NB/SH/T 0843-2023 Evaluation of petrochemical industry testing systems - Statistical techniques

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1. Method number / full name / English name / replacement relationship

• Standard number: NB/SH/T 0843—2023
• Chinese full name: Evaluation of petrochemical industry testing systems - Statistical techniques
• English name: Evaluate analytical measurement system performance of petrochemical industry—Statistical techniques
• Replacement relationship: Replaces NB/SH/T 0843—2010 "Evaluation of petrochemical industry analytical testing systems - Statistical techniques". Compared with the 2010 edition, apart from structural adjustments and editorial changes, the main technical changes are given in the foreword a) to z) (including changing the document name, changing the normative references, changing terms and definitions/abbreviations/symbols, changing 6.2.2 and 6.2.2.1, changing 7.1 to 7.1.1 and adding 7.1.2, deleting 7.3.2, symbolizing formulas, changing 8.3 and adding a working procedure diagram, changing "less than 15" to "fewer than 20" in 8.4.1, changing 8.6.2/8.6.3, changing 8.7.2/8.7.3 and adding 8.7.4/8.7.5, adding 8.8/8.9, adding 9.4, changing multiple places in Annex A, changing Annex B, adding Annex C, etc.).
• Publication/implementation: Published on 2023-02-06, implemented on 2023-08-06.
• Secretariat: Subcommittee on Petroleum Fuels and Lubricants of the National Technical Committee for Standardization of Petroleum Products and Lubricants (SAC/TC280/SC1).
• Proposer: China Petrochemical Corporation.
• Drafting organizations: Luoyang Technology R&D Center of Sinopec Engineering (Group) Co., Ltd., Sinopec (Luoyang) Technology Co., Ltd.
• Main drafters: Jia Ran, Wang Guiying, Li Yi, Bai Zhengwei, Lü Dawei.
• Annex attributes: Annex A is a normative annex; Annexes B and C are informative annexes.
• Previous versions: First published in 2010 as NB/SH/T 0843—2010; this is the first revision.

2. Scope of application and non-applicability

• This document specifies the procedure design and operating methods for continuous monitoring of the stability, precision and bias of petroleum and petroleum product testing systems using some generally accepted statistical control procedures and tools.
• It applies to stable testing systems whose results are expressed as continuous numerical values, such as laboratory methods or confirmed online testing systems; it also applies to monitoring the difference between two testing systems that measure the same property, provided that both testing systems have been evaluated by the statistical methods described in ASTM D6708 and the system bias is appropriate.
• Note: This document does not list all selection conditions applicable to the testing systems of this document, nor all conditions for determining the frequency of application of this document. Factors to be considered: (1) the frequency of use of the testing system; (2) the criticality of the parameter being measured; (3) the system stability and precision obtained from historical data; (4) economy; (5) requirements of regulations, contracts or test methods.
• Note 1: For determination of the effectiveness of a univariate online testing system, reference may be made to ASTM D3764.
• Note 2: The two testing systems that measure the same property may be laboratory methods or confirmed online testing systems.
• This document assumes that for a testing system under statistical control, a normal distribution is sufficient to describe and predict its behavior. Note: For non-normally distributed processes, these tools may be applied after transforming the test results; for further guidance, consult a statistician.
• Not applicable: The control chart methods and workflows described in this document are not applicable to final results calculated by combining multiple separate testing systems or to different instruments running the same test method (see 3.1.2 Note 2).

3. Method principle

According to industry-recognized test methods, use the testing system to periodically measure QC samples and check standard materials, and use control charts and other statistical techniques to screen, plot and interpret the test results in order to determine the statistical control state of the testing system; as quality control data increase, calculate and periodically update the statistical estimates of the precision and bias of the testing system. As part of a separate effectiveness verification process, QC samples and check standard materials may be randomly distributed to the testing system as blind samples or double-blind samples for routine measurement to verify whether the calculated precision and bias can represent the routine operation of the testing system.

4. Reagents and materials (purity / preparation)

This document is a statistical techniques method; the source text does not contain chemical reagents and solution preparation content. The "materials" involved are reference material types:

