upgrade control chart parameters when a significant amount of additional
data is available or when the previously determined parameters are no longer
pertinent due to changes in the system.

Note: Ordinarily, upgrading is merited when the amount of new data is equal
to that already used to establish the parameters in use, or when at least seven
additional data points have been recorded.

Calculate x and s for the new set of data and examine for significant
differences from the former using the t-test and F-test, respectively. If the
tests fail and results are significantly different, determine the reason for the
difference, if possible, and decide whether corrective action is required. If
data does not agree within statistical limits, establish new parameters using
the most recent data and note the reasons for not using previous data. If no
significant differences between the data sets are found, pool all data and
calculate new control chart parameters based on all existing data.

Frequency of Measurement

The check standard should be measured and plotted with sufficient frequency to
minimize the risk of loss of data during the period from last-known-in to first-
known-out of control condition. It is good practice to measure the check standard at
least once during each period when a set of test measurements is made. For critical
calibrations or those of highest accuracy, it is desirable to alternate measurements of
test items and check standards, but for real-time evaluation it is preferable to
incorporate the check standard in the calibration design as in SOP 5 or SOP 28.

Whenever there has been a long period of inactivity, it is good practice to make a
series of measurements of the check standard and to plot the results on a control chart
to demonstrate attainment of statistical control prior to resuming measurements with
that specific calibration system.

Control charts should be updated as close to real time as feasible to effectively
monitor the measurement process to prevent the possible release of questionable data
resulting in recall.

Use of Control Charts

4.1.

Monitoring a Measurement Process
Use the following criteria to interpret control chart results.

4.1.1. If plotted points are stable and randomly distributed within the warning
limits, decide that the system is in control.

Page 4 of 5


December 2003

SECTION 3. PHYSICAL STANDARDS. -- Weights and measures that
are traceable to the U. S. prototype standards supplied by the Federal
Government, or approved as being satisfactory by the National Institute of
Standards and Technology, shall be the State primary standards of weights
and measures, and shall be maintained in such calibration as prescribed by
the National Institute of Standards and Technology. All secondary
standards may be prescribed by the director and shall be verified upon
their initial receipt and as often thereafter as deemed necessary by the
director.

SECTION 12. POWERS AND DUTIES OF THE DIRECTOR. -- The
director shall:

12 (a) Maintain traceability of the State standards to the National Institute
of Standards and Technology, as evidenced by laboratory Recognition.

The approach described above is recommended by NIST because each State that participates in
the Weights and Measures Division Laboratory Recognition Program has the capability of
evaluating its own State standards with the necessary documentation referencing the national
standards. The Laboratory Recognition Program provides interaction between the State standards
laboratories and NIST, ensuring satisfactory laboratory conditions suitable for primary standards
in addition to the proper use of NIST procedures in standards calibration. Thus, each State
program is evaluated and, if found in compliance, is Recognized as being capable of performing
the measurements listed on the Certificate of Measurement Traceability.

GLP 4

Page 2 of 2




GMP 14

March 2003

Where M,y represents the mass of the sensitivity weight.

Calculations

No special calculations are associated with this practice. See each mass SOP for
calculation of sensitivity within the procedure.

Uncertainty

No uncertainty calculations are associated with this practice. See the appropriate SOP
for the calculations of uncertainty. (The uncertainty of the sensitivity weight does not
need to be included in calculations of uncertainty since the uncertainty value is

distributed across the range of use. However, it does no harm to incorporate it in
uncertainty calculations when spreadsheets are set up to handle all of the data.)

Page 4 of 4


IR 6969 Revisions

Table 9.11
NBS replaced NIST in the reference because this reference was originally published by NBS.

Page 3 of 3


Reference Tables

Table 9.2 Z-Factors for Two-sided Confidence Intervals
for the Normal Distribution

* Confidence Level, % Z Factor
50 0.68
67 1.00
15 1.15
90 1.645
95 1.960
95.28 2.000
99.00 2.575
99.74 3
99.993 4 4
99.999 95 5
100 - 10° 6
100 - 10°? 7
100 - 10°'* 8
100 - 108° 9
100 - 10° 10

Page 3 of 13

December 2003


December 2003

8.2 Estimation of Standard Deviation from the Differences
of k Sets of Duplicate Measurements

Given k differences of duplicate measurements, di, do, d3, ..., dk, a useful formula for estimating
the standard deviation is:

Ld

Sq = where sq is based on k degrees of freedom.

Note that d, = x; — x;’, for example.

i

The values dj, dp etc., may be differences of duplicate measurements of the same sample (or
object) at various times, or they may be the differences of duplicate measurements of several
similar samples (or objects).

8.3 Estimation of Standard Deviation from the Average
Range of Several Sets of Measurements

The range, R, is defined as the difference between the largest and smallest values in a set of
measurements.

Given Ry, Ro, Rs, -.., Rk

(R, +R, +R, +..+R,)

Mean, R=
k

pl

Standard deviation can be estimated by the formula, s, =

a

The value of d} will depend on the number of sets of measurements used to calculate s, ‘g» and on
the number of measurements in each set, i.e., 2 for duplicates, 3 for triplicates, etc. Consult a
table such as Table 9.1 for the appropriate value of d) to use. The effective number of degrees
of freedom for s, is in the table.

8.4 Pooling Estimates of Standard Deviations
Estimates of the standard deviation obtained at several times may be combined (pooled) to

obtain a better estimate based upon more degrees of freedom. The following equation may be
used for this purpose:

5 Ee te =i +...+ (my =I) 55

where

(n, -1)+(@, —1) + ( -1)+...+(%, =)

s, will be based on (n, -1)+(n, -1)+(1, -1)4... + (ny —1) degrees of freedom.

Statistical Techniques Page 2 of 10


March 2003

Table A-1. Variables for conventional (apparent) mass equation

Variable Description
PN density of the object N at 20 °C in g/cm?
density of the conventional (apparent) mass scale at
id 20 °C in g/em?

There are at present two apparent mass scales in wide use. The older is based on
px = 8.4000 g/cm’ at 0 °C with a coefficient of volumetric expansion of 0.000054/ °C
and the more recent (Conventional Mass) specifies g = 8.0000 g/cm? at 20 °C. The
quantity My,4 is a function of the particular conventional or apparent mass scale,
which has been used in its calculation. OIML IR 33 only recognizes Conventional

Mass.

5.4. Sensitivity

The response of a balance under load to an additional small weight:

sensitivity =

M,,) 1- 22
Moy = PaVow _ Pow

AR AR

Table A-2. Variables for sensitivity equation

Variable Description
Sensitivity balance sensitivity (mass per division)
Mow mass of the small, additional weight
Pa density of the air

Pow density of the small, additional weight

Vow volume of the small, additional weight
change in balance reading due to the addition of the small weight,

AR :
balance deflection

6. Apparatus

In order to ascertain the density of air at the balance, the following measuring instruments
are necessary: thermometer, barometer, and hygrometer. Ideally, these instruments should
be placed in or next to the balance case (as near the measurement location as is practical).
It may only be practical for the thermometer or temperature sensor to actually be placed
inside the balance chamber. A calculator or computer will be extremely useful for this

procedure.

Appendix SOP 2

Page 9 of 22


March 2003

Comparison Weighing - Mechanical Balance

For mass calibrations, the unknown object must be compared to a known mass standard.
Comparison weighing eliminates the errors of the built-in weights, reduces disturbances during
the measurement because dial settings are not changed during the measurement, and can cancel
the effect of drift by selecting the appropriate weighing design. Comparing the unknown, X, to a
standard, S, eliminates the built-in weights from the measurement: thus, the built-in weights act
only as counterweights; they do not affect the difference measured between X and S.
Consequently, the dial settings must not be changed during a comparison measurement;
otherwise the built-in weights would be part of the measurement.

When comparison measurements are made on a single pan mechanical balance, all readings are
taken from the optical scale. The unknown and the standard must have nearly the same mass so
that the difference between them can be measured on the optical scale. If the masses of the
unknown and the standard are significantly different, small mass standards are used as tare
weights with either the unknown or the reference standard or both to obtain an observed mass
difference that is significantly less than one-fourth the range of the optical scale.

As part of a comparison measurement, the mass value of a scale division is determined by
performing a sensitivity determination. The small mass standard used as part of the weighing
design to calibrate the optical scale is called the sensitivity weight and should have a mass
between 1/5 and 1/2 the range of the optical scale, inclusive. Additionally, the mass of the
sensitivity weight should have a mass that is at least twice the observed mass difference between
the standard and the unknown. Since the maximum size of the sensitivity is limited to one-half
the range of the optical scale, it may be necessary to carry tare weights with the standard and the
unknown to ensure that the observed difference between them is less than one-half the mass of
the sensitivity weight. The value of the sensitivity weight should include the correction plus its
nominal value. For high precision calibrations, the inclusion of the air buoyancy correction for
the sensitivity weight is critical. See GMP 14 for detailed guidance on the selection of sensitivity
weights.

The first readings for the standard and the unknown in a comparison on a single pan balance
should fall in the first quarter of the optical scale, but well ahead of zero, so the balance drift will
not result in negative values for any readings. Although negative numbers may be used in
calculations, they are avoided to simplify calculations and reduce calculation errors. Because the
sensitivity weight may have a mass as large as one-half the range of the optical scale and the
measured difference between the standard and the unknown may be as large as one-fourth the
range of the optical scale, it is necessary to obtain the first two readings in the first quarter of the
optical scale so all readings will remain on-scale for the measurement. In this way it is not
necessary to change the dial settings to measure the difference between the standard and the
unknown.

GMP 10 Page 4 of 6


March 2003

Appendix A
Based on “The Basic Theory of Air Buoyancy Corrections”
by Richard S. Davis*
1. Introduction

In performing measurements of mass, the balance or scale used acts as a force transducer.
The force produced by an object to be weighed in air has two components: one
proportional to the mass of the object, and the other proportional to its volume. The latter
component, or buoyant force, may under some circumstances be large enough to require
correction. The following shows under what circumstances buoyancy corrections are
required as well as how they are made.

2. Scope
The method for applying buoyancy corrections presented below applies to mass
measurements made in air. The density of air is computed from auxiliary measurements of
temperature, pressure and relative humidity after which the buoyancy corrections are
calculated directly from the Principle of Archimedes. The following weighing situations
are considered.
2.1. Two-Pan Balance
2.2. Single-Pan Balance
2.2.1. With Built-In Weights
2.2.2. With Electronic Control
3. Summary of Method
In general, buoyancy corrections are applied to mass measurements by calculating the
difference in volume between the unknown weight and the standard, multiplying this
volume difference by the density of air at the balance or scale, and adding the product to
the mass of the standard. The density of air is computed from an equation of state using
measured values for the temperature, pressure and relative humidity of the air.

4. — Significance and Use

Buoyancy corrections generally must be applied when determining the mass of an unknown
object to high accuracy. The corrections may become important even at modest accuracies

3Richard S. Davis, formerly of the National Institute of Standards and Technology, Mass Group.

Appendix SOP 2 Page 7 of 22


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suonenongy amssord - || aur rou op sanqes st ALON yup - i “AngDIS =
4 ° . el SuBMYos - : Mt .
ea OL sweuns ne 7 suostreduoo Aroyer0qef19qUN swystom aie ot
sprepucys sonpea.yooapuey, le no [eusotn = uo poalosgo sorouedaxosip- | | 98 ‘AyuwaUn] ‘uorwIqleD uowsuedxo youwoup -
‘Aaiqionpordes Auprumy ‘sinssoad “oanyezaduroy som nodes mone ia " &ysuap -
SuIMOYS BVEp UIqoL punoY - ‘10y Ajurepaoun uaurdinbo - pang wroongg (uiodos uoryeaqiyeo) yuresos -
quowomsvayy 01 parwjasuy s10yRg] JUOWIHOMAU UIA Sprepurys ou) JO YUP ~ aif JO UOHRLASP prepuels - 4 suMouyuy pue
°n “| pare1oossy Aiureraoun prepuers, Ssprepueys 94D “woNBAqHTeD YIM
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Aqurepoouy) uonesqyeD papuedxg
SSUJA] 1OJ JAVYD MOLT
Aqurezz9009)



March 2003

Test No.: TI-01-056
Page 2 of 2

uncertainty is multiplied by a coverage factor of 2 to give an expanded uncertainty, which defines an interval having a level of confidence of
approximately 95 percent. The expanded uncertainty presented in this report is consistent with the 1993 ISO Guide to the Expression of
Uncertainty in Measurement. The expanded uncertainty is not to be confused with a tolerance limit for the user during application.

The Standards of the Compliant Calibration Laboratory are traceable to the National Metrology Institute, and are part of a comprehensive
measurement assurance program for ensuring continued accuracy and measurement traceability within the level of uncertainty reported by this
laboratory. The laboratory test number identified above is the unique report number to be used in referencing measurement traceability for
artifacts identified in this report only.

Supplemental Information

Description of artifacts submitted for testing:

Twenty one metric weights from 1 kg to 10 mg, marked ASTM Class 4. Weights from 1 kg to 1 g: two-piece weights, with assumed density of
8.0 g/cm’, Weights from 500 mg to 50 mg: sheet weights, with assumed density of 16.6 g/cm’. Weights from 30 mg to 10 mg: sheet weights,
with assumed density of 2.7 g/cm’.

Conditions of artifacts submitted for testing:

Artifacts showed evidence of improper handling. Fingerprints and dents were visible on the surface of the weights.

Treatment of artifacts prior to testing:

Artifacts were cleaned with cheesecloth and ethyl alcohol. Thermal equilibrium time/conditions: ten days next to balances in mass lab.

