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SOP No. 28

Recommended Standard Operating Procedure

for

Using Advanced Weighing Designs

1 Introduction

Purpose 

Advanced weighing designs use a combination of double substitution comparisons 

of weights of equal nominal value or a series of weights in ascending or descending 

order; standard(s), unknown weights, and an additional standard called a check 

standard. The weights are intercompared using an equal-arm, single-pan 

mechanical, full electronic, or a combination balance utilizing built-in weights and 

a digital indication. The specific SOP for the double substitution procedure for each 

balance is to be followed. Weighing designs provide two methods of checking the 

validity of the measurement using an F-test to check the measurement process and 

a t-test to evaluate the stability of the standard and check standard. Hence, the 

procedure is especially useful for high accuracy calibrations in which it is critical 

to assure that the measurements are valid and well documented. This procedure is 

recommended for precision calibration of laboratory working standards that are 

subsequently used for lower level calibrations, for routine calibration of precision 

mass standards used for calibration of other mass standards, and for surveillance of 

mass reference and working standards.

Prerequisites

Calibrated mass standards, with recent calibration values and which have 

demonstrated metrological traceability to the international system of units 

(SI), which may be to the SI through a National Metrology Institute such as 

NIST.

Standards must be evaluated to ensure that standard uncertainties for the 

intended level of calibration are sufficiently small. Reference standards 

should only be used to calibrate the next lower level of working standards 

in the laboratory and should not be used to routinely calibrate customer 

standards.

Verify that the balance used is in good operating condition with sufficiently 

small process standard deviation as verified by F-test values, pooled shortterm standard deviations, and by a valid control chart for check standards, 

or preliminary experiments to ascertain its performance quality when new 

balances are put into service. See NISTIR 56721 for a discussion on the 

performance levels expected for use of these procedures as part of a 

 1

Fraley, K. L., Harris, Georgia G. L., NISTIR 5672, Advanced Mass Calibration and Measurement Assurance 

Program for State Calibration Laboratories.
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laboratory measurement assurance program to ensure traceability of 

laboratory standards.

Verify that the operator is experienced in precision weighing techniques, 

and has had specific training in SOP 2, SOP 4, SOP 5, SOP 29, and is 

familiar with the concepts in GMP 10. Further, the operator must have been 

trained in the creation of data files and the operation of the NIST Mass Code 

when it is used for data reduction as recommended. Example data sets and 

sample observation sheets are available in the Advanced Mass Seminar 

offered by the NIST Office of Weights and Measures.

Laboratory facilities must comply with the following minimum conditions 

to meet the expected uncertainty possible with this procedure and to comply 

with the balance manufacturer’s operating conditions specified for the 

balance. Equilibration of balances and weights requires environmental 

stability of the laboratory within the stated limits for a minimum of 24 hours 

before a calibration.

Table 1. Environmental conditions.

Echelon2 Temperature Requirements During a Calibration Relative Humidity 

(%)

I

OIML E1, ASTM 000, 00, 0

Lower and upper limits: 18 °C to 23 °C

Maximum changes: ± 0.5 °C / 12 h and ± 0.3 °C / h 40 to 60 ± 5 / 4 h OIML E2, ASTM 1

Lower and upper limits: 18 °C to 23 °C

Maximum changes: ± 1 °C / 12 h and ± 0.7 °C / h

1.2.5.1 It is important that the difference in temperature between the 

weights and the air inside the mass comparator is as small as 

possible. Keeping the reference weight and the test weight inside, or 

next to, the mass comparator before and during the calibration can 

reduce this temperature difference. Standards and test artifacts must 

be allowed to reach equilibration in or near the balance before 

starting measurements.

 2 Echelon I corresponds to weights of Classes OIML E1 and E2, Echelon II corresponds to weights of Classes OIML 

F1 and F2.
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2 Methodology

Scope, Precision, Accuracy

This method can be performed on any type of balance or mass comparator using 

the appropriate double substitution method for the weighing instrument. Because 

considerable effort is involved, this weighing design is most useful for calibrations 

of the highest accuracy. The weighing design utilizes a combination of double 

substitutions to calibrate a single unknown weight, or a group of related weights in 

a decade. This method introduces redundancy into the measurement process and 

permits two checks on the validity of the measurement; one on accuracy and 

stability of the standard using an integrated t-test and the other on process 

repeatability using an F-test. A least-squares best fit analysis is done on the 

measurements to assign a value to the unknown weights. The standard deviation of 

the process depends upon the resolution of the balance and the care exercised to 

make the required weighings. The accuracy will depend upon the accuracy and 

uncertainty of the calibration of the restraint weights and the precision of the 

comparison.

