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SOP 8

Recommended Standard Operating Procedure

for

Medium Accuracy Calibration of Mass Standards

by

Modified Substitution

1 Introduction

This SOP describes procedures to be followed for calibration and conformity 

assessment of mass standards for particular classes of documentary standards (e.g., 

NIST Class F, ASTM1 Class 5, 6, 7 or OIML2 Classes M1, M2, and M3) where the 

uncertainty is usually much smaller than the tolerance application provided the 

laboratory maintains standards and balances used for higher precision work. This 

procedure permits the metrologist to report that the weights being calibrated were 

compared against a reference standard with the results reported on the laboratory 

calibration certificate. The comparison is important because the built-in weights of 

a balance do not represent laboratory standards or provide metrological traceability 

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 limits, but does not eliminate errors due to drift. 

The procedure incorporates measurement assurance steps to ensure the validity of 

the standards and the measurement process through the use of check standards. 

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, OIML R111, and/or NIST Handbook 105-1 documentary 

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. If uncertainty to tolerance ratios 

are greater than required, SOP 7 (single substitution) or SOP 4 (double substitution) 

procedures are preferred. SOP 8 may be used for any nominal values provided 

adequate standards and equipment are available. Detailed measurement ranges, 

standards, equipment, and uncertainties for this SOP are generally compiled in a 

separate document in the laboratory.

Note: When using SOP 8, the laboratory often uses working standards that are 

equivalent or only slightly better than customer’s weights. If this is the case, the 

working standards must have a higher level of calibration than the weights being 

calibrated. Therefore, the laboratory will need standards, balances, procedures, and 

uncertainties better than the customer weights and this procedure to calibrate the 

laboratory working standards.

 1 ASTM International (formerly the American Society for Testing and Materials) publishes the E617 standard for 

mass specifications and tolerances.

2 OIML is the International Organization for Legal Metrology. Weight classes are published in OIML R111, which 

is freely available at http://www.oiml.org.
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Prerequisites

Valid calibration certificates with appropriate values and uncertainties must 

be available for all the standards used in the calibration. All standards must 

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 

not be used to routinely calibrate customer standards using this procedure.

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 the 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 7, SOP 8, SOP 29, and GMP 10. 

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. The laboratory should have demonstrated environmental controls 

for a minimum of 24 hours before a calibration. 

Table 1. Environmental conditions.

Echelon3 Temperature Requirements During a Calibration Relative Humidity

(%) 

III Lower and upper limits: 18 °C to 27 °C

Maximum changes: ± 5 °C / 12 h and ± 3 °C / h 40 to 60 ± 20 / 4 h 

As a practical guideline, a waiting time of 24 hours is recommended for 

weights calibrated with this procedure to become equilibrated in the 

laboratory. If weights are extremely hot or cold additional equilibration may 

be needed to address problems with condensation and frozen surfaces. 

Weights must be completely dry prior to calibration. Minimum 

equilibration times are provided in the following table. 

3 Echelon III corresponds to weights of Classes OIML M1, M2, and M3, NIST Class F or ASTM Classes 5, 6 and 7. 

Uncertainty values must be fully assessed if this procedure is attempted for any higher-class weights. This procedure 

does not provide adequate redundancy for OIML Classes E1 or E2 , ASTM Classes 000, 00, 0, or 1 and SOP 5 or 

SOP 28 must be used. 
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Table 2. Stabilization time.

Temperature Range for the Artifact Minimum

Equilibration Time

Inside upper or lower limits > 18 °C and < 27 °C None 

Outside of upper or lower limits < 18 °C or > 27 °C 24 hours/overnight 

2 Methodology 

Scope, Precision, Accuracy 

This method is applicable to all lower echelon mass calibration 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 calibrated mass standard. 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 calibrated 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 calibrated is determined by 

comparing its reading to the reading obtained for the reference standard. A weight 

is within tolerance when the absolute value of its error plus its uncertainty does not 

exceed the tolerance established for the class of weight. 

