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SOP 30

Recommended Standard Operating Procedure

for a 

Process Measurement Assurance Program

1 Introduction

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 using this 

Standard Operating Procedure (SOP). See also NISTIR 6969, SOP 9, and 

NISTIR 7383, SOP 17 and 20. 

Prerequisites

A Standard Operating Procedure for the calibration that describes 

and provides rigor and consistency in the calibration process.

Check standards that represent the standard and/or the items to be 

calibrated. Check standards must 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 reference 

values must be determined by a higher level of calibration than the 

procedure being monitored, and preferably using an independent 

standard, process, or laboratory competent to work at that level. As 

a minimum, the check standard may be calibrated within the 

laboratory only if qualified to work at the next higher level and using 

a procedure one level higher than the calibration process to be 

controlled. 

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).

A calculating system for statistical control that calculates standard 

deviations, control limits, F-tests, t-tests, root-sum-of-the-squares 

(RSS), and creates control charts. 
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2 Summary 

Scope 

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 

and warning limits. The limits are used to establish process uncertainties 

and to control future measurement performance.

Methodology Description

Process Measurement Assurance Program (PMAP) is used for defining, 

measuring, analyzing, improving, and controlling the measurement process 

and uncertainty as the calibration is performed through the use of suitable 

check (control) standards. The uncertainty includes effects of the 

measurement instrument, the operator, the procedure, the standards, and the 

environment over time. 

Each process is modeled to meet the following objective for determining 

and controlling 1) the measurement process; 2) the calibration and check 

standards; or 3) a balance of both the process and the standards. 

The check standard is selected to evaluate the standard deviation of the 

process, sp, other process uncertainties, uo such as material density or air 

density accuracy, and possible bias, ud of the process (see SOP 29). Initial 

measurements for the check standard should be performed immediately 

after calibrating the reference or working standards and after the servicing 

of the measurement instrument. 

Control measurements of the check standard are graphed on control charts 

for visual examination of process performance and are evaluated against 

statistical control limits. 

Statistical tools, F-tests 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 control limits; and when evaluating uncertainty statements.
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Table 1. Symbols and descriptions.

Symbol Description

Sc Control measurement of check standard

Scs Accepted value of check standard

U Expanded Uncertainty (of the process)

uc Combined standard uncertainty

us Standard uncertainty of the standard

uo Standard uncertainty of other factors

ud Standard uncertainty of differences

sp Standard deviation of the process

k Coverage factor

3 Procedure

Define the System to be Monitored

Define and 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 (us). 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 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 (us), the PMAP measurement may vary from the 

calibration process to allow inserting the check standard 

measurement close to the measurement of the calibration standard. 

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.
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Define and Calibrate Check Standards

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, Sc, should be calibrated to establish its accepted 

value 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 1⁄4 

as often) than the calibration standard. For example, 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 being calibrated to evaluate the two 1000 g calibration 

standards. The selected check standard should be calibrated using a 

calibration standard other than the calibration standard(s) it will be 

controlling.

Measure – Perform Initial Measurements 

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, initial control chart 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.

Make the control measurements by duplicating the calibration 

process where the check standard is substituted for the calibrated 

item. Measure the check standard and determine its calculated value 

by completing calculations as described in the calibration SOP.
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Record the calculated value of the check standard. Evaluate the 

initial bias (difference) between the mean of the measured check 

standard values and the accepted value for Sc from its calibration 

report. Use the normalized error process as defined in SOP 9 to 

evaluate the bias, considering uncertainties of both the observed 

mean value and the calibrated reference value of the check standard. 

If a simple check of the bias shows that it is within one standard 

deviation, more extensive analysis, such as that described in SOP 9,

is not required. 

Bias (deviation) of check standard = Observed mean of Sc –

Accepted Sc

Repeat the initial measurements 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, at least 30 are recommended for estimates and 

control of uncertainties.

Analyze – Create and Prepare Control Charts

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 is identified near the center of the chart. The y-axis of the 

control chart should extend plus and minus three standard deviations 

from the mean ( ) x of the control measurements. Control 

measurements may be charted as deviation from the accepted value 

of the check standard or as the observed measurement result, or as a 

calculated correction. However, care must be taken to understand 

the impact of updating calibration values for the standards on the 

data maintained in the charts. (For example, it is generally preferred 

to plot the calculated mass or conventional mass rather than to track 

the history of the observed differences to another standard or 

instrument as it is possible not all measurement influences will be 

included in the difference value depending from what data the 

difference is calculated.)

Plot initial measurements on the control chart and evaluate it with 

reference to the accepted value of the check standard. Record the 

date, time, and information tags with data.
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Establish control chart parameters by calculating the mean and the 

estimate of the standard deviation,sp of the check standard reference 

measurements. Control chart parameters to establish limits are as 

follows: 

Reference Line = Calibrated Check Standard value, S

c

Mean Line =

x of measured 

S

c data

3s Action Limits=

x ± 3 

s

p

2s Warning Limits=

x ± 2 

s

p

Process Bias =MeasuredS

c

– Calibrated S

c value

Establish Reference Limits 

Establish reference control limits 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.

Analyze Process Performance at Specific Intervals

3.3.5.1 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.

3.3.5.2 Evaluate current process performance using the control 

measurement results 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 ensure detection of changes in the 

calibration uncertainty statements.

3.3.5.3 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 
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deciding when to recalibrate calibration standards and 

service the measurement instrument. 

Use the F-test to evaluate if a significant change in the 

standard deviation or process performance has occurred.

2

 large

2

 small

( ) F-test = 

( )

p

p

s

s

Eqn. (1)

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 between sequential 

samples of data (e.g., old and new). 

new old

2 2

new old

new old

(bias ) (bias ) t-test = 

( ) ( )

n

p p s s

n

−

+

Eqn. (2)

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. Keep track of 

the signs and trends associated with bias over time.

Improve the Process 

Take action based on the results of statistical evaluation. If F-tests and ttests reveal no significant change in process performance, use the current 

data analysis to establish new process reference limits, control chart and 

uncertainty statements. 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-tests 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 against 

established reference limits until the next calibration interval.
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Control the Process

Measure Check Standards 

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 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 reference standards, the frequency of control 

measurements should be less than 1⁄4 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 changes in the calibration standard being controlled.

Continue the measurement assurance procedure 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 procedure.