Summary 

A restraint weight, S, in some cases two restraint weights, S1 and S2, an unknown 

weight, X, or group of unknown weights, and a check standard, Sc are compared in 

a specific order typically using the double substitution procedure although other 

procedures may be appropriate. The balance and the weights must be prepared 

according to the appropriate method for the balance being used. Once the balance 

and weights have been prepared, all readings must be taken from the reading scale 

of the balance without adjusting the balance or weights in any way. Within a double 

substitution all weighings are made at regularly spaced time intervals to minimize

effects due to instrument drift. Because of the amount of effort required to perform 

weighing designs, the procedure includes an air buoyancy correction using the 

average air density as determined immediately before and after the weighings, driftfree equation for calculating the observed differences, correction for the cubical 

coefficient of expansion when measurements are not made at 20 °C, an average 

sensitivity for the balance over the range of measurements made, and the 

international formula for air density.3

Apparatus/Equipment Required

Precision analytical balance or mass comparator with sufficient capacity 

and resolution for the calibrations planned.

 3 See NISTIR 6969, Selected Procedures for Mass Calibrations, SOP 2, Air Density Calculations. Use Option B. The 

difference between Option A and Option B in SOP 2 is less than the uncertainty associated with assumptions made in 

the air density equations.
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2.3.1. Calibrated reference standards (usually starting at 1 kg or 100 g), calibrated 

check standards for each decade (e.g., 1 kg, 100 g, 10 g, 1 g, 100 mg, 10 mg, 

1 mg for the seven series between 1 kg and 1 mg) and working standards. 

2.3.2. Calibrated sensitivity weights and tare weights selected to comply with the 

requirements of SOP 34. Note: The calculations performed by the Mass 

Code do not take into consideration the value of any tare weights used in 

the weighing design. Additional calculations will be required when tare 

weights are used.

2.3.3. Uncalibrated weights to be used to adjust the balance to the desired reading 

range if needed.

2.3.4. Forceps to handle the weights, or gloves to be worn if the weights are moved 

by hand. Forceps and gloves must be selected to avoid damage or 

contamination of mass standards.

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

(calibration not required; this is used to ensure consistent timing of the 

measurement). If an electronic balance is used that has a means for 

indicating a stable reading, the operator may continue to time readings to 

ensure consistent timing that can minimize errors due to linear drift.

2.3.6. Calibrated barometer with sufficiently small resolution, stability, and 

uncertainty (See SOP 2, e.g., accurate to ± 66.5 Pa (0.5 mmHg)) to 

determine barometric pressure.4

 

2.3.7. Calibrated thermometer with sufficiently small resolution, stability, and 

uncertainty (see SOP 2, e.g., accurate to ± 0.10 °C) to determine air 

temperature.4

2.3.8. Calibrated hygrometer with sufficiently small resolution, stability, and 

uncertainty (see SOP 2, e.g., accurate to ± 10 percent) to determine relative 

humidity.4

Procedure

Preliminary Procedure

2.4.1.1 Weights are visually inspected for cleanliness and damage.

2.4.1.2 If cleaning weights, it is important to clean weights before any 

measurements are made because the cleaning process may change 

the mass of the weight. Cleaning should not remove any significant 

 4 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 limits specified are recommended for high precision 

calibration.
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amounts of weight material. Weights should be handled and stored 

in such a way that they stay clean. Before calibration, dust and any 

foreign particles shall be removed. Care must be taken not to change 

the surface properties of the weight (i.e. by scratching the weight). 

If a weight contains significant amounts of dirt that cannot be 

removed by the methods cited above, the weight or some part of it 

can be washed with clean alcohol, distilled water, or other solvents. 

Weights with internal cavities should normally not be immersed in 

the solvent to avoid the possibility that the fluid will penetrate the 

opening. If there is a need to monitor the stability of a weight in use, 

the mass of the weight should, if possible, be determined before 

cleaning. 

2.4.1.3 If weights are cleaned with solvents, they must be stabilized for at 

least 7 to 10 days.

2.4.1.4 Before making measurements, 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, or use a 

thermal soaking plate next to the balance with weights covered. 

Thermal equilibration time is particularly important with weights 

larger than 1 gram. An alternative heat source such as a heat lamp 

may further improve temperature stability in front of the balance. 