Equipment & Standards:

Balance Range Stds Used Calibration due
AT1005 1 kg to 200 g Set H 2/31/2002
AT106 100 gto 10g Set H 2/31/2002
UMTS/6 5 gto 10mg SetH 2/31/2002

Assumed Density of Reference Standards:

Lkg tol g: 7.94 g/m’ 500 mg to 10 mg: 8.41 giem’

Procedure used:

Double Substitution (NIST HB 143, SOP 4)

Environmental conditions at time of test:

Temperature: 20.1 °C to 20.2 °C Barometric Pressure: 752.7 mmHg, Relative Humidity: 43.35 % to 43.40 %

Date artifacts were received: February 15, 2001 Date of report preparation: March 3, 2002

Date of test: February 25, 2001
Due date per customer’s request: February 25, 2002

Josh Balan IT

Test performed by: Josh Balani II
Metrology Expert
Member: ARMAP
NCSLI
NCWM
ASQ

This document does not represent or imply endorsement by the Compliant Calibration Laboratory, NMI, or any agency of the State and/or
national governments. This document may not be reproduced, except in full, without the written permission of the Compliant Calibration

isn ovtog OT

SOP 1 Page 6 of 6


Good Measurement Practices


March 2003

Parameter Test Item Recommended SOP
ASTM, OIML Class 1,2 (S, S-1) SOP 5, 3-1 Weighing Design (preferred)
Class E2 Modified SOP 4/5, to be used to incorporate
for use in balance measurement control with SOP 4
calibration
ASTM, OIML Class 0, 1 (S) Weighing Designs per TN 952, TN 844, IR
Class E1 5672, SOP 28, with appropriate check standards
for use as laboratory
standards
Volume
HB 105-2 Glass flasks SOP 16, Volume Transfer (acceptable, SOP 14
preferred)
HB 105-3 20 L test measures SOP 18, Volume Transfer (single delivery from
(5 gal or 10 gal) slicker plate type standard; if glass standards
SOP 19)
HB 105-3 Large graduated neck SOP 19, Volume Transfer for Graduated Neck
type provers - used for | Type Provers
meter verification
HB 105-4 LPG provers SOP 21, Volume Transfer for LPG Provers
HB 105-7 Dynamic Small SOP 26, Waterdraw Calibration of Dynamic
Volume Provers Small Volume Provers
Laboratory standards SOP 13, Gravimetric Calibration with a Single
Glassware: burets, Pan Mechanical Balance OR
pipetes, flasks SOP 14, Gravimetric Calibration with an
Electronic Balance
Laboratory standards SOP 14, Gravimetric Calibration with an
Laboratory slicker Electronic Balance OR
plate standards SOP 15, Gravimetric Calibration with an Equal
Arm Balance
Micropipetes SOP 13, Gravimetric Calibration with a Single
Pan Mechanical Balance OR
SOP 14, Gravimetric Calibration with an
Electronic Balance
GMP 12 Page 2 of 4



SOP 30

2.5.6.3

2.5.6.4.

December 2003

ensure detection of changes in the calibration uncertainty
statements.

Use statistical tools at specific calibration intervals to evaluate
current data performance to reference data that was
established at calibration of standards and at the service of the
measurement instrument. This evaluation will assist in
deciding when to recalibrate calibration standards and service
the measurement instrument.

Use the F test to evaluate if a significant change in (sp)
performance has occurred.
2

F test = Go tree)

(s, cout).

The current and previously established reference standard
deviations are compared and evaluated using F test table
values based on degrees of freedom in the measurements.

Use the t-test to evaluate if a significant change in
measurement process bias has occurred.

(Bias 4.) — (Bias a3)
Gp sen)” | Be a)

1 sew D og

ttest=

The current (new) and previous (old) reference bias is
compared and evaluated using t test table values based on the
degrees of freedom in the measurements.

Take action based on the results of statistical evaluation. If F
and t tests reveal no significant change in process
performance, use the current data analysis to establish new
process reference limits, control chart and uncertainty
statements (as described in 2.5.3 and 2.5.4). If the process has
a stable history, it is permissible to pool the current data with
previous reference limits to establish new reference limits,
control chart, and uncertainty statements. Continue control
measurements until the next calibration interval.

If F and t tests reveal significant change in the measurement
process, investigate the specific cause. If the cause for the
change cannot be identified and corrected, then collect new
reference data to establish new reference limits and process
uncertainties. If a specific cause is found and corrected, and
subsequent control measurements indicate an “in-control”
status, continue collecting control measurements and test

Page 8 of 9






March 2003

3.4. Step 4. Convert all factors to standard uncertainties

In those cases where the uncertainty factors were determined statistically (Type A
methods), the standard deviation is used to represent the standard uncertainty. In other
cases, estimates must be made to ensure that the quantified uncertainties represent “one-
standard-deviation” values or a k=1 coverage level. The appropriate distribution factor
must be used when converting values.

3.5. Step 5. Calculate the combined uncertainty

The combined standard uncertainty, 1, includes the standard uncertainty reported for the
standards used, u,, the standard uncertainty of the measurement process, sp, the standard
uncertainty from other sources, %, which includes all other factors the laboratory
considers significant, the standard uncertainty due to factors related to the measured item
but unrelated to the measurement process, uy, and finally, the standard uncertainty due to
bias or differences, ug, when ug is included. The standard uncertainties are combined
using the root-sum-of-the-squares (RSS) method as follows:

= 2 2 2 2 2
Uc= Sp tu, tu; +u, +,

Table 1. Symbol descriptions

Symbol Description
U Expanded uncertainty
Uc combined standard uncertainty
Sp standard uncertainty (standard deviation) of the “process”
Us standard uncertainty of the “standard”
Uo standard uncertainty of “other factors”

standard uncertainty of factors “unrelated” to the measurement

Un

process

standard uncertainty of “differences” (may be treated in different
Ud

ways)
k coverage factor

SOP 29 Page 7 of 11


SOP 4

2.5.1.3.

2.5.1.4.

December 2003

balances, to ensure that the measured differences determined
through the use of the optical scale or electronic range have
valid accuracy and traceability (See GMP 14, Table 2). (e.g.,
The optical scale is calibrated each time the procedure is
performed through the use of a sensitivity weight). The
uncertainty of the sensitivity weight does not generally need to
be included in calculations of uncertainty since the uncertainty
value is distributed across its range of use.

If a sensitivity weight will be used, select one that is:

a. Single-pan balance - between 4 and % the range of the
optical scale, and at least 4 times the mass difference
between X and S.

b. Full electronic balance - at least 4 times the mass difference
between X and S, but not exceeding 1 percent of the
balance capacity.

c. Combination balance - between 4 and 4 the range of the
digital indications, and at least 4 times the mass difference
between X and S.

d. Mass comparator — at least 4 times the mass difference
between X and S, but not exceeding 4 of the digital range.

A sensitivity weight is not required if the electronic mass
comparator that is used has been tested (with supporting
data available) to determine that the balance has sufficient
accuracy, resolution, repeatability, and stability so that no
advantage is gained through the use of a sensitivity weight.
For example, any possible errors must be less than what
contributes to the uncertainty. When a mass comparator is
used without a sensitivity weight, the sensitivity must be
periodically verified and documented.

Determine which optional sequence will be used, A or B.
Optional sequence A uses the standard on the balance for the
first and fourth observations and the unknown on the balance for
the second and third observations; this is often called the
“SXXS” sequence. Optional sequence B starts with the unknown
on the balance first and last with the standard on the balance for
the second and third observations; this is often called the
“XSSX” sequence. The primary advantage of sequence B is less
handling of the mass standards. The advantage of sequence A is
in the case where the unknown is a summation of weights that
require careful arrangement on the balance pan only once.

Adjust the single pan balance or the combination balance so the
first two readings of the double substitution fall in the first
quarter of the optical scale or digital indications. The zero
adjustment and tare adjustment may be used. Small weights
may be placed on the balance pan to reach the desired reading
range. These weights remain on the pan throughout the double

Page 5 of 18


December 2003

9. Reference Tables

Table 9.1 Use of Range to Estimate Standard Deviation

Table 9.2 Z Factors for Two-sided Confidence Intervals

Table 9.3 Student t-Variate

Table 9.4 Critical Values for the F-test, Fo.975

Table 9.5 Critical Values for the F-test, Fo.99

Table 9.6 Two-sided Tolerance Interval Factors

Table 9.7 Factors for Computing Two-sided Confidence Intervals for
Table 9.8 Density of Air-free Water

Table 9.9 Density of Air

Table 9.10 Coefficient of Linear and Cubical Expansion for Materials Commonly Used
in Laboratory Apparatus and Standards

Table 9.11 A Short Table of Random Numbers

Reference Tables Page 1 of 13


GMP 13

March 2003
Mass - Option B

NIST

[-———,

Monitoring kg., kg..
Primary Metric & aa
Avdp Standards

Laboratory
Standards
Metric/Avdp

‘

+,

| Client
Laboratory Field Echelon |, It
Level Working Calibration
Standards Workload
Client
Echelon Ill
Calibration
Workload

Page 5 of 11


Appendix SOP 2

Table B-2. _e, approximation in terms of temperature

Temperature (°C) e; (mm Hg)
18 15.48
18.5 15.97
19 16.48
19.5 17
20 17.54
20.5 18.09
21 18.65
21.5 19.23
22 19.83
22.5 20.44
23 21.07
23.5 21.72
24 22.38
24.5 23.07
25 23.77
25.5 24.49
26 25.23
26.5 25.99
27 26.77
27.5 27.57
28 28.39
28.5 29.23
29 30.09
29.5 30.98

Page 22 of 22

March 2003


December 2003
Table 9.4 Critical values for the F-Test, Fo.975
n= degrees of freedom for numerator _n2 = degrees of freedom for denominator

ayy 2 3 4 5 6 7 8g 9 10 2 15 20 24 30 40
n2
1 647.8 | 799.5 | 864.2 | 899.6 | 921.8 | 937.1 | 948.2 | 956.7 | 963.3 | 968.6 | 976.7 | 984.9 | 993.1 | 997.2 | 1001 | 1006
2 38.51 | 39.00 | 39.17 | 39.25 | 39.30 | 39.33 | 39.36 | 39.37 | 39.39 | 39.40 | 39.41 | 39.43 | 39.45 | 39.46 | 39.46 | 39.47
3 17.44 | 16.04 | 15.44 | 15.10 | 14.88 | 14.73 | 14.62 | 14.54 | 14.47 | 14.42 | 14.34 | 14.25 | 14.17 | 14.12 | 14.08 | 14.04
4 12.22 | 10.65 | 9.98 | 9.60 | 9.36 | 9.20 } 9.07 | 898 | 8.90 }| 8.84 | 8.75 | 8.66 } 8.56 | 851 846 | 8.41
5 10.01 | 8.43 | 7.76 | 7.39 | 7.15 | 698 | 685 | 6.76 | 668 | 662 | 652 | 643 | 633 | 628 | 623 | 6.18
6 881 | 7.26 | 6.60 | 623 | 5.99 | 5.83 | 5.70 | 5.60 | 5.52 | 5.46 | 5.37 | 5.27 | 5.17 | 5.12 | 5.07 | 5.01
7 8.07 | 654 | 5.89 | 5.52 | 5.29 | 5.12 | 4.99 | 4.90 | 4.82 | 4.76 | 4.67 | 4.57 | 4.47 | 442 | 436 | 4.31
8 757 | 6.06 | 542 |} 5.05 | 482 | 4.65 | 4.53 | 4.43 | 4.36 | 4.30 | 4.20 | 4.10 | 4.00 | 3.95 | 3.89 | 3.84
9 721 | 5.71 | 5.08 | 4.72 | 4.48 | 4.32 | 4.20 | 4.10 | 4.03 | 3.96 | 3.87 | 3.77 | 3.67 | 3.61 | 3.56 | 3.51
10 6.94 | S46 | 483 | 4.47 | 4.24 | 4.07 | 3.95 | 3.85 | 3.78 | 3.72 | 3.62 | 3.52 | 3.42 | 3.37 | 3.31 3.26

ih 6.72 | 5.26 | 4.63 | 4.28 | 4.04 | 3.88 | 3.76 | 3.66 | 3.59 | 3.53 | 3.43 | 3.33 | 3.23 | 3.17 | 3.12 | 3.06

12 6.55 | 5.10 | 4.47 | 4.12 | 3.89 | 3.73 | 3.61 | 3.51 | 3.44 | 3.37 | 3.28 | 3.18 | 3.07 | 3.02 | 2.96 | 2.91

13 641 | 4.97 | 435 | 4.00 | 3.77 | 3.60 | 3.48 | 3.39 | 3.31 | 325 | 3.15 | 3.05 | 2.95 | 289 | 284 | 2.78

14 6.30 | 4.86 | 4.24 | 3.89 | 3.66 | 3.50 | 3.38 | 3.29 | 3.21 | 3.15 | 3.05 | 2.95 | 284 | 2.79 | 2.73 | 2.67

1s 6.20 | 4.77 | 4.15 } 3.80 | 3.58 | 3.41 | 3.29 | 3.20 | 3.12 | 3.06 | 2.96 | 286 | 2.76 | 2.70 | 2.64 | 2.59

16 6.12 | 4.69 | 4.08 | 3.73 | 3.50 | 3.34 | 3.22 | 3.12 | 3.05 | 2.99 | 289 | 2.79 | 268 | 263 | 2.57 | 2.51

17 6.04 | 462 | 4.01 | 3.66 | 3.44 | 3.28 | 3.16 | 3.06 | 2.98 | 2.92 | 2.82 | 272 | 262 | 256 | 250 | 2.44

18 5.98 | 4.56 | 3.95 | 3.61 3.38 | 3.22 | 3.10 } 3.01 | 2.93 | 2.87 } 2.77 | 2.67 | 256 | 2.50 | 2.44 |] 238

19 5.92 | 4.51 | 3.90 | 3.56 | 3.33 | 3.17 | 3.05 | 2.96 | 2.88 | 2.82 | 2.72 | 262 | 2.51 | 245 | 2.39 | 2.33