• QC sample (quality control sample): a stable and homogeneous substance whose physical and/or chemical properties should be similar to those of typical samples measured by the testing system; it needs to be properly stored, ensure sample integrity, have sufficient quantity, and be usable for a long time (3.1.23).
• Check standard material (check standard): a material with an accepted reference value used to determine the accuracy of the testing system; preferably a certified reference material traceable to a national primary standard, or a material with an accepted reference value determined through interlaboratory testing; for some testing systems, a pure single-component compound with a known value or a mixture with a calculated value obtained by simple mass/volume mixing may be used (3.1.4 and note).
• Effectiveness verification sample (VA sample): a QC sample or check standard material used to verify the precision and bias estimated from routine quality assurance tests (3.1.20).
• Requirements for the accepted reference value (ARV) of the check standard material: when prepared from a material tested by multiple testing systems under reproducibility conditions, ARV should be the average of the test results after statistical testing and removal of outliers; when the average of interlaboratory comparison samples is used as ARV, its standard deviation should be calculated from at least 16 non-outlier results conforming to a normal distribution (each participating laboratory provides one test result), and this standard deviation must be statistically smaller than the reproducibility standard deviation of the test method; the F test may be used to check whether the result is acceptable (6.2.2).
• Note 1: The uncertainty of ARV is inversely proportional to the square root of the number of values used in calculating the average; the bias test in this standard assumes that the uncertainty of ARV is negligible relative to the precision of the testing system; if fewer than 16 values are used in calculating the average, this assumption may not hold (6.2.2 Note 1).
• Note 2: Examples of acceptable comparison tests include CNAS and laboratory comparison activities authorized by the Certification and Accreditation Administration of the People's Republic of China, or ASTM D02.CS92 ILCP procedures, ASTM D02.01 N.E.G, ASTM D02.01.A regional exchanges, and international quality assurance comparison programs managed by the Alberta research committee, etc. (6.2.2 Note 2).
• Example: Pure solvent 2,2- dimethylbutane may be used as a check standard material for measuring Reid saturated vapor pressure (SH/T 0794) (6.2.3).
• QC sample storage warning: Properly store samples to ensure that they remain stable, intact and homogeneous during storage and use; volatile samples (such as gasoline) stored in large containers are likely to lose light components due to repeated opening and closing, and may be stored by cooling the sample and dispensing it into small containers, but the amount in each small portion should be sufficient for one test; oxidizable samples may be dispensed into small containers, filled with inert gas before sealing, and kept sealed until use (6.1.6 warning).

5. Instruments and equipment

This document is a statistical techniques method; the source text does not contain a list of dedicated instruments and equipment. The equipment/system concepts involved are:

• Testing system (measurement system): a system comprising one or more components or subsystems (such as a sampler, test equipment, instrument, display device, data processor, printing or output device, etc.) that measures a property of an unknown sample according to a test method (3.1.2).
• Note: A standard test method (for example, GB/T 17144, SH/T 0175) is an example of a testing system (3.1.2 Note 1).
• Online testing system: When using QC samples to monitor the operation of an online testing system, it is very useful to equip it with a device having automatic extraction, mixing, storage and transfer functions (6.1.1 note).
• For handling after instrument replacement or repair, see 8.9.

6. Recommended operating conditions

• Test QC samples and check standard materials under laboratory intermediate precision conditions (7.4.1). Note: It is inappropriate to use data obtained under repeatability conditions to estimate the long-term precision obtained under laboratory intermediate precision conditions (7.4.1 note).
• Laboratory intermediate precision conditions: conditions under which test results are obtained by one or more operators, at the same location, using the same testing system that may include multiple components or subsystems, according to the same test method, over a period of not less than 15 days, on samples randomly drawn from the same sample (3.1.15). Note: It is necessary to include fluctuations from all sources in normal long-term operation; all operators who routinely use the testing system need to provide data; when the test method is used with relatively high efficiency and multiple QC test results can be obtained within 24h, only test results obtained at intervals of at least 4h may be used to calculate intermediate precision (3.1.15 note).
• Main factors for determining test frequency: 1) the frequency of use of the testing system; 2) the criticality of the parameter being measured; 3) the system stability and precision obtained from historical data; 4) economy; 5) requirements of regulations, contracts or test methods (7.4.2).
• It is recommended to analyze QC samples immediately at the beginning of a series of tests or after a change to the testing system (7.4.3).
• The test procedure developed needs to ensure that all personnel who routinely operate this system participate in testing QC samples (7.4.4).
• Handle and test QC samples and check standard materials in the same way and under the same conditions as routine test samples (7.4.5).
• Unless otherwise specified in the method, QC samples and check standard materials should be randomly inserted for testing during normal operation of the testing system (7.4.6). Note: Avoid special treatment of QC samples to obtain good results (7.4.6 note).
• Control chart recommendations: individual observation control chart (I chart), range control chart of two measurements (MR chart), applying criterion 1 (additional run rules) or criterion 2 (EWMA) (8.3.1).
• For the EWMA exponential weighting factor λ, 0.2 to 0.4 is recommended (A.5.2.2). Note: λ=0.4 better simulates the operating effect of traditional control charts, and λ=0.2 can better predict the next measurement value; when λ=0.2, it is 1σ, and when λ=0.4, it is 1.5σ (A.5.2.2 note).
• Minimum data collection requirement: at least 20 data must be collected (with preprocessing if necessary) before initial evaluation can be performed (8.4.1); if after discarding suspicious data the data are insufficient, fewer than 20, testing should continue to supplement them and then screening should be repeated (8.4.2).
• Note: Some examples in Appendix A have not been updated and use 15 data points to illustrate calculation and plotting methods; however, this is not intended to negate the mandatory requirement of a minimum of 20 data points (A.1 note).