Conduct preliminary measurements to determine the size of the 

sensitivity weight and any tare weights that are required following 

SOP 34; adjust the balance to the appropriate reading range of the 

balance indications and exercise the balance. Refer to the 

appropriate double substitution method for details.

Weighing Designs

Table 2 shows the most common comparisons to be made as referenced in 

NBS Technical Note 952, Designs for the Calibration of Standards of Mass, 

J. M. Cameron, M. C. Croarkin, and R. C. Raybold, 1977. Each series is 

characterized by the number of observations, n, the degrees of freedom, d.f.,

associated with the standard deviation, the number of weights in each 

design, k (not shown in this table), the number of restraints (standards), and 

check standards, along with appropriate positions within the design*.

*Positions for check standards must be carefully considered as subsequent 

equations may be dependent on the position of use. 
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Table 2. Common weighing designs.

Design 

ID Description nObservations

d.f.

Degrees of 

freedom

Restraint

Position

Check Std

Positiona

A.1.1 3-1 Weighing Design5 3 1 1 3

A.1.2 4-1 Weighing Design 6 3 1, 2 3 or 4

A.1.4 5-1 Weighing Design 10 6 1, 2 3, 4, or 5

A.2.1 6-1 Weighing Design 8 3 1, 2 3, 4, 5, or 6

C.1a 5, 3, 2, 1, 1 Design (descending) 8 4 1, 2, 3 5 or 4

C.1 5, 3, 2, 1, 1 Design (ascending) 8 4 5 4

C.2 5, 3, 2, 1, 1, 1 Design (descending) 11 6 1, 2, 3 4, 5, or 6

C.2 5, 3, 2, 1, 1, 1 Design (ascending) 11 6 6 4 or 5

C.9 a 5, 2, 2, 1, 1 Design (descending) 8 4 1, 2, 3, 4 5

C.9 5, 2, 2, 1, 1 Design (ascending) 8 4 5 4

C.10 5, 2, 2, 1, 1, 1 Design (descending) 8 3 1, 2, 3, 4 5 or 6

C.10 5, 2, 2, 1, 1, 1 Design (ascending) 8 3 6 4 or 5

a

If these designs are NOT the last in a series, there is no position for a check standard.

The “restraint” is another name for the standard used in the comparison. 

Matrices are shown in Technical Note 952. Determine the best design prior 

to beginning the series. The series shown allow calibration of any 

commonly found set of mass standards in the 5, 2, 2, 1 combination or the 

5, 3, 2, 1 combination. See the supplemental job aid spreadsheet associated 

with NISTIR 5672 for many additional weighing designs that identify 

associated restraint and check standard positions, with the associated K1 and 

K2 values needed for calculating between-time standard deviations. 

Measurement Procedure 

Record the pertinent information for all weights being intercompared on a 

suitable data sheet unless an automated data collection system is being used 

to collect the data and create a data file. Record or collect the laboratory 

ambient temperature, barometric pressure, and relative humidity 

immediately before and immediately after each series of intercomparisons. 

3 Calculations 

Calculations are completed by the NIST Mass Code as described in NBS Technical Note 

1127, National Bureau of Standards Mass Calibration Computer Software, R. N. Varner, 

 5

Design a.1.1. with inverted order (y3, y2, and y1), with restraint in position 1 (B) is detailed in SOP 5.
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and R. C. Raybold, July 1980, with updates to conform to the international formula for 

calculating air density and the ISO/IEC Guide to the Expression of Uncertainties as 

described in the NIST Technical Note 1297 and minor error corrections to the original 

code. The Mass Code performs two statistical tests (t-test and F-test) to verify both the 

value of the restraints and check standards, and to verify that the measurement process was 

in control during the comparisons.

Calculating Effective Densities and Coefficients of Expansion for Summations6:

Some designs use a summation mass and sometimes the individual masses of this 

summation will be constructed from different materials that have different densities 

and coefficients of expansion. The following equations will be used to calculate the 

effective density and effective coefficient of expansions for the summation that will 

be needed as input for the data file. The subscripts 5, 3, and 2 refer to the individual 

masses that comprise the summation. This approach may also be needed with a 5, 

2, 2, 1 combination. E.g., a summation of 1 kg, might be 500 g, 300 g, and 200 g 

(or 500 g, 200 g, 200g, and 100 g). A summation for 100 g would be 50 g, 30 g, 

and 20 g (or the equivalent of a 5221 series). A metric calibration of a 4 oz weight 

would need to add up to 113.389 g (probably 100 g, 10 g, 3 g, 300 mg, 100 mg) 

and then must also address unequal nominal values as shown in the equations in 

SOP 4, 5, and 7 as applicable.