20 587 | 446 | 3.86 | 3.51 3.29 | 3.13 | 3.01 | 2.91 | 2.84 | 2.77 | 2.68 | 257 | 246 | 241 2.35 } 2.29

21 5.83 | 4.42 | 3.82 | 3.48 | 3.25 | 3.09 | 2.97 | 287 | 2.80 | 2.73 | 2.64 | 253 | 242 | 237 | 2.31 2.25

2 5.79 | 438 | 3.78 | 3.44 | 3.22 | 3.05 | 2.93 | 2.84 | 2.76 | 2.70 | 2.60 | 2.50 | 2.39 | 233 | 2.27 | 2.21

23 5.75 | 4.35 | 3.75 { 341 | 3.18 | 3.02 | 2.90 | 2.81 | 2.73 | 2.67 | 2.57 | 247 | 236 | 230 | 224 | 218

24 5.72 | 432 } 3.72 | 338 | 3.15 | 2.99 | 287 | 2.78 | 2.70 | 2.64 | 2.54 | 244 | 233 | 227 | 2.21 | 215

25 5.69 | 4.29 | 3.69 | 3.35 | 3.13 | 2.97 | 2.85 | 2.75 | 2.68 | 2.61 | 2.51 | 241 | 230 | 2.24 | 218 | 2.12

26 5.66 | 4.27 | 3.67 | 3.33 | 3.10 | 2.94 | 2.82 | 2.73 | 2.65 | 2.59 | 249 | 239 | 2.28 | 2.22 | 2.16 | 2.09

27 5.63 | 4.24 | 3.65 | 3.31 3.08 | 2.92 | 2.80 | 2.71 2.63 | 2.57 | 2.47 | 2.36 | 225 | 2.19 } 2.13 | 2.07

28 5.61 | 4.22 | 3.63 | 3.29 | 3.06 | 2.90 | 2.78 | 2.69 | 2.61 | 2.55 | 245 | 234 | 223 | 2.17 | 241 | 205

29 5.59 | 4.20 | 3.61 | 3.27 | 3.04 | 288 | 2.76 | 2.67 | 2.59 | 2.53 | 243 | 232 | 221 | 2.15 | 2.09 | 2.03

30 5.57 | 4.18 | 3.59 | 3.25 | 3.03 | 287 | 2.75 | 2.65 | 2.57 | 2.51 | 241 | 231 | 220 | 2.14 | 207 | 201

40 5.42 | 4.05 | 3.46 | 3.13 | 2.90 | 2.74 | 262 | 2.53 | 245 | 239 | 229 | 2.18 | 2.07 | 201 | 1.94 | 1.88

60 5.29 | 3.93 | 3.34 | 3.01 | 2.79 | 2.63 | 2.51 | 241 | 233 | 2.27 | 2.17 | 2.06 | 1.94 } 1.88 | 1.82 | 1.74

120 SAS | 3.80 | 3.23 | 289 | 2.67 | 2.52 | 2.39 | 2.30 | 2.22 | 2.16 | 2.05 | 1.94 | 182 | 1.76 | 1.69 1.61

oo 5.02 | 3.69 | 3.12 | 2.79 | 2.57 ] 241 | 2.29 | 219 | 2.11 2.05 | 1.94 | 183 | 1.71 1.64 1.57 1.48

For use for a one-tailed test of equality of standard deviation estimate at 2.5 % level of confidence, or for a
two-tailed test at 5 % level of confidence.

Reference Tables Page 5 of 13



March 2003

Test No.: TI-01-056
APPENDIX C - Example Page 1 of 2

BUREAU OF STANDARDS
PO Box 12345
City, State 12345-1234

COMPLIANT CALIBRATION LABORATORY
123 Some Ave.
City, State 12312-1231

REPORT OF CALIBRATION
FOR
1 kg to 10 mg weight kit

(Twenty-one metric weights)

Maker: DENTROM LAKE Lab Test No. : TI-01-056
Serial No.: 27269 NMI Test No.: 822/1234
SUBMITTED BY
YOUR CUSTOMER, INC.
Customer's Address
City, State

‘Conventional Mass Conventional Mass Expanded
(g) Correction (mg) Uncertainty

(mg)

1 000.000 82 0.82
500.000 71 0.71
299.999 87
200.000 67
100.000 411

50.000 318
30.000 117
19.999 987
10.000 011
5.000 022
3.000 112
1.999 965
1,000 117
0.500 013 2
0.300 022 3
0.200 001 7
0.100 001 3
0.050 001 8
0.030 001 1
0.020 000 9
0.009 999 7

‘The data in the above table of this report only applies to those items specifically listed on this report.

Uncertainty statement:

‘The combined standard uncertainty includes the standard uncertainty reported for the standard, the standard uncertainty for the measurement
process, the standard uncertainty for any uncorrected errors associated with buoyancy corrections, and a component of uncertainty to account for
any observed deviations from NIST values that are less than surveillance limits. The combined standard

SOP 1 Page 5 of 6


1.0

SOP 4

December 2003

SOP No. 4

Recommended Standard Operations Procedure
for

Weighing by Double Substitution Using a Single-Pan Mechanical
Balance, a Full Electronic Balance, or a Balance with Digital
Indications and Built-In Weights

Introduction

Ll.

1.2.

Purpose

The double substitution procedure is one in which a standard and an unknown
weight are intercompared twice to determine the average difference between the
two weights. Errors in any built-in weights or in the balance indications are
eliminated by using the balance only as a comparator and by calibrating the
balance indications over the range of use for the measurement with a sensitivity
weight. Accordingly, the procedure is especially useful for high accuracy
calibrations. The procedure does not incorporate measurement control steps to
ensure the validity of the standards and the measurement process; additional
precautions must be taken.

Prerequisites

1.2.1. Verify that valid calibration certificates are available for the standards
used in the test.

1.2.2. Verify that the standards to be used have sufficiently small standard
uncertainties for the intended level of calibration. Primary standards
should not be used at this level.

1.2.3. Verify that the balance is in good operating condition with sufficiently
small process standard deviation as verified by a valid control chart or
preliminary experiments to ascertain the performance quality when a new
balance is put into service.

1.2.4. Verify that the operator is experienced in precision weighing techniques
and has had specific training in SOP 2, SOP 4, SOP 29, GMP 4, and GMP
10.

1.2.5. Verify that the laboratory facilities comply with the following minimum
conditions to meet the expected uncertainty possible with this procedure.

Page 1 of 18


December 2003

Table 1. Environmental conditions
Echelon * Temperature Relative aumidity
I 18 °C to 27 °C, maximum change 2.0 °C/h 40 to 60+ 20/4h

2. Methodology

2.1.

2.2.

2.3.

24.

SOP 8

Scope, Precision, Accuracy

This method is applicable to all lower echelon mass calibration (tolerance testing)
provided that the uncertainty requirements can be met. The achievable precision
using this procedure is appropriate, provided the expanded uncertainty of the
measurement is no more than one-third of the permissible tolerance of the mass
standard tested. The accuracy achievable with this procedure depends on the
accuracy of the calibration of the working standards and the precision of the
intercomparison.

Summary

The mass to be tested is compared with a calibrated working standard by a
modified substitution procedure. The comparison may be made using a
single-pan, an equal-arm, or a fully-electronic balance. The reference standard is
placed on the balance to obtain a convenient reference point and a sensitivity test
is conducted. The error (departure from nominal value) of the weight tested is
determined by comparing its reading to the reading obtained for the reference
standard. A weight is considered to be within tolerance when the absolute value
of its error plus its uncertainty does not exceed the tolerance established for the
particular class of weight.

Apparatus/Equipment

2.3.1. Single-pan, equal arm, or full-electronic balance with sufficient capacity
for the load tested and with readability equal to or less than one-tenth of
the acceptable tolerance tested.

2.3.2. Mass standards calibrated with an expanded uncertainty of one-tenth or
less than the tolerance tested. The calibration values must be traceable to
NIST.

2.3.3. Calibrated sensitivity weights.

2.3.4. Uncalibrated counterweights, 7, of approximately the same mass as the
standard weights (for option C).

Procedure - Option A
Use of Single-Pan Balance
2.4.1. Select a reference standard of the same nominal value as the weight under

test. Place the standard on the balance pan. Adjust the optical scale
reading (See GMP No. 4) to approximately midscale using uncalibrated

Page 2 of 12


SOP 8

2.7.

2.6.4.
2.6.5.

2.6.6.

2.6.7.

2.6.8.

December 2003

Remove all weights from the balance pan.

Place the weight to be tested on the balance pan. Record the reading as
Xn.

After several weights have been tested (no more than 10 without
rechecking the standard) recheck the zero as in 2.5.3 and record the
reading. The difference between this indication and the previous one for
the standard indicates a balance drift. This drift will normally be small. If
the drift exceeds 10 % of the tolerance applicable to the weights under test
or affects a measurement result to the extent that a weight may be out of
tolerance, the measurement should be repeated and more frequent checks
of the standard should be made or a more appropriate procedure should be
used.

Readjust the zero at any time that a significant difference is observed
when rechecking a standard.

Calculate the mass correction for each weight using the equation

Cy = Cy + (Xp-O}) = C, + Xn (when O; is zeroed)

Procedure - Option C

Use of Equal Arm Balance

2.7.1.

Select a reference standard of the same nominal value as the weight under
test. Place the standard on the left balance pan together with small,
calibrated weights equal to the correction required for the standard,

. provided it is light. If (and only if) the standard is heavy, do nothing

2.7.2.

2.7.3.
2.7.4,

further at this point but follow instructions in 2.6.4. Add sufficient
counterweights to the right pan to obtain a sum of turning points of
approximately twice midscale value. If necessary, number the graduated
scale such that adding weights to the left pan will increase the balance
reading. Record the sum of the turning points as 0).

Add an appropriate calibrated sensitivity weight to the left pan and record
the sum of the turning points as 02. Calculate the sensitivity,

sensitivity = Moy
(0, -0,)
where CM,y is the conventional mass of the sensitivity weight.
Remove all weights from the left pan.
Place weight to be tested on the left pan. If the standard used in 2.6.1 was
heavy, add small correction weights to the left pan, equivalent to the
correction required for the standard. Add small, calibrated tare weights as

required to left or right pan to obtain an approximate balance and record
the sum of the turning points as X,.

Page 5 of 12


GMP 11

2.3.

March 2003

Procedure

2.3.1.

Identification of Parameters

Critical Parameters

Components that contribute more than 25 % of a measurement’s uncertainty are
identified as critical parameters. To ensure an accurate evaluation of
performance, calibration intervals are determined to meet a 99 % reliability
target. Critical parameters are checked and defined below:

Mass Critical Parameters (The example provided below corresponds to Option
A in Mass Traceability in GMP 13.)

Balance Performance

Balance performance in Echelon 1 weighing processes is evaluated in every
measurement series. An F-test ratio evaluates the observed standard deviation of
the process against the accepted standard deviation of the process. The balance
performance component is also tested with a check standard in each weighing
series. The check standard value is evaluated with a t-test by compared the
observed value to the accepted reference value. All other weighing processes
have incorporated measurement control procedures and control charts that are
evaluated as data is collected.

Mass Standards
Mass standards are dynamic with use. Wear, contamination and other factors
can cause drift from accepted values. Thus, the following intervals have been

set:

Table 1. Calibration intervals for mass standards

Item Initial Cal Interval (months) Source
Pl.kg+Pl.. kg 48 NIST
Cl. kg+Cl.. kg (alternating 2 years) 48 NIST
P30 kg - P2 kg 12 Lab
P500 g - Pl mg 6 Lab
C500 g - Cl mg 6 Lab
W25 kg - W1 mg 12 Lab
P Pound Standards 24 Lab
W Pound Standards 12 Lab
P = primary; C = check/control; W = working standards

Page 2 of 6


SOP 30

December 2003

2.5.5 Make PMAP Control Measurement

2.5.5:1

Control measurements of the check standard should be made
periodically to ensure that the current measurement
performance remains in control of the established reference
limits. Control measurements should be tested for “in” or
“out” of control status and charted on the control chart. The
frequency of the control measurements is dependent on the
objective of the PMAP application.

When the objective is to determine and control the calibration
process uncertainties, control measurements should be made
during the calibration process to ensure the calibration results
are accurate and within reference uncertainty statements.
Control measurements should be made prior to returning
calibrated items to the customer. A minimum of 25 control
measurements are required within the calibration period or
interval assigned to the calibration standards and the
calibration process.

When the objective is to control calibration standards,
working standards, or primary standards, the frequency of
control measurements should be less than 4 the use of the
standard being controlled. The reduction in measurements
ensures that the check standard receives less use and wear
than the standard being controlled. Control measurements are
charted and the Process Bias (observed mean value —
accepted) is evaluated to detect any significant change in the
calibration standard being controlled.

2.5.6 Evaluate Process Performance at Specific Intervals

2.5.6.1

2.5.6.2

Examine each control measurement data point as it is charted.
Evaluate each data point for its control status and investigate
causes for out of control data. Analyze the measurement
process uncertainty, including the process standard deviation
(sp), process bias, and other uncertainties quarterly or every
five to ten data points to ensure that significant changes in
uncertainties do not occur.