7. Sampling and Test Sample Preparation

• QC sample preparation (6.1): select a material that is stable, homogeneous, and similar in properties to typical samples (6.1.1); estimate the quantity required per batch to meet the amount needed by the test system and the amount needed for statistical purposes within the expected time period (6.1.2); collect the sample into a container and store it separately (6.1.3); mix thoroughly to ensure homogeneity (6.1.4); perform necessary measurements to ensure the characteristics meet the intended use (6.1.5); package and/or store according to the requirements of the specific test system to ensure that all samples taken from a batch of QC samples have the same properties; if necessary, subdivide the sample in 6.1.3 into smaller containers to ensure integrity over a long period (6.1.6).
• Preparation of check standard material (6.2): a commercially available standard reference material may be used as check standard material when it is suitable in quantity, quality, and composition (6.2.1); it may also be prepared from a material that has been tested by multiple test systems under reproducibility conditions (6.2.2); for some test systems, a single-component pure substance with a known value or a simple mixture with a calculated value may be used (6.2.3).
• VA sample distribution (6.3, 7.7.1): QC samples and check standard materials may be randomly distributed to test systems as blind samples or double-blind samples for routine determination.
• Blind sample distribution: when distributing quality control samples and check standard material samples for analysis, the analyst is not told the expected value (3.1.9).
• Double-blind sample distribution: when distributing check standard materials or quality control samples for analysis, the analyst is not told the expected value of the sample, nor whether it is a check standard material or a quality control sample (3.1.13).
• Retained sample retesting (7.7.2.3): retain previously analyzed samples and retest them as unknown samples under intermediate precision conditions in the laboratory; usually, because retained samples do not have ARVs, only precision data can be obtained; generally, the difference between replicate determination data is plotted on a control chart to estimate precision; if precision depends on the level of the measured value, the result difference is expressed in units of the standard deviation of the test system precision at the mean of the two test results.

8. Analytical Procedure

8.1 Pretreatment of Test Results (8.2)

• Purpose of pretreatment: to standardize the scale of the control chart so that data obtained from multiple check standard materials or different batches of QC samples with different levels can be compared on one chart (8.2.1).
• If different QC samples are plotted on different control charts in actual measurement units, pretreatment is not required (8.2.2).
• Case 1: when all test results come from one or more batches of check standard material with the same ARV, or when the test system precision does not change with the level of the measured value, use formula (1): Ii = Yi − Xi (8.2.3.1).
• Case 2: when test results come from multiple batches of check standard material with different ARVs, and the test system precision changes with the level of the measured value, use formula (2): Ii = (Yi − Xi) / √(sARV² + σARV²) (8.2.3.2). Here sARV is the standard error at the ARV value level (related to the ARV uncertainty, provided by the check standard material provider); σARV is the intermediate precision standard deviation at the ARV level. If ARV is obtained from multi-laboratory test data, the standard error of ARV may be calculated by statistical theory methods using the standard deviation of non-outlier and normally distributed data from multiple laboratories (see 8.2.3.3 note). If ARV is not obtained from multi-laboratory test data, the user should use acceptable techniques to determine the standard error at the ARV value level (8.2.3.3). Note: It is recommended that the method for determining the standard error of ARV be established under the guidance of a statistician (8.2.3.3 note).
• Pretreatment of VA sample results is the same as in 8.2.2 and 8.2.3 (8.2.4).

8.2 Control Charts (8.3)

• It is recommended to use I chart, MR chart, criterion 1 (additional run rules), or criterion 2 (EWMA) for: (a) routine recording of test results for QC samples and check standard materials; (b) timely assessment of whether the test system is in statistical control. The I chart can detect sudden special causes that cause large deviations from the expected value of QC samples; criterion 1 or criterion 2 can identify small sustained changes or drifts in the entire test system; the MR chart can identify changes in the overall fluctuation of the test system (8.3.1). Note: The control charts and statistical techniques selected in this document are simple and easy to use, but this does not mean that equivalent or more advanced methods cannot be used (8.3.1 note).
• Control chart plotting is divided into two stages (8.3.2): the first stage includes evaluation of initial measurement results (for QC samples) and establishment of a control chart using representative evaluation results and statistical values; the second stage includes evaluation of subsequent test results for QC samples in time sequence using the expected values determined in the first stage, as well as periodic re-evaluation of the expected statistical values of all results, and updating the expected statistical values determined in the first stage when necessary; the main process refers to Figure 1.