Apparatus/Equipment 

Single-pan (Option A and A1), full-electronic balance (Option B), or equalarm balance (Option C) with sufficient capacity for the load calibrated and 

with resolution equal to or less than one-tenth of the applicable tolerance of 

the standards to be calibrated. 

Calibrated working standards, of nominally equal mass to the unknown 

mass standards being calibrated. Mass standards must have an expanded 

uncertainty less than one-tenth of the tolerance calibrated. 

Calibrated sensitivity weights, and tare weights if needed, with current 

calibration certificates selected according to SOP 34. 

Uncalibrated counterweights, T, of approximately the same mass as the 

standard weights (for option C). 

Calibrated environmental equipment to monitor laboratory conditions and 

to perform buoyancy corrections if needed. See SOP 2 for appropriate 

accuracy limits. 
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Procedure - Option A, Use of Single-Pan Mechanical Balance 

Select a reference standard of the same nominal value as the weight being 

calibrated. Place the standard on the balance pan. Adjust the optical scale 

reading (See GMP No. 4) to approximately 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 O1.

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), or another value < 2 % of 

nominal stated by the laboratory, the nominal value of a division can be 

used for tolerance testing.

Remove the sensitivity weight and adjust the optical scale to account for the 

corrected value of the 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. The direction and magnitude of the deviation from 50.0 mg 

indicates the actual deviation of the calibrated weight from nominal. 

Remove the Standard.

Place the weight to be calibrated on the balance pan, read the optical scale 

and record the reading as Xn. 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. E.g., A scale indication of 30.1 mg will indicate that the calibrated 

weight is 19.9 mg lighter than nominal.

After several weights have been calibrated (no more than 10 unknown 

weights may be calibrated without rechecking the standard or check 

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 5 % to 10 % (limits determined by the laboratory) of the tolerance 

applicable to the weights being calibrated 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. The average drift may be 

monitored over time to be included as a component of the uncertainty; 

otherwise 5 % to 10 % of the applicable tolerance, as determined by the 
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laboratory, as a rectangular distribution may be included in the uncertainty 

calculations.

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 A1, Use of Single-Pan Mechanical Balance 

Select a reference standard of the same nominal value as the weight being 

calibrated. 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 O1.

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 the 

sensitivity is within ± 2 % of nominal value (usual case) of the scale 

division), or another value < 2 % of nominal stated by the laboratory, 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 calibrated on the balance pan, read the optical scale,

and record the indication as Xn. Using Eqn. (1) calculate the mass correction 

of the weight. The mass error is the deviation from the nominal value.

Monitor drift. 

After several weights have been calibrated (no more than 10 unknown 

weights may be calibrated without rechecking the standard or check 

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. Evaluate and account for drift per Section 2.8.

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:

1 ( ) CC XO xs n =+ − Eqn. (1)
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Procedure - Option B, Use of Full Electronic Balance 

Select a reference standard of the same nominal value as the weight being 

calibrated. Place the standard on the pan. Zero the balance and record the 

stable reading as O1. A stopwatch may be used to monitor consistent timing 

of balance stability but is not required. 

Add a calibrated sensitivity weight (sw ≥ 2 times the tolerance but not 

exceeding 0.5 % of the balance capacity) and record the reading as O2. 

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. This value may be monitored less frequently 

than each operation if stability of the sensitivity factor has been 

demonstrated and documented.

Remove the sensitivity weight and zero the balance, O3, so weight 

differences, d, can be read directly from the balance indications.

Remove all weights from the balance pan.

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

Xn.

Monitor drift.