Evaluate current performance using the control measurements
described in 2.5.5 to establish the current standard deviation
of the process (sp), process bias and other uncertainties.
Perform each evaluation at specific calibration intervals
established by the calibration of standards and service of the
measurement instrument. This evaluation, referred to as
“calibration” of the process, is performed at intervals that will

Page 7 of 9


December 2003

Table 9.7 Factors for Computing Two-sided Confidence Limits for a (Part 1)

Degrees of 0 = 0.05 a =0.01 a =0.001
Su Si Su St Su SL
1 17.79 0.3576 86.31 0.2969 844.4 0.2480
2 4.859 0.4581 10.70 0.3879 33.29 0.3291
3 3.183 0.5178 5.449 0.4453 11.65 0.3824
4 2.567 0.5590 3.892 0.4865 6.938 0.4218
5 2.248 0.5899 3.1715 0.5182 5.085 0.4529
6 2.052 0.6143 2.764 0.5437 4.128 0.4784
7 1.918 0.6344 2.498 0.5650 3.551 0.5000
8 1.820 0.6513 2311 0.5830 3.167 0.5186
9 1.746 0.6657 2173 0.5987 2.894 0.5348
10 1.686 0.6784 2.065 0.6125 2.689 0.5492
i 1.638 0.6896 1.980 0.6248 2.530 0.5621
12 1.598 0.6995 1.909 0.6358 2.402 0.5738
13 1.564 0.7084 1.851 0.6458 2.298 0.5845
14 1.534 0.7166 1.801 0.6549 2.210 0.5942
15 1,509 0.7240 1.758 0.6632 2.136 0.6032
16 1.486 0.7808 1.721 0.6710 2.073 0.6116
7 1.466 0.7372 1.688 0.6781 2.017 0.6193
18 1.448 0.7430 1.658 0.6848 1,968 0.6266
19 1.432 0.7484 1.632 0.6909 1.925 0.6333
20 1417 0.7535 1.609 0.6968 1.886 0.6397
21 1.404 0.7582 1.587 0.7022 1.851 0.6457
2 1391 0.7627 1.568 0.7074 1.820 0.6514
23 1.380 0.7669 1.550 0.7122 1.791 0.6568
24 1.370 0.7709 1.533 0.7169 1.765 0.6619
25 1.360 0.7747 1518 0.7212 1.741 0.6668

From: NBS Handbook 91, p T-34

Reference Tables

Page 8 of 13



This page is blank.

vi


2.2.

March 2003

Summary

This uncertainty analysis process follows the following steps:

1) the measurement process is clearly specified;

2) uncertainty sources are identified and characterized;

3) uncertainty sources are quantified;

4) uncertainty sources are converted to standard uncertainties;

5) the combined uncertainty is calculated;

6) the expanded uncertainty is calculated;

7) the expanded uncertainty is evaluated against appropriate tolerance or calibration
limits; and

8) measurement results are reported.

Special methods for handling bias/errors are addressed as well.

3. | The Process of Measurement Uncertainty Estimation

3.1.

3.2.

SOP 29

Step 1. Specify the process.

Clearly specify the measurement process in question, including the item being measured
and the input quantities upon which it depends. This will usually require a quantitative
expression related to the process. Where possible, you may reference an SOP or other
method description along with the specific standards and measurement assurance
process that is used to adequately complete this step.

Step 2. Identify and characterize uncertainty sources.

Identify all possible sources of uncertainty in a comprehensive list, characterizing them
based on the evaluation method that will be used to quantify them (Type A, statistical
methods or Type B, scientific judgement) and to categorize them based on their
relatedness with something such as a flow chart (shown as Appendices), a cause and
effect diagram, or an uncertainty budget table. Using the expression identified in 3.1
provides a good starting point. All of the parameters in this expression may have an
uncertainty associated with them. When there are discrete steps in the measurement
process, additional uncertainties may be associated with each.

What follows are the most common uncertainties associated with metrological
measurements. Keep in mind that this list is exhaustive. Each item listed below is
identified as a standard uncertainty u, when determined using Type B methods of
evaluation and a standard uncertainty s, when determined with Type A methods of
evaluation (statistical methods). Each standard uncertainty is further defined by an
arbitrary subscript related to the source for ease in remembering that source.

3.2.1, Standard uncertainty from the measurement process, sp, (Type A evaluation).

Page 2 of 11


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SOP 30

2.5.1.2.

December 2003

ensure that the check standard values will determine the
variability and the maximum bias that result from the process
and the calibration standard. Determining and controlling
expanded uncertainty requires duplicating the calibration
process and determining where in the process to insert the
control measurement using the check standard. When the
objective of PMAP is to control the uncertainty of the
calibration standard (u,), the PMAP measurement may vary
from the calibration process to allow inserting the check
standard measurement close to the measurement of the
calibration standard (see appendix, Model SOP 8). Diagram
the calibration process to establish how many check standards
and PMAP applications are required to meet objectives. Also,
diagram the process to determine where in the process to
insert the control measurements of the check standard.

Select and Calibrate Check Standard

For calibration process uncertainty determination and control,
select a check standard that approximates the item to be
calibrated. The selected check standard should be selected to
evaluate maximum random variation (sp) and bias of the
process. The check standard selected should also be used to
evaluate other objectives (uo) of the specific calibration
process. For multiple ranges of use, a check standard and
PMAP application will be required for various portions of the
range. For example, Double Substitution (SOP 4) will require,
at a minimum, a check standard for each decade (1000 g, 100
g, 10 g, 1 g, 100 mg, and 10 mg) on each balance used. The
selected check standard should be calibrated to establish its
accepted value (S.) with an uncertainty level sufficient to
control the calibration process uncertainty. The calibration of
the check standard must be completed using a standard which
is independent of the calibration standard that the PMAP
process is designed to control.

For control of the calibration standard, use a check standard
that is not part of routine measurement and that will evaluate
the changes in the calibration standard’s accepted value, not
the maximum random variation of the process. The check
standard used to control the calibration standard should be
used less frequently (less than ’4 as often) than the calibration
standard. For example, in (SOP 28), using Design A.1.2 (a
4-1 weighing design) at 1000 g, requires the selection of a
1000 g check standard that is measured less frequently than
the item under test in order to evaluate the two 1000 g
calibration standards. The selected check standard should be

Page 4 of 9


GMP 13

Volume - Option A

NIST

Volume Group or

Mass Group

Mass Standards

Volume Standards
5 gal , 25 gal,
100 gal

Client Volume
Transfer
Calibration
Workload
(5 gal or larger)

Laboratory
Mass Standards
Metric/Avdp

Client
Gravimetric
Volume Calibration
(5 gal or smaller)

Page 7 of 11

March 2003


Table of Contents

Foreword
Good Laboratory Practices

1 Quality Assurance of the Measurement Process

4 Periodic Recalibration Of State Standards

9 Rounding Expanded Uncertainties and Calibration Values
11 Painting Weights

Good Measurement Practices

1 Reading Turning Points On An Equal Arm Balance

10 Understanding Factors Affecting Weighing Operations

11 Assignment and Adjustment of Calibration Intervals for Laboratory
Standards

12 Standard Operating Procedure Selection

13 Ensuring Traceability

14 Selection and Use of Sensitivity Weights in Weighing Procedures

Standard Operating Procedures

1 Preparation of Test/Calibration Reports

2 Applying Air Buoyancy Corrections

4 Weighing by Double Substitution Using a Single Pan Mechanical
Balance, a Full Electronic Balance, or a Balance with Digital
Indications and Built In Weights

7 ~~ Weighing by Single Substitution Using a Single Pan Mechanical
Balance, a Full Electronic Balance, or a Balance with Digital
Indications and Built In Weights

8 Medium Accuracy Calibration of Mass Standards by Modified
Substitution

9 Control Charts for Calibration of Mass Standards

29 Assignment of Uncertainty

30 Process Measurement Assurance Program

Reference Materials

Statistical Techniques (Updated Section 8 of NBS Handbook 145,
1986)

Reference Tables (Updated Section 9 of NBS Handbook 145, 1986)

iii

GLP 1-1
GLP 4-1
GLP 9-1
GLP 11-1

GMP 1-1
GMP 10-1
GMP 11-1

GMP 12-1

GMP 13-1
GMP 14-1

SOP 1-1
SOP 2-1
SOP 4-1

SOP 7-1

SOP 8-1

SOP 9-1

SOP 29-1
SOP 30-1

8-1

9-1


March 2003

GMP 13

Good Measurement Practice
for
Ensuring Traceability

1. Introduction

1.1

1.2

Purpose

Traceability is defined as “the property of a result of a measurement or the value of a
standard whereby it can be related to stated references, usually national or
international standards, through an unbroken chain of comparisons all having stated
uncertainties”.' Traceability ensures that the measurements are accurate
representations of the specific quantity subject to measurement, within the uncertainty

of the measurement.

To ensure traceability, suitably calibrated standards that are appropriately maintained
and cared for, proper standard operating procedures, continuous measurement
control, surveillance, and suitable documentation must all be present.

Test numbers issued by NIST should not be used nor required as proof of the
adequacy or traceability of a test or measurement. Having a NIST number does not
provide evidence that the measurement value provided by another organization is
traceable. (See section 1.3.3.)

Prerequisites
Traceability can be characterized by the following essential elements:

1.2.1 Unbroken chain of comparisons. A documented system of comparisons
going back to a standard acceptable to the parties, usually a national or
international standard;

1.2.2 Measurement uncertainty. The measurement uncertainty for each step in the
traceability chain must be calculated according to defined methods and must
be stated so that an overall uncertainty for the whole chain may be calculated
(see SOP 29);

1.2.3. Documentation. Each step in the chain must be performed according to
documented and generally acknowledged procedures (see GMP 12) and the
results must be documented (i.e., in a calibration report, see SOP 1);

1 ISO VIM, 2 ed., 1993, definition 6.10

GMP 13

Page 1 of 11


1.

SOP 8

December 2003

SOP No. 8
Recommended Standard Operations Procedure
for
Medium Accuracy Calibration of Mass Standards

by
Modified Substitution

Introduction

1d.

1.2.

This SOP describes procedures to be followed for determining whether or not
mass standards are within the tolerances specified for a particular class of
standards (e.g., NIST Class F, ASTM Class 5, 6, 7 or OIML Classes Mj, Mo, and
M3) where the uncertainty is much smaller than the tolerance application. The
described procedures permit the metrologist to report that the weights under test
were compared against a reference standard with the results reported on the
laboratory report form. The comparison is important because the built-in weights
of a balance do not represent laboratory standards unless they have been formally
calibrated. If a State law or other regulation requires that field weights be
compared against the State (or reference) standards, this procedure can be used to
fulfill this requirement. It is suitable for calibration when moderate accuracy is
required, and does not eliminate errors due to drift. The procedure does not
incorporate measurement control steps to ensure the validity of the standards and
the measurement process; additional precautions must be taken. The expanded
uncertainty with this procedure must be < 1/3 of the tolerance per ASTM and
OIML standards. If uncertainty to tolerance ratios are greater than recommended,
SOP 7 (single substitution) or SOP 4 (double substitution) is preferred.

Note: If you use SOP 8, you are most likely using working standards that are
equivalent to your customer’s weights. If this is the case, the working standards
should be at a higher level of calibration than the weights being calibrated with
them. Therefore, you will need a better balance and procedure to calibrate your
working standards than the one used to calibrate your customer’s weights.

Prerequisites

1.2.1. Verify that valid calibration values are available for the standards used in
the test.

1.2.2. Verify that the working standards to be used have sufficiently small
standard uncertainties for the intended level of calibration. Primary
standards should not be used at this level.

1.2.3. Verify that the balance that used is in good operating condition with
sufficiently small process standard deviation as verified by a valid control
chart or preliminary experiments to ascertain the performance quality
when a new balance is put into service.

1.2.4. Verify that the operator is experienced in precision weighing techniques
and has had specific training in SOP 7, SOP 8, SOP 29, and GMP 10.

1.2.5. Verify that the laboratory facilities meet the following minimum
conditions to meet the expected uncertainty possible with this procedure.

Page 1 of 12




March 2003

GLP 9

Good Laboratory Practice
for
Rounding Expanded Uncertainties and Calibration Values

A calibration is not complete until the expanded uncertainty associated with the calibration is
determined and reported. Each Standard Operating Procedure (SOP) includes information
regarding the calculation of uncertainties. The expanded uncertainty is generally reported with
approximately a 95 % confidence interval. The confidence interval is determined by multiplying
a coverage factor (usually 2) times the root sum square of properly combined Type A and Type B
evaluated components according to the ISO/IEC Guide to the Expression of Uncertainty in
Measurement (GUM).

The steps for reporting corrections and uncertainties are as follows:

1. Round the uncertainty to two significant figures.
2. Round the correction/error to the last figure affected by the uncertainty.
3. Report the rounded correction and uncertainty.

Zeros, which follow a decimal point, when there are only zeros ahead of the decimal point, are
not considered significant figures.

Rounding Rules

Use the following rules to round measurement data, consistent with its significance:

1. When the digit next beyond the one to be retained is less than five, keep the
retained figure unchanged. For example: 2.541 becomes 2.5 to two significant
figures.

2. When the digit next beyond the one to be retained is greater than five, increase the
retained figure by one. For example: 2.453 becomes 2.5 to two significant
figures.

3. When the digit next beyond the one to be retained is exactly five, and the retained
digit is even, leave it unchanged; conversely if the digit is odd, increase the
retained figure by one (even/odd rounding). Thus, 3.450 becomes 3.4 but 3.550
becomes 3.6 to two significant figures.

Note: Even/odd rounding of numbers provides a more balanced distribution of

results. Use of computer spreadsheets to reduce data typically follows the practice
of rounding up.

GLP 9 Page 1 of 3




SOP 9

December 2003

SOP No. 9

Recommended Standard Operating Procedure
for
Control Charts for Calibration of Mass Standards

Introduction

1.1. This SOP describes procedures for the development of control charts and their use
for demonstrating attainment of statistical control of a mass calibration process.

1.2. Prerequisites

The use of this SOP requires that appropriate apparatus, methodology, and standards
are available, and that the laboratory thoroughly understands the basic principles of
the measurement process used and has had sufficient experience to perform the
necessary operations required for the measurements of concern.