532

5 3 2

532

Effective Density MMM

M M M

ρρρ

+ + =         + +       

Eqn. (1)

5 3 2

532

532

5 3 2

532

Effective Cubical Coefficient of Expansion = 

M M M

M M M

ααα

ρρρ

ρρρ

        + +       

        + +       

Eqn. (2)

Table 3. Variables for Above Equations.

Variable Description

M Mass (g)

ρ Density (g/cm3

)

α Cubical Coefficient of Expansion (/°C)

4 Measurement Assurance

4.1.The within process standard deviation is incorporated into the NIST Mass Code and is 

used to conduct an F-test of the observed standard deviation versus the pooled/accepted 

standard deviation of the process at a 95 % confidence level. See NISTIR 6969, Section 

8.9 for details of the F-test. 

 6

Jaeger, K B., and R. S. Davis, NIST Special Publication 700-1, A Primer for Mass Metrology, November 1984.
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4.2.Weighing designs integrate a suitable check standard (See GLP 1, SOP 9 and SOP 30).

4.3.The check standard value is calculated and immediately evaluated to verify that the 

mass is within established limits; a t-test is incorporated to compare the observed value 

against accepted value at a 95 % confidence level. This statistical test is incorporated 

in the NIST Mass Code. See NISTIR 6969, Section 8.16 for details and statistics that 

are used.

4.4.The mean value of the check standard over time is also compared to an appropriate 

reference value of the check standard with respect to their applicable expanded 

uncertainties to evaluate bias and drift over time. Excessive drift or bias must be 

investigated and followed with suitable corrective action. See NISTIR 6969, SOP 9, 

Section 3.6 for assessment methodology.

4.5.Check standard measurement results obtained over time are used to calculate the 

standard deviation of the measurement process, st.

5 Assignment of Uncertainty

The NIST Mass Code generates uncertainties as a part of the data reduction. Proper input 

in the data file is critical for obtaining valid results and is dependent upon a well 

characterized measurement process. See NISTIR 5672 for a discussion on the input for 

standard uncertainties in the data file. Comprehensive calculations of the uncertainties for 

weighing designs must be completed outside of the NIST Mass Code at this time, and a 

supplemental job aid spreadsheet is posted on the NIST OWM website with this SOP for 

that purpose. 

Calculating the standard uncertainty, us, of the starting restraint in the first series:

Usually the starting restraint will be one or several 1 kg (or 100 g) mass standards 

that have calibrations and density determinations from a National Metrology

Institute or an accredited laboratory. The uncertainty of the standard as stated on a 

calibration report is divided by the appropriate coverage factor, dependent on the 

confidence interval stated in the calibration certificate. 

One starting restraint scheme (a single starting standard), where Us is the 

uncertainty from NIST which must be divided by the proper coverage 

factor, k.

s

s

U

u

k = Eqn. (3)
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Multiple starting restraint schemes with standards calibrated at the same 

time against the same starting standards, i.e., dependent calibration (more 

than one starting standard):

1 2

1 2

123

123

, 

 

, .

s s

s

ss s

s

U U

u

k k

or

UUU

u etc

kkk

= +

=++

Eqn. (4)

Multiple starting restraint schemes with standards NOT calibrated at the 

same time as the starting standards, i.e., independent calibration (more than 

one starting standard):

2 2

1 2

1 2

2 2 2

123

123

 , 

 

 

, .

s s

s

ss s

s

U U

u

k k

or

UUU

u etc

kkk

  

= +      

    

= ++          

Eqn. (5)

Calculating the within-process standard deviation, sw, for each series:

For each weighing design, the observed within process standard deviation, sw, 

along with its degrees of freedom, d.f., is pooled using the technique described in 

NISTIR 6969 Section 8.4.

( ) ( ) ( )

k

k k

w df df df

df s df s df s

s ... 

 ... 

1 2

2 2

2 2

2

1 1

+ + +

+ + + = Eqn. (6)

Calculating the between-time standard deviation, sb, for each series:

Establish a standard deviation over time, st, for each check standard over time. If a 

plot of the check standard shows no apparent drift, the between-time standard 

deviation may be calculated. The following formulae are used to calculate the 

between-time standard deviation for the series. If sb

2 is less than zero, then sb is 

treated as zero. See the supplemental job aid spreadsheet associated with NISTIR 
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5672 for many additional weighing designs, and variations on the designs noted in 

this section. The file lists restraint and check standard positions, with the associated 

K1 and K2 factors needed for calculating between-time standard deviations.