After several weights have been calibrated ((no more than 10 unknown 

weights may be calibrated without rechecking the standard and check 

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. Evaluate and account for drift per Section 2.8

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:

1 1 ( ) , when is zeroed CC XO CX O xs n sn =+ − =+ Eqn. (2)
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Procedure - Option C, Use of Equal Arm Balance 

Select a reference standard of the same nominal value as the weight being 

calibrated. 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 needed, add sufficient counterweights to the right pan 

to obtain a sum of turning points of approximately twice the 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 O1.

Add an appropriate calibrated sensitivity weight to the left pan and record 

the sum of the turning points as O2. Calculate the sensitivity using this 

equation:

( 2 1 ) sensitivity = CMsw

O O− Eqn. (3)

where CMsw is the conventional mass of the sensitivity weight.

Remove all weights from the left pan.

Place the weight to be calibrated on the left pan. If the standard used in 2.7.1

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 the left or right pan to obtain an approximate balance and record 

the sum of the turning points as Xn.

Calculate the mass correction of the calibrated weight(s) as follows. 

2.7.5.1 If added tare weights are placed on the left pan (tx).

( ) 1

2 1

) x

sw

x n t

CM C (X O CM

 O - O 

  = − −      

Eqn. (4)

2.7.5.2 If added tare weights are placed on the right pan (ts).

( ) 1

2 1

s

sw

x n t

CM C (X O ) CM

 O O 

  = − +     −  

Eqn. (5)

Monitor drift.

After several weights have been calibrated (no more than 10 unknown 

weights may be calibrated without rechecking the standard or check 

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. Evaluate and account for drift per Section 2.8.
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Drift Evaluation 

Drift effects will normally be very small. If the drift exceeds 5 % to 10 % (limits 

determined by the laboratory, not to exceed 10 %) of the tolerance applicable to the 

weights being calibrated, 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. The average drift may be monitored over time to be included as a component 

of the uncertainty; otherwise 5 % to 10 % of the applicable tolerance, as determined 

by the laboratory, as a rectangular distribution may be included in the uncertainty 

calculations.

Tolerance Evaluation

Compare the correction plus the expanded uncertainty of the calibrated weight(s)

with the tolerance for the class of weights to which it belongs. If the absolute value 

of the correction plus the expanded uncertainty is numerically smaller than the 

tolerance, the weight is within tolerance. If the correction is larger than permissible, 

the weight is 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 closer to the nominal value where possible.

Laboratories may set suitable alternative limits, taking care to ensure that the mass 

value plus (or minus) the uncertainty is within the tolerance limits. 
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Table 3. Example of weighing sequence.

Measurement No. Weights on Pan Observation

1 S O1

2 S + sw O2

3 S O3

4 X1 O4

5 X2 O5

6 X3 O6

7 X4 O7

8 X5 O8

9 X6 O9

10 X7 O10

11 X8 O11

12 X9 O12

13 X10 O13

14 Sc O14

15 S O15

3 Calculations

Air buoyancy corrections are generally not made with the modified substitution, 

although with the use of spreadsheets and the need to record environmental 

conditions, there is no reason why the buoyancy correction may not be routinely 

included (mass densities must be known or assumed). When performed, use SOP 

2, Option B.

Evaluate the sensitivity of the balance:

( 2 1 ) sensitivity = CMsw

O O− Eqn. (6)

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. This value may be monitored less frequently on electronic balances if 

stability of the sensitivity factor has been demonstrated and documented. If 

corrections for sensitivity are not made, an uncorrected systematic error may be 

incorporated into the uncertainty but the balance sensitivity requires periodic 

evaluation; the uncertainty value may be calculated as 2 % of the applicable 

tolerance as the sensitivity is multiplied by the difference between the standard and 

the unknown (d). 

Calculate the conventional mass correction, Cx, for the unknown weight as 

Cx = CMi – Nx, according to the optional sequence used. In each case, the 

conventional mass corrections for the standard weight(s) are included.
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Table 4. Symbols used.