Summary

An appropriate check standard (or contro] standard) is incorporated into the measurement

process and weighed at established intervals, the results are plotted on an x (X-bar) chart.
The abscissa (x) represents the sequence of measurements and the ordinate (y) the measured
values. A central line is drawn, indicating the mean (x ) of the measured values and control
limits are indicated within which the results of measurements are expected to be randomly
distributed, based on statistical considerations. The system is considered to be in statistical
control when the individual values are within the designated limits. The system is
considered to be out of control if an excessive number of values are present outside
established limits, unusual trends are observed, or if the mean exceeds the control limits.
The statistical information on which the control limits are based can be used to calculate
confidence limits for measurements made while the system is demonstrated to be stable and
in a state of statistical control.

Procedure
3.1. Definition of Monitored System

The monitored system is considered to consist of the balance, the standard operating
procedure, the laboratory environment, the check standard or control standard, the
operator, and any other sources that contribute to the variance or bias of the
measurement data. Any of the above that can be considered to be constant or
negligible contributors to the variance may be consolidated and monitored by a
single control chart. Any that cannot be so considered (for example: different
standard, different balance, different SOP) may require separate control charts.

Page 1 of 5


3.

SOP 7

December 2003

Calculations

3.1.

3.2.

M,

s

No air buoyancy correction. Calculate the conventional mass correction, C,, for
the test weight as follows, according to the optional sequence used. In each case,
the conventional mass corrections for the standard weight(s), C;, the conventional
mass of the tare weights, CM, and CM, , and the conventional mass of the

sensitivity weight, CM,,, are included. The symbols N, and Nx refer to the
nominal values of S and X, respectively. If no tare weights, and equal nominal
values are used, those terms may all be deleted from the equations.

3.1.1. Optional Sequence A (SXX)

c= 6, 40M, 0M, + (0, -0,) | eel | 4 n -N,
37 M2

3.1.2. Optional Sequence B (XSS)

c=, +0m,- cm, +(0,-0,) | Me | am, =,
37 M2

Air Buoyancy Correction
3.2.1. Calculate the air density, ,, as described in the Appendix to SOP No. 2.

3.2.2. Calculate the mass of the test weight, M;, and its mass correction C, using
the mass of the standard weight(s), the tare weights and the sensitivity
weights according to the optional sequence used.

3.2.2.1. Optional Sequence A (SXX)

uy [1-2]
[1-2 Jxme (1-2 Jas, [1-2 400.0) — Pe

Ps Pr. (0, - 0,)

te

2)

Page 7 of 15


March 2003

Appendix SOP 2 Page 6 of 22


March 2003

GMP 10

Good Measurement Practice
for
Understanding Factors Affecting Weighing Operations

Good laboratory techniques and practices, as well as good standards and balances, are required to
obtain good mass measurements. Errors can arise from a variety of sources, such as balance
drift, air currents, lack of thermal equilibrium, magnetic or electrostatic fields, and to
manipulative skills using the balance. The magnitude and significance of these errors depends
upon the laboratory environment, the balance, and the accuracy required for the measurement.
Different methods of weighing are used to eliminate or reduce the effects of sources of error.
Particular sources of error and ways to eliminate the errors are discussed with the weighing
procedures. The accuracy required for a measurement and the criticality of the measurement
often influence the choice of the weighing method used in the measurement. Regardless of the
procedure used, several practices should be followed to promote good measurements.

Environment and Preparation

First, the balance should be installed in a laboratory having good temperature and humidity
control. The requirements for temperature stability increase as more precision is needed in the
measurement. For high precision measurement, the temperature should not vary by more than
+1 °C ina 24 h period throughout the year and should vary by less than 0.5 °C during the course
of any one measurement series (typically less than 1 h). General laboratory measurements can
probably withstand temperature variations of + 2 °C per day. Varying temperatures result in
balance drift and in unequal temperatures for the air, balance, and objects to be weighed. The
relative humidity should be maintained between 40 % and 60 %. If the relative humidity falls
significantly below 40 %, electrostatic discharge may be generated both in and near the balance.
This can result in erratic readings and make precision weighing impossible. If precision mass
standards are cleaned, they should stabilize in the laboratory environment for seven to ten days.

Thermal and environmental equilibrium are critical for mass calibrations. This is why each mass
SOP will provide instruction that the environment must be stable and the weights set in or near
the balance for 24 hours prior to a calibration. The test objects, balances, reference standards,
and air should all be in thermal equilibrium. When possible, the objects to be weighed and the
reference standards should be placed either in the balance chamber or adjacent to the balance so
all can come to the same thermal equilibrium. If there is a lack of thermal equilibrium,
convection currents will be generated when an object is on the balance pan and an erroneous
reading may result. These types of errors are likely to go unnoticed when check standards are
handled the same way, so care must be taken to reduce the likelihood of their occurrence. Tests
have shown that these types of errors depend upon the temperature differences among the objects
and the balance, and on the geometry of the objects being weighed. On 20 g standards of greatly
differing geometry, studies have shown that errors as large as 0.2 mg can occur for a 4 °C
temperature difference among the standards and the balance. Errors as large as 3 mg have also
been observed at 1 kg loads when standards were stored in a cabinet, and unknown test items

GMP 10 Page | of 6


3.3.

SOP 29

3.2.5.3.

3.2.5.4.

3.2.5.5.

March 2003

several options given in the following section. In ALL cases,
the method used to incorporate bias must be clearly reported.

Adding the bias to the expanded uncertainty (e.g., used in PMAP
software). In this case, the bias is simply added to the expanded

U + bias = (u, *k)+bias

uncertainty and is reported as such.

Example when uncertainties for the laboratory data and the reference data
are considered equivalent (e.g., laboratory data is compared to another
laboratory’s data).

In this case, a rectangular distribution is considered where the value
might possibly be anywhere within the range shown for each laboratory
data point. This method is referenced in section 4.6 of NIST Technical
Note 1297. This approach may also be used in the case where a standard
is predictably drifting with use over time. In this case, a mid-range value
is chosen and ug (uncertainty for differences) is calculated as follows:

u,= bias 1 or more simply : 0.29 d, where dis the bias

d 2 3

Example when uncertainties for the laboratory data are considered
secondary to a reference value (e.g., the difference between the laboratory
data and NIST data). This method was originally published in 1994.

In this case, a reference value is given precedence over the laboratory
data and a mid-range value is not chosen. The extreme value is more
probable. In this case, the following equation may be used:

bias
u, =—= or more simply : 0.577 d, where d is the bias
4B Py

Step 3. Quantify uncertainty estimates

All uncertainty estimates identified in the previous step must be quantified in units that
represent the measured values. Type A methods of evaluation usually provide quantified
estimates in the units of interest.

Type B methods of evaluation may be conducted with spreadsheets using the basic
expression identified in the SOP or identified when the process was specified. Scenario
testing can be done to determine the impact and quantify specific variables on the final
measured quantity. The knowledge gained in this step often proves useful in identifying
potential areas of improvement.

Page 6 of 11


March 2003

GLP 1

Good Laboratory Practice
for the
Quality Assurance of the Measurement Process

Quality Assurance of the Measurement Process means establishing, documenting, implementing,
and maintaining a quality system appropriate to the laboratory’s scope of activities. Having such
a system in place will allow the laboratory to know, within the limits of a measurement process,
that a measurement is valid with respect to its traceability, accuracy, and precision.

The validity of tests and calibrations should be monitored with quality control procedures.
Statistical techniques are used to record and monitor charted measurement results to permit the
detection of trends. The metrologists and laboratory management should plan and review the
results from quality assurance monitoring.

Other steps taken to ensure the quality of the measurement process may include, but are not
limited to:

e the regular use of Standard Reference Materials (SRMs) and /or internal quality
control using secondary reference materials;

participation in interlaboratory comparisons (round robins);

test replications with same and/or different methods;

recalibration of retained items;

correlation of different characteristics of an item; and

proper calibration intervals.

Each measurement parameter in the laboratory’s scope of activities should be reviewed and
analyzed to determine the validity of the measurement process.

The standards and the measurement process for each parameter must be in a state of statistical
control. Statistical control means that the variability of the measurement process is known and
stable; when a process is in statistical control, we can assume that the reported measurement
uncertainties are valid. The National Institute of Standards and Technology provides technical
guidance and support to the State weights and measures laboratories to develop measurement
control programs that provide measurement assurance. The objective of these programs is to
evaluate the entire measurement process including:

procedures;
standards;
equipment;
personnel; and
environment.

GLP 1 Page 1 of 2


SOP 29

March 2003

3.2.3. Standard uncertainty due to other factors, Up (Type B evaluation.)

These are factors related to the measurement equation, but distinct from the
standard uncertainties associated with the process and the standards. These items
are often much smaller in a well-controlled process than the standard uncertainties
associated with the process and the standards. Examples are given in the flow
charts.

The laboratory must carefully consider any other components of uncertainty that
might contribute to the uncertainty of the measurement. In mass measurements,
these might include effects from the magnitude of air buoyancy corrections as
discussed in SOP 2, when these corrections are not made, or the uncertainty from
the calculation of air density when buoyancy corrections are made (also discussed
in SOP 2).

Additionally, the laboratory should include any other components that are not
negligible, such as the uncertainty associated with the density of the standards, the
density of the unknown test items, effects due to lack of thermal equilibrium
during the test, or known and quantified effects due to magnetized mass standards.
Each component that is considered should be included as an additional standard
uncertainty Uo1, 402, 403, etc., and included in the RSS equation when data shows
these factors to be significant. Note that components of uncertainty are not limited
to those mentioned. Documentation of each component evaluated should be
maintained to complete the documentation required by ISO/IEC 17025.

3.2.4. Standard uncertainty due to factors unrelated to the measurement process, Uy.

These are factors that may be related to characteristics of the items being testing or
of the standard and are usually minimized in well-known and controlled
measurement processes.

3.2.5. Special uncertainties from other sources (Type B evaluations). Includes bias or

unidentified errors.

It is a general requirement of the GUM that corrections be applied for all
recognized and significant systematic effects. Where a correction is applied based
on a bias, an estimate of the associated uncertainty must then be included in the
uncertainty analysis. Due to the various approaches present in the metrology
system, several examples and possible approaches are presented in the section on
calculating the combined or expanded uncertainties. At this stage, a determination
must be made with regard to 1) identifying cause and 2) level of significance.

Page 4 of 11


December 2003
Table 9.11 A Short Table of Random Numbers

46 96 85 77 27 9286 26 45 21 89 91 71 42 64 64 58 22 75 81 74 91 48 46 18
44 19 15 32 63 5587 77 33 29 45 00 31 34 84 05 72 90 44 27 78 22 07 62 17
34 39 80 62 24 3381 67 28 11 34 79 26 35 34 23 09 94 00 80 55 31 63 27 91
74 97 80 30 65 0771 30 01 84 47 45 89 70 74 13 04 90 51 27 61 34 63 87 44
22 14 61 60 86 3833 71 13 33 72 08 16 13 50 56 48 51 29 48 30 93 45 66 29
40 03 96 40 03 4724 60 09 21 21 18 00 05 86 52 85 40 73 73 57 68 36 33 91
52 33 76 44 56 1547 75 78 73 78 19 87 06 98 47 48 02 62 03 42 05 32 55 02
37 59 20 40 93 1782 24 19 90 80 87 32 74 59 84 24 49 79 17 23 75 83 42 00
11 02 55 47 48 8474 36 22 67 19 20 15 92 53 37 13 75 54 89 56 73 23 39 07
10 33 79 26 34 5471 33 89 74 68 48 23 17 49 18 81 05 52 85 70 05 73 11 17
67 59 28 25 47 8911 65 65 20 42 23 96 41 64 20 30 89 87 64 37 93 36 96 35
93 50 75 20 09 1854 34 68 02 54 87 23 05 43 36 98 29 97 93 87 08 30 92 98
24 43 23 72 80 6434 27 23 46 15 36 10 63 21 59 69 76 02 62 31 62 47 60 34
39 91 63 18 38 2710 78 88 84 42 32 00 97 92 00 04 94 50 05 75 82 70 80 35
74 62 19 67 54 1828 92 33 69 98 96 74 35 72 11 68 25 08 95 31 79 11 79 54
91 03 35 60 81 1661 97 25 14 78 21 22 05 25 47 26 37 80 39 19 06 41 02 00
42 57 66 76 72 9103 63 48 46 44 01 33 53 62 28 80 59 55 05 02 16 13 17 54
06 36 63 06 15 0372 38 O1 58 25 37 66 48 56 19 56 41 29 28 76 49 74 39 50
92 70 96 70 89 8087 14 25 49 25 94 62 78 26 15 41 39 48 75 64 69 61 06 38
91 08 88 53 52 1304 82 23 00 26 36 47 44 04 08 84 80 07 44 76 51 52 41 59
68 85 97 74 47 5390 05 90 84 87 48 25 O1 11 05 45 11 43 15 60 40 31 84 59
59 54 13 09 13 8042 29 63 03 24 64 12 43 28 10 01 65 62 07 79 83 05 59 61
39 18 32 69 33 4658 19 34 03 59 28 97 31 02 65 47 47 70 39 74 17 30 22 65
67 43 31 09 12 6019 57 63 78 11 80 10 97 15 70 04 89 81 78 54 84 87 83 42
61 75 37 19 56 9075 39 03 56 49 92 72 95 27 52 87 47 12 52 54 62 43 23 13
78 10 91 11 00 6319 63 74 58 69 03 51 38 60 36 53 56 77 06 69 03 89 91 24
93 23 71 58 09 7808 03 07 71 79 32 25 19 61 04 40 33 12 06 78 91 97 88 95
37 55 48 82 63 8992 59 14 72 19 17 22 51 90 20 03 64 96 60 48 01 95 44 84
62 13 11 71 17 2329 25 13 85 33 35 07 69 25 68 57 92 57 11 84 44 01 33 66
29 89 97 47 03 1320 86 22 45 59 98 64 53 89 64 94 81 55 87 73 81 58 46 42
16 94 85 82 89 0717 30 29 89 89 80 98 36 25 36 53 02 49 14 34 03 52 09 20
04 93 10 59 75 1298 84 60 93 68 16 87 60 11 50 46 56 58 45 88 72 50 46 11
95 71 43 68 97 1885 17 13 08 00 50 77 50 46 92 45 26 97 21 48 22 23 08 32
86 05 39 14 35 4868 18 36 57 09 62 40 28 87 08 74 79 91 08 27 12 43 32 03
59 30 60 10 41 3100 69 63 77 01 89 94 60 19 02 70 88 72 33 38 88 20 60 86
05 45 35 40 54 0398 96 76 27 77 84 80 08 64 60 44 34 54 24 85 20 85 77 32
71 85 17 74 66 2785 19 55 56 51 36 48 92 32 44 40 47 10 38 22 52 42 29 96
80 20 32 80 98 0040 92 57 51 52 83 14 55 31 99 73 23 40 07 64 54 44 99 21
13 50 78 02 73 3966 82 01 28 67 51 75 66 33 97 47 58 42 44 88 09 28 58 06
67 92 65 41 45 3677 96 46 21 14 39 56 36 70 15 74 43 62 69 82 30 77 28 77
72 56 73 44 26 0462 81 15 35 79 26 99 57 28 22 25 94 80 62 95 48 98 23 86
28 86 85 64 94 1158 78 45 36 34 45 91 38 51 10 68 36 87 81 16 77 30 19 36
69 57 40 80 44 9460 82 94 93 98 01 48 50 57 69 60 77 69 60 74 22 05 77 17
71 20 03 30 79 2574 17 78 34 54 45 04 77 42 59 75 78 64 99 37 03 18 03 36
89 98 55 98 22 4512 49 82 71 57 33 28 69 50 59 15 09 25 79 39 42 84 18 70
58 74 82 81 14 0201 05 77 94 65 57 70 39 42 48 56 84 31 59 18 70 41 74 60
50 54 73 81 91 0781 26 25 45 49 61 22 88 41 20 00 15 59 93 51 60 65 65 63
49 33 72 90 10 2065 28 44 63 95 86 75 78 69 24 41 65 86 10 34 10 32 00 93
11 85 01 43 65 0285 69 56 88 34 29 64 35 48 15 70 11 77 83 O01 34 82 91 04
34 22 46 41 84 7427 02 57 77 47 93 72 02 95 63 75 74 69 69 61 34 31 92 13