Because of the way the Kn values are used to solve for sb, it is possible to get a 

negative value in which case, zero is used as the value for sb. NOTE: K factors as 

used in this section are not the same coverage factors that use the lower case k in 

uncertainty calculations.

For the 3-1 design with a single restraint, and a check standard that is either 

another single weight or a summation, the between time standard deviation 

is calculated using the following formula. The check standard may be in any 

other position.

2 22

1

2

1

2

2 2 2

1

0.8165

1.4142

1 0.8165

1.4142

b tw

b tw

s s Ks

K

K

K

s ss

= −

=

=

= −

Eqn. (7)

Using a 4-1 design with two restraints, and the check standard is the 

difference between the two restraints, the next equation may be used to 

calculate the between-time standard deviation. If another weight in the 

series is used as the check standard, another equation is needed.

2 22

1

2

1

2

2 2 2

1

0.7071

1.4142

1 0.7071

1.4142

b tw

b tw

s s Ks

K

K

K

s ss

= −

=

=

= −

Eqn. (8)

Using a 4-1 design with two restraints, and with a single check standard 

occupying any of the remaining positions, the next equation may be used to 

calculate the between-time standard deviation.

1

2 22

2

1

2

2 2 2

1

0.6124

1.2247

1 0.6124

1.2247

b t w

b tw

s s Ks

K

K

K

s ss

= +

=

=

= −

Eqn. (9)
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Using a 5-1 design with two restraints, and the check standard is the 

difference between the two restraints, the next equation may be used to 

calculate the between-time standard deviation. If another weight in the 

series is used as the check standard, another equation is needed.

2 22

1

2

1

2

2 2 2

1

0.6325

1.4142

1 0.6325

1.4142

b tw

b tw

s s Ks

K

K

K

s ss

= −

=

=

= −

Eqn. (10)

Using a 5-1 design with two restraints, and with a single check standard 

occupying any of the remaining positions, the next equation may be used to 

calculate the between-time standard deviation.

2 22

1

2

1

2

2 2 2

1

0.5477

1.2247

1 0.5477

1.2247

b tw

b tw

s s Ks

K

K

K

s ss

= −

=

=

= −

Eqn. (11)

In the second descending series (C.2), six weights are involved (500 g, 

300 g, 200 g, 100 g, Check 100 g, and a summation 100 g). Calculate the 

standard deviations of the mass values for the Check 100 g (st) and plot the 

results to evaluate the presence or lack of drift. If no drift is present, the 

following formula is used to calculate the between-time standard deviation 

for this series and all subsequent C.2 series. Subsequent series include the 

following check standards: 100 g, 10 g, 1 g, 100 mg, 10 mg, and 1 mg. If 

sb

2 is less than zero, then sb is treated as zero.

2 22

1

2

1

2

2 2 2

1

0.3551

1.0149

1 0.3551

1.0149

b tw

b tw

s s Ks

K

K

K

s ss

= −

=

=

= −

Eqn. (12)
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If a C.1 descending series is used, the following equation is used to calculate 

the between-time standard deviation when the check standard is in either of 

the last two positions:

2 22

1

2

1

2

2 2 2

1

0.4175

1.0149

1 0.4175

1.0149

b tw

b tw

s s Ks

K

K

K

s ss

= −

=

=

= −

Eqn. (13)

The between-time formulae shown here are those that are most common 

and are for descending series only. If another restraint or check standard is 

used, or if an ascending series is used, another formula will be needed. 

These formulae are statistically derived, based on the least squares analysis 

of the weighing design, and assume a normal, non-drifting distribution of 

measurement results. Equations for some other weighing designs may be 

calculated using the NIST Electronic Engineering Statistics Handbook. 

Section 2.3.3.2 “Solutions to Calibration Designs” gives an overview for 

deriving the solutions to weighing designs. It also provides the unifying 

equation for sb (it is called sdays in the electronic handbook). To clarify the 

difference in terminology and notation the unifying equation for sb is 

presented as:

2

1

2

1

2

2

2

1

s K s

K

sdays = −

t

w

days b

s s

s s

s s

≡

≡

≡

2

1

2 2

1

2

2

1

b t w s K s

K

s = − Eqn. (14)

Section 2.3.4.1 “Mass Weights” provides the solutions for 17 weighing 

designs used for decreasing weight sets, 6 weighing designs for increasing 

weight sets and 1 design for pound weights. K1 is found in the portion of 

the solution titled “Factors for Repeatability Standard Deviations”, and K2

is found in the portion titled “Factors for Between-Day Standard 

Deviations”.