Symbol Description 

CMi Conventional mass of weight i

Ns Nominal value of the standard, S

Nx Nominal value of the unknown, X

Ci Conventional mass correction of weight i

d Measured difference between X and S

Calculate the conventional 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:

CCd x s = + Eqn. (7)

1 ( – ) CC XO xs n = + Eqn. (8)

Note: If an electronic balance is used and zeroed with the standard on the balance, 

O1 is “0" and d becomes the Xn balance reading.

Calculate the conventional 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 = ( Xbalance reading nominal reference point − N ) Eqn. (9)

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:

1 ( ) C C CM CM X O N N x s ts tx n =+ − + − +−s x Eqn. (10)

4 Measurement Assurance

Duplicate the process with suitable check standards for each nominal load or a 

designated number of check standards per balance (See GLP 1, SOP 9, and SOP 

30).

Evaluate the value against the expected limits and plot the check standard value on 

the control chart to monitor changes over time.

All values must be entered in the control chart, even if failing this statistic, unless 

a mistake (i.e., typographical error) is identified and corrected, to ensure the 

variability obtained for the process is not unduly reduced over time. The observed 

value of the check standard is compared to the accepted mean value of the check 

standard and divided by the standard deviation for the check standard observations 

over time. 
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A t-test may be incorporated to check the observed value of the check standard 

against the accepted value using the following equation and a 95 % confidence 

level. The t-statistic is calculated for stability analysis. This equation monitors 

stability over time, but should not be used to assess for bias. A calculated t-value 

less than two is within the warning limits of the process. A calculated t-value 

between two and three represents a value between the warning limits and 

control/action limits. A calculated t-value exceeding three represents a value 

outside of the control/action limits and suitable action must be taken. Calculated 

values of the t-statistic may also be monitored over time to determine the presence 

of drift.

( ) p

c c

s

S S

t − =

Eqn. (11)

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

standard deviation of the measurement process, sp.

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 SOP 9, Section 3.5.3

and Section 8.16 for assessment methodology.

Where SOP 9 is followed and check standards are used for 2 to 3 nominal values 

per balance, more frequent calibration intervals may be needed to monitor the 

working standards and the larger standard deviation of the nominal values 

bracketing the nominal value should be used. If check standards were already 

checked on a given day and found to be in control, additional evaluations may be 

conducted, but are not required.

5 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, uo. 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 an approximate 95 %

level of confidence. See SOP 29 for the complete standard operating procedure for 

calculating the uncertainty. 

The expanded uncertainty for the standard, U, is obtained from the calibration 

certificate. The combined standard uncertainty, uc, is used and not the expanded 

uncertainty, U, therefore the reported uncertainty for the standard will usually be 

divided by the coverage factor k. Where the coverage factor or confidence interval 

is not given, the laboratory should either contact the calibration provider to obtain 

the correct divisor or use a value of k = 2, assuming that the expanded uncertainty 

was reported with an approximate 95 % confidence interval (95.45 %).
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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. Where the standard deviation 

of the measurement process from the control chart is less than the resolution of the 

balance being used, the laboratory may round up to the value of the balance division 

or use the larger of the standard deviation of the process or the following estimate 

for repeatability is used to represent the standard deviation of the process:

0.6

3 p

d s d = ≈ Eqn. (12)

Uncertainty associated with allowable drift. Include the monitored average drift for 

each balance and procedure as a rectangular distribution, or include a value that is 

between 5 % and 10 % of the applicable tolerance (limit set by laboratory policy) 

for the weight, again as a rectangular distribution. Whenever the drift exceeds the 

limit of drift stated by the laboratory, conduct a root cause analysis to determine 

the cause; this situation may require fewer weights to be calibrated in the weighing 

series, service of the balance, better environmental controls, additional training, and 

practice by the metrologist, or increasing the allowable drift limits (not to exceed 

10 %). 