From: NBS Handbook 91, p T-82

Reference Tables Page 13 of 13


March 2003

Electrostatic fields can also cause errors in measurements. If there is a static charge in a
mechanical balance, the balance may give erratic readings and lack repeatability. If the object
being weighed has a significant electrostatic charge, it may result in measurement errors and may
leave a static charge on the balance. Electrostatic charges are of particular concern when plastic
containers are placed on the balance.

Care should be taken to remove electrostatic charges from objects being weighed by grounding
the objects, if necessary, before placing them on the balance. To prevent the build-up of static
electricity in a balance, the relative humidity in the laboratory should be maintained between
40 % and 60 %. The water vapor in the air will serve to drain off electrostatic charges from the
balance.

Balances utilizing the magnetic force restoration principle for weighing should be checked to
verify that the magnetic field generated by the magnetic cell in the balance does not exist around
the balance pan. If the shielding of the magnetic cell is inadequate, measurement errors may
occur when weighing ferromagnetic objects or when the balance is placed on a surface comprised.
of ferromagnetic material.

GMP 10 Page 6 of 6


December 2003

Using Estimate of Standard Deviation, s

In the usual situation, s is known, based on U degrees of freedom and the formula for use is:

y+
dn
Variable Description
x sample mean
Ss estimate of standard deviation
n number of measurements on which the mean is based
t Student's ¢ value, based on the confidence level desired and
the U_ degrees of freedom associated with s (see Table 9.3).

Note that fz as N—>0, For many practical purposes, the standard deviation may be
considered as known when estimated by at least 30 degrees of freedom.

8.7 Confidence Interval for ©

The standard deviation, ©, is ordinarily not known but is, instead, an estimated value based on a
limited number of measurements, using procedures such as have been described above. Such
estimates may be pooled, as appropriate, to obtain better estimates. In any case, the uncertainty
of the estimated value of the standard deviation may be of interest and can be expressed in the
form of a confidence interval, computed as indicated below.

The interval is asymmetrical because the standard deviation is ordinarily underestimated when
small numbers of measurements are involved due to the fact that large deviations occur
infrequently in a limited measurement process. Indeed, it is the general experience of
metrologists that a few measurements appear to be more precise than they really are.
The basic information required to compute the interval is an estimate of the standard deviation, s,
and the number of degrees of freedom on which the estimate is based. The relationships to use
are:

Lower limit Bz,s

Upper limit Bus

Interval Bis to Bus
The values for By and By depend upon the confidence level and degrees of freedom associated

with s. Values for use in calculating the confidence level are given in Table 9.7. A more
extensive table (Table A-20) is available in NBS Handbook 91 [19].

Statistical Techniques Page 5 of 10


Example: With Buoyancy Corrections
Double Substitution Data Sheet

December 2003

(Optional Sequence A)
SXXS
Laboratory data and conditions:
Operator HO
Date 8/24/86 Temperature 22.3 °C
Balance MSSA Pressure 753.5 mm Hg
Nominal Load 10g Relative Humidity 45%
Standard deviation of the process, from control chart, sy 0.002 9 mg
Mass standard(s) data:
ID Nominal Mass Correction* Front ity va) hae pense
S 10g -0.679 mg 0.014 mg 3 8.00
x 10g TBD TBD 2 7.84
sw Smg -0.0227 mg 0.000 28 2 8.5
ty — _ _ _ _
ty -- — — — _—
S. 10g 0.321 mg 0.025 mg 2 8.0

*Mass Correction = True Mass if using buoyancy correction. Mass Correction = Conventional Mass if NOT using
buoyancy correction. Density is used only with buoyancy corrections.

Observations:
Observation No. Weights Balance Observations, Units mg
Time: 8:35 AM
1 (0) S+t,
2 (O,) X+h
3 (Os) X+ i + sw
4 (0) S+ ist sw
Time: 8:47 AM

Measurement Assuran

ce (Duplication of the Process):

Observation No. Weights Balance Observations, Units
Time: 9:00 AM.
1(0) S+t 1 $270
2 (O;) Set tse 24271
3 (03) Set tse + sw 7} 248
4 (0) S+ tt sw 6 | 248
Time: 9:10 AM

Note: dotted line represents decimal point

SOP 4

Page 13 of 18


SOP 29

3.2.1.1.

3.2.1.2.

March 2003

Standard deviation from a measurement assurance chart or control chart.

The value for sp is obtained from the control chart limits and the current
knowledge that the measurements are in a state of statistical control.
This will have to be ascertained by measuring at least one check standard
during the course of the current measurements.

Standard deviation from a series of measurements.

Measure a stable test object at least seven times, no two measurements of
which may be made on the same day. Calculate the standard deviation in
the conventional manner. The latter is the value of sp, keeping in mind
that it does not fully represent the measurement process under all
typically encountered conditions.

Note: Repetitive measurements made on the same day estimate only
the short-term standard deviation of the process.

3.2.2. Standard uncertainty for the standards, us (Type B evaluation).

3.2.2.1.

3.2.2.2.

3.2.2.3.

When using standards calibrated by another laboratory.

The information for the standards comes from the calibration report,
generally reported as an expanded uncertainty with its coverage factor
(k). The expanded uncertainty is simply divided by k to obtain the
combined uncertainty for the standard, u,, which represents the u, when
used in your laboratory.

When using a standard calibrated in your laboratory (Type B evaluation).

If the standard was calibrated in your own laboratory, calculate the
combined standard uncertainty, u,, at k=1 and use that as the standard
uncertainty for the standard, ug.

When using more than one standard (Type B evaluation).

When more than one standard is used in a calibration, the standard
uncertainty for each, us), Us, Us;, etc., is included in the RSS equation if
the standards have had independent calibrations. When calibrations are
performed at the same time, the standards may be dependent, so the
standard uncertainties may be added (us; + us2) to determine a value to
represent us. (This will be the case with two 1 kg standards that were
calibrated at the same time using a weighing design and subsequently
used together as standards (restraints) in a weighing design.)

Page 3 of 11


SOP 4

2.5.1.5.

December 2003

substitution. Once the balance has been adjusted to the desired
position, neither the balance dials, the zero and tare adjustments,
nor the small weights placed on the balance pan, are to be
changed during the measurement.

If the balance is equipped with a pan arrestment mechanism,
arrest the pan between each observation.

2.5.2. Measurement Procedure, Optional Sequence A (SXX‘S)

Table 3. Optional Sequence A
Measurement No. | Weights on Pan Observation
1 St ts O,
2 X+h O2
3 X+ t+ sw O03
4 S+t,+ sw O41

All observations should be recorded on suitable data sheets, such as those in the
appendix. Record the laboratory ambient temperature, barometric pressure, and
relative humidity.

2.5.2.1.

2.5.2.2.

2.5.2.3.

2.5.2.4.

2.5.2.5.

Observation 1. Place the standard weight(s), S, along with ¢, on
the balance pan. If equipped with a pan arrestment mechanism,
release the balance pan. When the pan is released, start the
stop-watch and record observation O; once the balance
indication has stabilized.

Observation 2. Remove weight(s) S and ¢, and replace with test
weight X and its tare weight, 4. Release the pan, time the
interval, and record observation O>.

Observation 3. Add the sensitivity weight, sw, to the weights of
observation 2. Release the pan, time the interval, and record
observation O3.

Observation 4. Remove weights X and ¢, and replace with S and
t,. The sensitivity weight, sw, remains on the balance pan.
Release the pan, time the interval, and record observation O4.

Compare the two differences (O2 — O,) and (O; ~ O,); they
should not differ from one another by more than 2 standard
deviations of the balance for this process and load. If this
difference is exceeded, reject the data and redo the

Page 6 of 18


March 2003

While other quality assurance programs could meet these objectives, the control programs
developed for measurement assurance greatly increase the comprehensiveness of the program.

The State laboratories typically provide measurement services in the disciplines of mass, volume,
and length. Some laboratories provide services in other measurement areas. Approximately
89 % of their workload is in mass standards calibration.' Mass calibration demands the greatest
precision and is the first discipline for which a measurement assurance program was developed
and implemented. Nevertheless, all measurement disciplines should have a measurement
assurance system in place.

The most recent improvement in assuring the quality of each measurement parameter in the State
Laboratories is the incorporation of a Process Measurement Assurance Program (PMAP).

A measurement assurance program consists of duplicating the measurement process by including
a check/control standard as surrogate for the test item. Measurements made throughout the year
will show all the conditions that are likely to affect the measurement process and their combined
effects. Controlled duplication of the process provides for the realistic evaluation of the
variability of the measurement process as one of the components in the estimation of the
measurement uncertainty.

Measurement results that are collected over several years may be statistically evaluated with
current results being compared to results from previous years. Any observed problems or changes
in the measurement results are investigated and if necessary, corrective action can be taken.
Ongoing monitoring establishes a continuous, comprehensive, internal measurement assurance
program in a State laboratory.

Data from internal measurement assurance programs is compared to the results of inter-
laboratory comparisons (round robins) in which the laboratory participates as part of the Regional
Measurement Assurance Program (RMAP) groups. (These groups consist of the metrologists of
the State laboratories and their counterparts in private industry in a geographic region of the
country. Six regional measurement assurance groups operate in the United States and its
territories. )

The strength of the measurement assurance approach lies in its applicability to a wide variety of
measurements with sufficient flexibility to permit each measurement control program to be
tailored to the particular needs of a given measurement area. The sophistication of the control
program depends on the criticality of the measurement.

' State Laboratory Program Workload Survey, 1999, NIST/OWM & NCWM Metrology Subcommittee
? See NISTIR 6176 and SOP 30.

GLP 1 Page 2 of 2


Appendix

Double Substitution Data Sheet
(Optional Sequence B)

December 2003

XSSX
Laboratory data and conditions:
Operator
Date Temperature
Balance Pressure
Load Relative Humidity

Process standard deviation from control chart, sp

Mass standard(s) data:

ID Nominal

Mass Correction*

Expanded Une:
From Cal. report

Une:
k factor

*Mass Correction = True Mass if using buoyancy correction. Mass Correction = Conventional Mass if
NOT using buoyancy correction. Density is used only with buoyancy corrections.

Observations:
Observation No. Weights Balance Observations, Units

Time:
1@Q) Xt H
2 (Oz) St+t i
3 (0) S4 it sw :
4 (O) X+ t+ sw H

Time:

Measurement Assurance (Duplication of the Process):

Observation No. Weights Balance Observations, Units

Time:

1(@) Se bse !

2 (0:) Sth i

3 (03) S+ t+ sw A

4 (0) Sct tye + sw i
Time:

Note: dotted line represents decimal point.
SOP 4 Page 12 of 18


December 2003

Example: Without Buoyancy Corrections

Double Substitution Data Sheet
(Optional Sequence B)

XSSX
Laboratory data and conditions:
Operator HO
Date 8/24/86 Temperature 22.3 °C
Balance CB 100 Pressure 753.5 mm Hg
Load 30 g & 1 troy oz Relative Humidity 45%
Process standard deviation from control chart, s, 0.018 mg
Mass standard(s) data:
ID Nominal Mass Correction* Fal repeat ee yon
Ss 30g 0.407 mg 0.022 mg 3 8
x ltoz TBD TBD 7.84
50 mg -0.084 00 mg 0.000 65 mg 2 8.5
t, lig 0.359 6 mg 0.006 3 mg 3 8.04
& None _ _ — _
Se 30g 0.907 mg 0.030 mg. 2 8

*Mass Correction = True Mass if using buoyancy correction. Mass Correction = Conventional Mass if NOT using
buoyancy correction. Density is used only with buoyancy corrections.