Note that there is a supplemental job aid spreadsheet that is available and 

includes many weighing designs with associated K1 and K2 values and the 

equations for calculating between time standard deviations. The latest 

version of this spreadsheet is posted on the NIST website with this Standard 

Operating Procedure. An additional spreadsheet job aid is available for final 

calculations of uncertainty using the output of the Mass Code report. 

Uncertainty associated with bias, ud. Any noted bias that has been determined 

through analysis of control charts and round robin data must be less than limits 
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provided in SOP 29 and may be included if corrective action is not taken. (See 

NISTIR 6969, SOP 29 for additional details.)

Example components to be considered for an uncertainty budget table are shown in 

the following table.

Table 4. Example Uncertainty Budget Table.

Uncertainty Component 

Description Symbol Source Typical Distribution

Uncertainty of the standard 

mass(es) (5.1) us Calibration certificate

Expanded 

uncertainty divided 

by coverage factor; 

combined for 

summations per SOP 

29, restraint 

uncertainties 

assigned based on 

design calculations in 

the associated 

spreadsheet

Accepted standard deviation of 

the process as standard deviation 

over time, within-process 

standard deviation, and between 

time standard deviations (5.2, 5.3)

sp

st

sw

sb

Control chart, standard 

deviation chart

Normal

Calculated based on 

K1 and K2 values for 

designs used

Uncertainty of the buoyancy 

correction ub OIML R111 Rectangular

Air temperature (for air density) ut SOP 2 or OIML R111 Rectangular

Air pressure (for air density) up SOP 2 or OIML R111 Rectangular

Air relative humidity (for air 

density) uRH SOP 2 or OIML R111 Rectangular

Air density (formula) uρa SOP 2 or OIML R111 Rectangular

Mass densities uρm

Measured and reported value

OIML R111 Table B.7

Typically, 0.03 g/cm3 to 

0.05 g/cm3

Rectangular

Uncertainty associated with bias 

(5.4) ud

Control chart, proficiency 

tests

See NISTIR 6969, 

SOP 29

Draft a suitable uncertainty statement for the certificate (e.g.,)

The uncertainty reported is the root sum square of the standard uncertainty of the 

standard, the standard deviation of the process, and the uncertainty associated with 

the buoyancy corrections, multiplied by a coverage factor of 2 (k = 2) for an 

approximate 95 percent confidence interval (95.45 %). Factors not considered in the 

evaluation: magnetism (weights are considered to meet magnetism specifications 

unless measurement aberrations are noted), balance eccentricity and linearity (these 
SOP 28 – 2019 Page 14 of 14

This publication is available free of charge from: https://doi.org/10.6028/NIST.IR.5672-201

9

factors are considered as a part of the measurement process when obtaining the 

standard deviation of the process when using a check standard with adequate 

degrees of freedom.

NOTE: Where inadequate degrees of freedom are available, k, is determined using 

the appropriate degrees of freedom and the 95.45 % column in the table from 

Appendix A of NISTIR 6969, SOP 29.

6 Certificate

See NISTIR 6969, SOP 1, for Preparation of Calibration Certificates. Report 

measurement results as printed in Tables I and II as generated by the Mass Code. 

Actual text of the Mass Code certificate must be modified for each laboratory to be 

ISO/IEC 17025 compliant and to reflect accurate uncertainty values. Report the 

mass, conventional mass, environmental conditions during the calibrations, mass 

density used (reported, measured, or assumed (specify which type is used)), and 

calculated expanded uncertainties with coverage factors. 

Compliance assessments.

Evaluate compliance to applicable tolerances as needed or required by the customer 

or by legal metrology requirements. Decision criteria for uncertainty and tolerance 

evaluations include two components: 1) the expanded uncertainty, U, must be < 1/3 

of the applicable tolerances published in ASTM E617 and OIML R111 standards 

and 2) the absolute value of the conventional mass correction value plus the 

expanded uncertainty must be less than the applicable tolerance to confidently state 

that mass standards are in or out of tolerance. Compliance assessments must note 

the applicable documentary standard and which portions of the standard were or 

were not evaluated.