Uncertainty associated with allowable sensitivity error, use. This procedure allows 

for up to 2 % error (stated by the laboratory) in the optical or electronic range of 

use. This may result in calibration errors up to 2 % of the applicable tolerance. This 

is potentially another uncorrected systematic error that may be treated as a 

rectangular distribution. This value may be monitored less frequently than each 

operation if stability of the sensitivity factor has been demonstrated. Whenever the 

sensitivity error exceeds the limit stated by the laboratory, conduct a root cause 

analysis to determine the cause; this situation may require service of the balance, 

better environmental controls, additional training, and practice by the metrologist, 

or increasing the allowable sensitivity error limits (not to exceed 2 %).

Uncertainty associated with uncorrected air buoyancy. When buoyancy corrections 

are not made, the resulting uncorrected systematic error may be treated as a

rectangular distribution, with the magnitude of the maximum uncorrected buoyancy 

correction determined using equations provided in SOP 2. The uncertainty 

associated with air density and its associated factors may be considered negligible 

for this procedure or may be calculated using the options provided in SOP 4 or 5. 

Uncertainty associated with bias that is observed in the check standards as 

determined through analysis of the control charts. When bias is observed in the 

control charts, it must be assessed according to the equations provided in SOP 29

and may be incorporated as an uncorrected systematic error using the equations in 

SOP 29.

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

the following table.
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Table 5. Example uncertainty budget table.

Uncertainty Component Description Symbol Source Typical 

Distribution

Uncertainty of the standard mass(es) (5.1) us Calibration certificate Normal divided by 

coverage factor

Accepted standard deviation of the process 

(5.2) sp

Control chart, standard 

deviation chart

Normal or 

estimated 

rectangular if actual 

sp is less than 

balance resolution

Uncertainty of the allowable drift (5.3) udrift

5 % to 10 % of the 

tolerance (stated by lab) Rectangular

Uncertainty of the allowable sensitivity 

error (5.4) use

SOP 8, < 2 % of the 

sensitivity times the 

applicable tolerance

Rectangular

Uncertainty of the maximum magnitude of 

the buoyancy correction (5.5) ub SOP 2 Rectangular

Uncertainty associated with bias (5.6) ud

Control chart, proficiency 

tests See SOP 29

Draft a suitable uncertainty statement for the certificate. For example: 

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. 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 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

Report results as described in SOP No. 1, Preparation of Calibration Certificates.

Report the conventional mass, environmental conditions during the calibrations, 

and calculated expanded uncertainties with coverage factor(s).

Conformity assessment.

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, OIML R111, and/or NIST 

Handbook 105-1 documentary standards and 2) the absolute value of the 
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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.
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Appendix - Modified Substitution Data Sheet

Laboratory data and conditions: 

Operator Before After

Date Temperature

Balance Pressure

Load Relative Humidity

Standard deviation of the 

process, from control chart, sp

Degrees of Freedom

Mass standard(s) data:

ID Nominal Mass 

Correction*

Expanded Unc: 

from cal. certificate

Unc: 

k factor

Density

g/cm3 

S

tS

X TBD TBD TBD

tx

Sc

tSc

sw

*Mass Correction = True Mass with buoyancy correction. Mass Correction = Conventional Mass with no buoyancy correction. 

Observations:

Observation No. Weights (Insert ID of X) Balance Observations, Units

Time:

1 (O1) S

2 (O2) S + sw

Error < 2 % of optical scale or electronic range? _____Yes_____No

3 (O3) S

4 (O4) X1

5 (O5) X2

6 (O6) X3

7 (O7) X4

8 (O8) X5

9 (O9) X6

10 (O10) X7

11 (O11) X8

12 (O12) X9

13 (O13) X10

14 (O14) (See Section 4.5) Sc

15 (O15) S 

Time: Drift < Specified Tolerance Limit? _____Yes_____No

Check Standard in Control? _____Yes_____No

Up to 10 unknown weights may be checked with this procedure if the drift is less than tolerance limits specified by the laboratory. 
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