Observations:
Observation No. Weights Balance Observations, Units mg
Time: 9:00 AM.
1 (0) X+h 20 | 93
2 (0,) Sth 17/21
3 (Os) S+ t+ sw 67 | 08
4 (Ov) X+t+sw 70: 81
Time: 9:05 AM.

Measurement Assurance (Duplication of the Process):

Observation No. Weights Balance Observations, Units
Time: 9:15 AM
1() Sth 20 } 95
2 (0) Set tse 21145
3 (03) Se+ tse + Sw 1; 32
4 (0) S+ it sw 70} 83
Time:_9:20 AM

Note: dotted line represents decimal point

SOP 4

Page 17 of 18


December 2003

linearity (these factors are considered as a part of the measurement process when obtaining the
standard deviation of the process).

Compliance Evaluation

You may need to evaluate the conventional mass correction and its uncertainty to determine if a
weight is or is not within specified tolerances. The magnitude of the expanded uncertainty must
be less than 1/3 of the tolerance to be able to perform that evaluation, according to ASTM
E 617-97 and OIML R111 documentary standards.

Load = 50 g
ASTM E 617 OIML R111
Class Tolerance (mg) Class Tolerance (mg)
1 0.12 Ey 0.10
2 0.25 F 0.30

If we look at three times the calculated expanded uncertainty: 0.043 mg x 3 = 0.129 mg, we
observe that the uncertainty complies with the 1/3 rule for ASTM Class 2, and OIML Class F;
but not ASTM Class 1 or OIML Class Ep.

Next, the weight value is considered to be within tolerance when the absolute value of its error
plus its uncertainty, do not exceed the tolerance established for the particular class of weight.

Value and uncertainty: 0.145 mg + 0.043 mg.

0.145 mg + 0.043 mg = 0.188 mg (upper limit of the value, or error bar if graphed)

0.145 mg — 0.043 mg = 0.102 mg (lower limit of the value, or error bar if graphed)

We can see that the correction of 0.145 is within these limits: 0.102 <C, < 0.188, therefore, the
value also complies with ASTM Class 2 and OIML Class Fj, and a compliance statement may be
included on the calibration report. .

Reporting

The conventional mass correction and uncertainty are reported as follows:

Cx = 0.145 mg + 0.043 mg

SOP 7 Page 15 of 15



March 2003

2.2. Apparatus/Equipment Required!
2.2.1. Barometer accurate to + 66.5 Pa (0.5 mm Hg) to determine air pressure.
2.2.2. Thermometer accurate to + 0.10 °C to determine air temperature.
2.2.3. Hygrometer accurate to + 10 % to determine relative humidity.
2.3. Estimating the Magnitude of the Air Buoyancy Correction
23 Estimate the magnitude of the air buoyancy correct, MABC, using the following
ormula:

MABC = (p, — p,)(Ve - V.)

2.3.2. The equation may also be represented as follows:

MABC = m,(p, ~ vo{ t - +)
Pr Py

Table 1. Variables for MABC equation

Variable Description of Variable

Pa air density at the time of the measurement in
mg/em?

Ln density of "normal" air; i.e., 1.2 mg/cm?
Mo nominal mass (in grams)
V, volume of the unknown weight, X in cm?
V, volume of the reference standard, S in cm
Ps density of reference standard, Sin g/cm?
px density of unknown weight, X in g/cm?

The relative magnitude of the correction can be compared to the expanded
measurement uncertainty to determine the importance of the air buoyancy correction
and the uncertainty components for a particular measurement.

The barometer, thermometer, and hygrometer are used to determine the air density at the time of the
measurement. The air density is used to make an air buoyancy correction. The accuracies specified are
recommended for high precision calibration. Less accurate equipment can be used with only a small
degradation in the overall accuracy of the measurement.

SOP 2 Page 2 of 22


March 2003

if the unknown object whose mass is to be determined has a density that differs widely
from that of the standards (weighing of water, for example). Many mass standards are
calibrated in terms of a so-called "apparent mass" [conventional mass] scale (See Chapter
7.3, Handbook 145). Use of this scale does not indiscriminately eliminate the need for
buoyancy corrections as is sometimes assumed.

5. Terminology
5.1. Weighing by Substitution

Substitution weighing is the procedure by which one determines the assembly of
standard weights that will produce nearly the same reading on a one-pan balance as
does the unknown object. The balance thus serves as a comparator. A two-pan
balance may be used in this mode if one of the pans contains a counterpoise and the
standards and unknown are substituted on the second pan. (See SOP No. 3.)

5.2. Mass

The term "mass" is always used in the strict Newtonian sense as a property intrinsic
to matter. Mass is the proportionality constant between a force on a material object
and its resulting acceleration. This property is sometimes referred to as "true mass",
"vacuum mass", or "mass in vacuum" to distinguish it from conventional [apparent]
mass.

5.3. Conventional [Apparent] Mass*

The mass of material of a specified density that would exactly balance the unknown
object if the weighing were carried out at a temperature of 20 °C in air of density
0.0012 g/em®. The mass, My, of an object, N, is related to its apparent mass My,4 by
the equation:

M, [: _ 0.0012 ]
Pw

~ (: - n00r2
Pp

“Pontius, P. E., Mass and Mass Values, NBS Monograph 122, 1974, pp 12-23, 26-33 described the concept of
apparent mass. The term conventional mass is described by O[ML R 33, the Conventional Value of Mass in Air.

Appendix SOP 2 Page 8 of 22


March 2003

to the same number of decimal places as the uncertainty statement, that is, 285 mg. Report the
correction as 285 mg + 33 mg.

Example 6

The length of a calibrated interval is computed to be 9.9994558 ft and the uncertainty is
0.0035617 in. First, make sure both values are reported in the same unit (i-e., convert the
uncertainty to ft, 0.000296808 ft.) Then, round the value to two significant figures, that is,
0.00030 ft. Then, round the length of the interval to the same number of decimal places as the
uncertainty value, that is, 9.99946 ft. Report the length of the interval as 9.99946 ft + 0.00030 ft.

Rather than stating the uncertainty value with each correction, it is also proper to place the

correction values in a column headed by the words "Correction" or "Error," etc., and place the
uncertainties (without plus or minus signs) in a column headed "Expanded Uncertainty".

GLP 9 Page 3 of 3


Statistical Techniques and Reference Tables


December 2003

Calculate the air density (SOP 2):

Pa = 1.179 5 mg/em? = 0.001 179 5 g/cm?

Use equation 3.2.2.1 for optional sequence A (SXXS) with buoyancy corrections3:

mi(rot) arte ]oa (rete) +f 2-adeta- a) u(r]

Ps A, p,, 2 a,-Q

| (2)

0.001795 (1.821- 1.268) + (6.798- 6.245) 7 | 2004773 (1-°4u2*)
sgosani {1 - HPS) 4 9-04 BERD AOR) + OTIS 6. 5
2 6.798- 1.821
M, =
, 1 _ 20011795
784

_ (9.997846 1+0.000 552957) _ 9 g99 941g

M,
0.99984949

Calculate the mass (true mass) correction:
C.= My — Nx
Cy = 9.999 904 1g — 10g = - 0.000095 9g = - 0.095 9mg
Calculate the conventional mass value:
(re)
CM, = Ps

[a]
8.0

3 Keep in mind that these equations may be truncated for the purpose of this example and minor differences
may be seen in the ending decimal places due to the use of calculators or spreadsheets.

SOP 4 Page 14 of 18




Appendix A - Traceability worksheet

Parameter: Mass, Volume, Length, Temperature, Other

March 2003

P Metric (g, L, m, °C) Cal. date Cal. Lab Interval
Range
Customary (Ib, gal, ft, °F)
Range
Ww Metric (g, L, m, °C) Cal. date Cal. Lab Interval
Range
Customary (Ib, gal, ft, °F)
Range
S Metric (g, L, m, °C) Cal. date Cal. Lab Interval
© | Range
Customary (Ib, gal, ft, °F)
Range
GMP 13 Page 11 of 11


SOP 4

December 2003

(RSS), and the expanded uncertainty, U, reported with a coverage factor of two (k=2), to
give us an approximate 95 percent level of confidence. See SOP 29 for the complete
standard operating procedure for calculating the uncertainty.

5.1. The expanded uncertainty for the standard, U, is obtained from the calibration
report. The combined standard uncertainty, u,, is used and not the expanded
uncertainty, U, therefore the reported uncertainty for the standard will usually
need to be divided by the coverage factor k.

5.2. The value for s, is obtained from the control chart data for check standards using
double substitution measurements. (See SOP No. 9.)

5.3. Other standard uncertainties usually included at this calibration level include
uncertainties associated with calculation of air density and standard uncertainties
associated with the density of the standards used.

5.4. | The expanded uncertainty, U, must be < 1/3 of the tolerance applicable as per
ASTM E617-97 and OIML R111 to classify mass standards.

Report

Report results as described in SOP No. 1, Preparation of Calibration/Test Reports.

Page 10 of 18


GMP 11

Table 3. Calibration intervals for volume standards

March 2003

Item Initial Cal Interval (months) Source
P100 gal standard 60 NIST
P25 gal standard * 60 Lab
P5 gal standard * 12 Lab
Glassware-
Autopipetes 5 L to 100 mL 120 Lab

*Gravimetric calibration for volumes 5 gallon or smaller, and all “slicker plate”
standards. Laboratory must be qualified for performing gravimetric calibrations.
Volume transfer is acceptable above 5 gallon.

*May be a “slicker plate” type. None are hand-held, “dump” style, test measures.

Temperature Critical Parameters

Temperature Comparison Performance

The measurement performance of each temperature comparison calibration is
evaluated with a check standard and can be verified periodically using triple

point cells, melting point cells, and ice baths (using documented procedures).

Initial Intervals
Temperature standards are dynamic with use. Shock, contamination and other
factors can cause drift from accepted values. Recalibration intervals are as

follows:

Table 4. Calibration intervals for temperature standards

Item Initial Cal Interval (months) Source

25.5 ohm SPRT 36 NIST
100 ohm PRT's 12 Lab
Standard Thermistor 12 Lab
Check Standards 6 Lab
Liquid-in-glass

standards 6 Lab

Secondary Parameters

Components that contribute less than 25 % but more than 1 % of a
measurement’s uncertainty are identified as secondary parameters. Secondary
parameters are assigned calibration intervals designed to meet a 95 % reliability
target. Secondary parameters are defined below:

Page 4 of 6


December 2003

The F-test is useful for comparing the precision of methods, equipment, laboratories, or
metrologists, for example. An inspection of Table 9.4 shows that when either of the values of s
is based on a small number of degrees of freedom, the F value is large. Consequently, the
significance of decisions based on small changes in precision can be supported statistically only
by a relatively large number of measurements. If such changes are suspected, but the data
requirement is difficult to meet, the decision may need to be made on the basis of information
about the measurement process itself.

The F-test is also useful for deciding whether estimates of the standard deviation made at various
times differ significantly. Such questions need to be answered when deciding on whether to
revise control limits of a control chart, for example.

8.10 Comparing a Set of Measurements with a Given Value

The question may arise as to whether a measured value agrees or significantly disagrees with a
stated value for the measured object. The evaluation can be based on whether or not the
confidence interval for the measured value encompasses the stated value. The confidence
interval is calculated using the expression

git

dn

as previously described in Section 8.6. In using this expression, n represents the number of
measurements used to calculate the mean, x, and t depends on the degrees of freedom, UV,
associated with s and the confidence level needed when making the decision. Note that one may
use historical data for estimating s, such as a control chart for example, in which case UV will
represent the degrees of freedom associated with establishment of the control limits and may be
considerably larger than n—-1.

8.11 Comparing Two Sets of Measurements with Regard to Their Means

This discussion is concerned with deciding whether the means of two measured values, , and p,
are in agreement. The data sets used for this purpose may consist of the following:

X4 xR
S4 SB
Ny. Ns

The first question to be resolved is whether s, and s, can be considered to be different

estimates of the same standard deviation or whether they do, indeed, differ. An F test may be
used for this purpose. However, it will be recalled that this is not sensitive to small real
differences, so the decision may need to be based on physical considerations, such as the known
stability of the measurement process, for example.

Case I

Statistical Techniques Page 7 of 10


December 2003

The variability of balance precision that is load dependent must be considered. For
many balances, precision is a function of load, and a distinct control chart is required
(in principle) for every load tested. This is not always feasible, except in the case of
SOP 5 or 28 where check standards are incorporated into the measurement process. ‘
Hence, control charts used for measurement assurance and evaluation of
measurement uncertainty are generally satisfactory if developed using data from
check standards at two or three intervals for each balance appropriately spaced
within the range of balance use, or at least with one check standard for each decade.
On balances where few nominal values (loads) are tested, a control chart should be
established for each load.

3.2. Selection, Care, and Calibration of Check Standards

3.2.1.

A check standard used in high precision calibration measurement must be
stable and normally be comparable to the primary standard or to the typical
calibration work, depending on what is being monitored. For lower order
calibrations, the check standard should simulate the laboratory's primary
standards to the extent feasible. It should be calibrated with an expanded
uncertainty equal to or better than the precision of the process being
monitored. All check standards should be cared for in the same way as
primary standards to prevent their damage or deterioration. Lower order
check standards should be recalibrated at regular intervals according to Good
Measurement Practice (GMP) 11 on Setting and Adjusting Calibration

Intervals.
Table 1. Recommended check standards for typical test situations
Balance Range of Measurement Check Standard(s)
Echelon III (Class F) 2 to 3 values per bal OR
per balance

ISOP 7, 8 5000 Ib to 0.001 Ib I chart per load

[Echelon IT 5000 Ib to 0.001 Ib 2 to 3 values per balance

SOP 3, 4, 6, 7 land 1000 kg to 1 mg OR 1 check standard per decade
leach nominal value incorporates

SOP 5 typically 1 kg to 1 mg la check standard
1 check standard per decade

SOP 28 typically 1 kg to 1 mg (e.g., 1 kg, 100 g, 10g, 1 g,
100 mg, 10 mg, 1 mg)

3.3. Establishing Control Chart Parameters

3.3.1.

