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SOP 17 

Standard Operating Procedure for

Control Charts of Check Standards 

1 Introduction 

Purpose 

This procedure may be used to develop and maintain control charts to monitor the 

statistical control of laboratory check standards when replicate measurements are 

made as a part of the standard operating procedure. This procedure may be used for 

volume, length, time, or other calibrations when replicate measurements are made. 

See SOP 20 for standard deviation charts.

Prerequisites 

The procedure to be monitored must match the calibration procedure that is 

used.

Either a check standard at each nominal value is used or a set of check 

standards are selected to monitor the range of items that are calibrated by 

the laboratory. 

Equipment 

A check standard is required and should be constructed of similar materials 

and design as the standards or devices under calibration. Check standards 

are maintained in the laboratory as a surrogate for items submitted for 

routine calibration. Examples of check standards might include a quality 

assurance reference flask (QARF), a test measure, an extra length standard,

or a stopwatch, taking care that all check standards are sufficiently similar 

to those submitted for calibration to obtain a suitable standard deviation of 

the measurement process and similar stability over time. 

All equipment designated in the applicable SOP. 

2 Procedure 

Summary 

A check standard is obtained and calibrated several times initially to establish a 

reliable mean value and to estimate the standard deviation of a calibration process 

using the applicable SOP to define the applicable measurement assurance. A 

reference value should be obtained from a suitable calibration laboratory or may be 

determined in the laboratory by using a more accurate and precise calibration than 

the one that will be monitored provided that the laboratory has adequate training 

and has demonstrated competency using the better procedure. Directions for 

preparing and using a control chart for monitoring the mean ( x ) and the standard 

deviation chart are given. The x control chart monitors the process with respect to 

both the standard and the variability, while the standard deviation chart monitors 
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its short-term precision. When the calibration process is determined to be in a state 

of statistical control, the calibrations made at that time may be considered valid and 

the standard deviation of the measurement process may be included in uncertainty 

calculations using SOP 29.

Note: If a full evaluation of potential bias is desired, it is best if the reference value 

of the check standard is provided by an outside laboratory accredited to perform the 

applicable calibrations taking care to ensure that the calibration provider has a 

sufficiently small uncertainty.

Measure: Obtain Initial Measurements

Calibrate the check standard a minimum of 12 times on different days to 

establish the baseline chart. A calibration is defined as the result of replicate 

measurements as required by the SOP (i.e., a complete test consists of the 

number of runs specified in the SOP). Calibrations may be made on 

successive days, but no two complete tests should be made on any single 

day. Note: 25 to 30 points are needed to determine valid uncertainties.

Tabulate the measurement data using the notation and a form such as the 

one contained in the Appendix of this SOP. The appendix provides an 

example for duplicate runs only; modifications are needed when other 

replicates are used. The data may be maintained in a spreadsheet or other 

electronic program in lieu of a paper form.

Analyze the Measurement Data

A standard deviation may be calculated for each set of runs according to the 

appropriate SOP. A pooled standard deviation is then determined for the 

measurement process. When all the runs have the same number of 

replicates, each test will have the same number of degrees of freedom and 

an average of the standard deviations may be used. Use of a standard 

deviation of replicate measurements is preferred to the use of Range charts

(see SOP 20 for guidance on Range charts).

Construction of Control Charts. See also SOP 9.

Construct the following control charts using the data of section 2.2.

Construct an x control chart for a check standard with the following control 

limits:

Reference value: (when available)

Central Line: x (mean of the average values)

Lower warning limit (LWL): 2

p x − s

Lower control (or action) limit (LCL): 3 p x − s

Upper warning limit (UWL): 2

p x + s

Upper control (or action) limit (UCL): 3 p x + s
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Construct a Standard Deviation chart using the same approach. You may 

use 2 and 3 as the respective multipliers for the Upper Warning Limit and 

Upper Control Limits, or see SOP 20. Note that there will be no negative 

numbers when calculating standard deviations.

Interpret Control Chart Data 

Demonstration of "in control" status indicates that the calibration process is 

consistent with the past experience of the laboratory. That is to say, there is 

no reason to believe that excessive systematic error or changes in precision 

have occurred. 

To the extent appropriate, the precision of measurement of the check 

standard may be extended to the calibration of other standards of similar 

nominal size made by the same measurement method.

Extension of the sp for the check standard to other calibrations assumes that 

all aspects of its calibration correspond to those for the other calibration. 

 
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Control the Measurement Process 

An appropriate check standard is calibrated each time the laboratory 

performs calibrations using the SOP or on a set periodic basis if many 

calibrations are performed by the laboratory. If the calibrations extend over 

several days, the check standard is calibrated daily. The values of x and sp

for each calibration of the check standard are plotted on the respective 

charts, preferably in sequential order. The limits on the charts are such that 

95 % of the values should fall within the warning limits and rarely should a 

value fall outside of the control limits, provided the system is in a state of 

statistical control.

If the plotted value of x lies outside of the control limits and the 

corresponding value on the standard deviation chart is within the control 

limits, a source of systematic error is suspected. 

If the values for the standard deviation chart fall outside of the warning 

limits but inside of the control limits, a decrease in precision is indicated. 

Other problems should be investigated.

No calibration data should be accepted when the system is out of control.

If the plotted values for either x , or sp are outside of the warning limits but 

inside of the control limits, a second set of duplicate calibrations should be 

made. If the new values are within the warning limits, the process may be 

considered in control. If they lie outside of the warning limits, lack of 

control is indicated. Investigation actions should be taken and attainment of 

control demonstrated before calibration measurements are considered 

acceptable. 

Even while the system is in an apparent state of control, incipient troubles 

may be indicated when the control data show short- or long-term trends, 

shifts, or runs. The t-test and F-test may be used to assess the significance 

of such observations (see NIST IR 6969 Sections 8.9, 8.10, and 8.11).
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Appendix

Check Standard Data for Control Chart

Check Standard Identification Nominal Value _____________

Test

Number Date Run 1 Run 2A Average of 

Runs

Standard 

deviation

1

2

3

4

5

6

7

8

9

10

11

12 

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

A Additional columns will be needed when replicate runs beyond two are used.
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This publication is available free of charge from: https://doi.org/10.6028/NIST.IR.7383-2019