SOP 9

The control chart parameters consist of the central line, the best estimate of
the mean of measurements of the check standard, and control (or “action”)

Page 2 of 5




March 2003

APPENDIX B ~ Sample Format
Recommended Format for Calibration Certificate

ABC COMPANY

123 Utopia Street
Anywhere, USA
Report of Calibration

Report Number:
Name of Device:
Model: Serial No:
Submitted by:
Calibration (date)
The ambient conditions were__-°C,_ % relative humidity and _____ mm Hg Barometric pressure.

The item tested was/was not in tolerance at time of calibration. Adjustments are noted and any out of tolerance data are
attached.

Data:

Nominal Value Correction or Error Expanded Uncertainty

The primary standards to which the above data are traceable are identified in this report. The calibration of these
standards is traceable to the National Institute of Standards and Technology. The cycling and certification of all
standards of measurement at this facility meet the requirements of ISO/IEC 17025.

Name of Standard Traceability Reference Calibration Date Next Calibration Due

Test Method:

Uncertainty Statement:

Test Results Approved by (name, title, date):

The results stated on this report relate only to the items specifically identified.
This test report or calibration certificate shall not be reproduced except in full, without written approval of the laboratory.

SOP 1 Page 4 of 6


Appendix
Modified Substitution Data Sheet

Laboratory data and conditions:

December 2003

Operator GH
Date 9/30/96 Temperature 22.5 °C
Balance] PM 2000 MC (2300 g) Pressure 747.5 mmHg
Load 5lb Relative Humidity 45%
Standard deviation of the process, from control chart, sp 0.85 mg
Mass standard(s) data:
D Nominal | Mass Comecion | earandeUne: | Une, | Density
Ss 5b 75 mg 0.50 mg 3 785
Xx Sib 7.85
sw Sg 0,000 002 g
ty None
ts None
Se Sib 2.4 mg 0.73 mg 2 7.95
Mass Correction = Conventional Mass if NOT using buoyancy correction. Density is used only with buoyancy
corrections.
Observations:
Observation No. Weights Balance Observations, Units 0.001 g
[Time: 11:00 am
1) S 01000
202) Stsw 4999
Esror < 2 % of optical scale or electronic range? Yes Noj
303) Ss ooo
4 (04) Xx, 205
5 (0s) Xx) 104
6 (06) X3 - 0089
7(07) Sc - 0005
8 (Os) Ss p03
(Time: 11:20 am Drift < 1/10 Tol. ?: Yes Noj

Up to 10 unknown weights may be checked with this procedure if the drift is less than 1/10 of the tolerance.

SOP 8

Page 11 of 12


December 2003

Appendix
Single Substitution Data Sheet
(Optional Sequence A)
SXX
Laboratory data and conditions:
Operator
Date Temperature
Balance Pressure
Load Relative Humidity
Standard deviation of the process, from control chart, sp

Mass standard(s) data:

: Mass Une: Une: Density
1D Nominal Correction | From cal. report | _k factor g/om?

S

x
sw
ts

ty

Mass Correction = True Mass if using buoyancy correction. Mass Correction = Conventional Mass if
NOT using buoyancy correction. Density is used only with buoyancy corrections.

Observations:
Measurement # Weights Balance Observations, Units
Time:
1 (O) Sth j
2 (O2) X+t A
3 (3) X+t.+ sw Hl
Time:

Measurement Assurance (Duplication of the Process):

Measurement # Weights Balance Observations, Units
Time:
1 ©) S+ ts i
2 (Os) Se+ tse :
3 (O03) Sct tse + sw
Time:

Note: dotted Jine represents decimal point.

SOP7 Page 11 of 15


December 2003

Example: Without Buoyancy Corrections
Single Substitution Data Sheet

(Optional Sequence A)
SXX
Laboratory data and conditions:
Operator HO
Date 8/27/86 Temperature 22.6 °C
Balance H 20 Pressure 751.7 mm Hg
Load 50g Relative Humidity 50%
Standard deviation of the process, from control chart, sp 0.018 mg

Mass standard(s) data:

D Nominal Conction From eal, report i faetor yom
Ss 50g 0.255 mg 0.033 mg 3 8.00
x 50g 7.95
sw 50 mg -0.084 mg 0.000 85 mg 2 8.5

ts

k

Sc 50g 0.315 mg 0.045 mg 2 8.00

Mass Correction = True Mass if using buoyancy correction. Mass Correction = Conventional Mass if
NOT using buoyancy correction. Density is used only with buoyancy corrections.

Observations:
Measurement # Weights Balance Observations, Units mg
Time: 3:40 PM
1() St+t 12! 62
2 (O2) X+k 12:51
3 (03) X+t.+sw 62:37
Time: 3:45 PM
Measurement Assurance (Duplication of the Process):
Measurement # Weights Balance Observations, Units __mg
Time: 3:50 PM
1 (0) Stt; 12 | 67
2 (02) Set te 12:73
3 (03) Sct tse + sw 62} 60
Time: 3:55 PM

Note: dotted line represents decimal point.

SOP7 Page 13 of 15


Foreword

This NIST IR of Selected Publications has been compiled as an interim update for a
number of Good Laboratory Practices, Good Measurement Practices, Standard Operating
Procedures, Statistical Techniques and Reference Tables. This interim publication will
be used as a reference document for the CD-ROM Mass Metrology Course being
prepared by the NIST Weights and Measures Division.

Many of these procedures are updates to procedures that were originally published in
NBS Handbook 145, Handbook for the Quality Assurance of Metrological
Measurements, in 1986, by Henry V. Oppermann and John K. Taylor. The updates have
incorporated many of the requirements noted for procedures in ISO Guide 25,
ANSI/NCSL Z 540-1-1994, and ISO/IEC 17025 laboratory quality systems. The major
changes incorporate 1) uncertainty analyses that comply with current international
methods and 2) measurement assurance techniques using check standards. No
substantive changes were made to core measurement processes or equations, with the
exception of SOP 2, Standard Operating Procedure for Applying Air Buoyancy
Corrections. The CIPM 1981/91 equation for calculating air density has been added to
SOP 2.

The following Practices and Procedures are new in this interim publication:

Good Measurement Practices for:
e Assignment and Adjustment of Calibration Intervals for Laboratory Standards
qd)
¢ Standard Operating Procedure Selection (12)
e Ensuring Traceability (13)
¢ Selection and Use of Sensitivity Weights in Weighing Procedures (14)

Standard Operating Procedures for:
« Assignment of Uncertainty (29)
« Process Measurement Assurance Program (30)

The essential portions of SOP 29, Standard Operating Procedure for Assignment of
Uncertainty were first published in 1994 for the NCSL Conference and Symposium and
to assist State weights and measures laboratories comply with the ISO Guide to the
Expression of Uncertainty in Measurements (1993).

Special thanks go to Val Miller and Jose Torres for the critical editorial reviews needed
to complete this interim publication; to the Minnesota Metrology Laboratory for early
drafts for GMP 11 and 13; and to Jerry Everhart for assistance with early drafts of SOP
30.

iii


December 2003

3.1.2. Optional Sequence B (XSSX)

C,=C,+CM, - CM, — (OP IQ OT CMs |in eN,
: 2 0,- 0,

3.2. Air Buoyancy Correction
3.2.1. Calculate the air density, ,, as described in the Appendix to SOP No. 2.
3.2.2. Calculate the mass M, of the test weight, and its mass correction C, using
the mass of the standard weight(s), the tare weights and the sensitivity

weights according to the optional sequence used.

3.2.2.1. Optional Sequence A (SXXS)

w(ea)on(e}a(eg) teeny)

p,, 2

| oy

3.2.2.2. Optional Sequence B (XSSX)

3.2.3. Calculate the mass correction C,, as follows:

Cy = M, - Nx

where N, is the nominal value for X.

SOP 4 Page 8 of 18


March 2003

Parameter Test Item Recommended SOP
HB 105-3 Large graduated neck | SOP 19, Volume Transfer for Graduated Neck
type provers - used as | Type Provers OR
laboratory standards SOP 14, Gravimetric Calibration with an
Electronic Balance OR
SOP 15, Gravimetric Calibration with an Equal
Arm Balance
Length
Tapes SOP 11, Tape to Tape OR
SOP 12, Bench Method (lower uncertainties)
Rigid Rules SOP 10, Rigid Rule
Pi Tapes SOP 23, Pi Tape Calibration
Liquid-in-Glass Thermometers
HB 105-6 Field standards for SOP 25
weights and measures
Timing Devices
HB 105-5 Field standards for SOP 24
weights and measures
Traffic Speed Gun Tuning Forks
For highway official SOP 22
use
Parameter Process Recommended SOP
Measurement Assurance
All Process Use of process measurement assurance
Measurement SOP 30 programs
Assurance
Use of check standards in procedure
Mass SOP 5, 28 TN 952, TN 844, NISTIR 5672
Mass SOP 4, 6, 7,8 SOP 9
GMP 12 Page 3 of 4



December 2003

against established reference limits until the next calibration
interval.

2.5.7. Continue the measurement assurance procedure as described in 2.5.2
through 2.5.6 to determine and control the measurement process
capability.

Significant changes in the measurement process capability can result
from the following:

* measurement procedure change;

* measurement instrument change;

¢ calibration standards change; and/or

location change.

These changes can require repeating the PMAP procedure (from 2.5
through 2.5.6).

SOP 30 Page 9 of 9


SOP 8

2.7.5.

2.7.6.

December 2003

Calculate the mass correction of the weight tested as follows.

275. 1. If added tare weights are placed on the left pan (¢,).
CM
C, = (x,-0)| _ jem,
' ( 0, - 07; )
2.7.5.2. If added tare weights are placed on the right pan (¢,)
C, = 1,-0)| Me | + OM,
( 0; - 0, )

After several weights have been tested (no more than 10 without
rechecking the standard), recheck the turning point 0;, as described in
2.6.1. Only a small difference should be observed. If the difference
exceeds 2 % of the sum of the turning points in O;, the measurement
should be repeated and more frequent checks of the standard should be
made or a more appropriate procedure should be used.

2.8. Tolerance Evaluation

2.8.1.

Compare the correction plus the expanded uncertainty of the weight tested
with the tolerance for the class of weights to which it belongs. If the
absolute value of the correction plus the expanded uncertainty is numeri-
cally smaller than the tolerance, the weight is considered to be within
tolerance. If the correction is larger than permissible, the weight is
considered to be outside the tolerance and appropriate action should be
taken. It is recommended that weights whose absolute value of the
correction exceeds 75 % of the tolerance limit be adjusted.

Page 6 of 12


9.999941 [ 1- one }
CM, = —
0.999 850
cm, = 99999041 (09998469) _ 9.99987351g
0.999 850
Cy = CM,- Ny

Cy = 9.999873 51g — 10g
Cy = - 0.000 126 49g = - 0.126 49 mg
Calculate the uncertainty for the calibration:

U=u,*2

December 2003

The uncertainty for the standard, U, must be divided by the k factor to determine the ws.

u, = (0.004 667)* + (0.0029)? + (0.000 000032)?

Uc = 0.005 494 623 6 mg

U = 0.005 494 6236 *2 = 0.010 989 247 3 mg

Uncertainty Statement

The uncertainty reported is the root sum square of the standard uncertainty of the standard, the
standard deviation of the process, and an uncorrected systematic error for lack of buoyancy
corrections, multiplied by a coverage factor of 2 (k=2) for an approximate 95 percent confidence
interval. Factors not considered in the evaluation: magnetism (weights are considered to meet
magnetism specifications unless measurement aberrations are noted), balance eccentricity and
linearity (these factors are considered as a part of the measurement process when obtaining the

standard deviation of the process).

SOP 4 Page 15 of 18


GMP 13

1.3

1.2.4

1.2.5

1.2.6

1.2.7

March 2003

Competence. The laboratories or bodies performing one or more steps in the
chain must supply evidence of technical competence (e.g., by maintaining
appropriate training records, participating in interlaboratory comparisons, and
by demonstrating that they are accredited by a recognized accreditation body);

Realization of SI Units. The primary national, international or intrinsic
standards must be primary standards for the realization of the SI units;

Periodic recalibration. Calibrations of standards (and equipment where
appropriate) must be repeated at established (may be defined through
measurement assurance) and appropriate intervals to preserve the traceability
of the standard over time and use (see GLP 4, GMP 11); and

Measurement assurance. A proper measurement assurance program must be
established to ensure the validity of the measurement process and the
accuracy of standard used (see SOP’s 9, 17, 20, 30).

Responsibility

1.3.1

Provider. Providing support for the claim of traceability of the result of a
measurement or value of a standard is the responsibility of the calibration
provider. Calibration reports and certificates must contain a traceability
statement.

User. Assessing the validity of a claim of traceability is the responsibility of
the user of that result or value. Verifying claims of traceability often includes
obtaining a calibration directly from a national metrology institute or another
laboratory that has achieved recognition or accreditation through a recognized
accrediting body.

Use of, or reference to, official test numbers of a national metrology institute.
Having an authentic test number does not provide assurance or evidence that
the measurement value provided by another organization is traceable. Not
only must there be an unbroken chain of comparisons, but each measurement
must be accompanied by a statement of uncertainty associated with the value.
Test report numbers should not be used nor required as proof of the
adequacy or traceability of a test or measurement. National and international
standards dealing with test and measurement quality requirements, such as
ANSI/NCSL Z 540-1, ISO 10012, ISO/IEC 17025 and the ISO 9000 series do
not require the use or reporting of specific test numbers to establish
traceability.

Page 2 of 11