8.3 Evaluation of Initial Results and Establishment of Control Charts (8.4)

• Use evaluation techniques to evaluate test results collected during the initial establishment stage of the test system or after major changes; at least 20 data must be collected (with preprocessing if necessary) before the following evaluation can be performed; the purpose of the evaluation is to determine that these data are suitable for establishing a control chart (see A.4 for details) (8.4.1). Note 1: These techniques can also be used to diagnose whether the system is out of control (8.4.1 note 1). Note 2: During the first stage of data collection, users may use the procedures described in 8.7.2.3, 8.7.3 (Q procedure), or 8.7.4 to monitor the performance of the test system (8.4.1 note 2).
• Screening suspicious data: for pretreated data, first screen out data that are inconsistent with other data (for example, data with transcription errors); then the generalized extreme studentized deviate GESD (see ASTM D7915) technique or other equivalent statistical techniques may be used for outlier evaluation; data considered suspicious must be investigated; data discarded at this stage must have definite evidence; if after discarding suspicious data the data are insufficient, fewer than 20, testing should continue to supplement them and then screening should be repeated (8.4.2).
• Screening abnormal situations: check for non-random situations, such as deviation in only one direction, abnormal clustering, cycling, etc.; the data may be plotted on a run chart (see A.3) and then the plotted points checked; if non-random situations exist, find the root cause, discard this set of data, and restart the evaluation procedure (8.4.3).
• Verify the normality assumption, data independence, and sufficient resolution: for a test system with no operating history, or as a diagnostic tool for initial data from a new batch of QC samples, it is very useful to determine that the data from the test system are independent, have sufficient resolution, and can be described by a normal distribution; this can be determined using a normal probability plot and the Anderson-Darling test (see A.4); if the results show a clear deviation from a normal distribution, or clearly insufficient measurement resolution (see A.4), refer to the guidance for case 2 in A.4.2.6 (8.4.4). Note: Data may become normally distributed after transformation, but such techniques are beyond the scope of this document (8.4.4 note).
• Establish control charts (8.4.5): if there are no obvious abnormal situations on the run chart and no obvious deviation from a normal distribution, begin establishing control charts (see A.5.1 to A.5.3).
  • I chart: calculate the center line and control limits and plot them on the run chart to generate the I chart (8.4.5.1).
  • Plot the MR chart and check for abnormal situations; if there are no obvious abnormal situations, calculate and plot the center line and control limits on the MR data point chart to complete the MR chart (8.4.5.2).
  • EWMA overlay chart: for the second stage, the EWMA values may be calculated and plotted on the I chart; calculate the EWMA control limits and plot them on the I chart (8.4.5.3).
• Use of control charts: regularly plot the pretreated data on these charts and interpret them immediately (8.4.6).

8.4 Use and Interpretation of Control Charts (8.5)

• Use the rules for control charts (see A.5) to determine whether the test data support the assumption that the test system is affected only by random variation (statistically controlled) (8.5.1).
• Detailed investigation of out-of-control points: as long as the assignable cause is considered not to be part of the normal process, after further data analysis, those out-of-control data caused by assignable causes should be excluded; regardless of whether the test system is in a controlled state or an out-of-control state, all data must be recorded (8.5.2).

8.5 Scheme for Periodically Updating Control Chart Parameters 1 (8.6)

• Scheme 1 applies to: control charts for accumulated test data of the same batch of QC samples or check standard materials when the system has not changed (8.6.1).
• After at least 20 new controlled data have been collected, perform an F test on the sample variance of the new data set and the sample variance used to calculate the control limits of the current control chart (see A.8). If the F test is not significant, and the number of data points used to calculate the current control limit values is fewer than 100, then statistically pool the old and new sample variances, use the updated pooled variance to calculate the current control limits, and if updated (see 8.6.2.2), calculate the center line of the I chart (the I used in formulas A.11–A.16) (8.6.2).
• If the F test result is not significant, and the number of data points for the sample variance used to calculate the current control limits is more than 100, then whether to statistically pool the old and new sample variances and whether to update the control limits of the current control chart shall be left to the user's own consideration and decision (8.6.2.1).
• If the F test result is not significant, then use the average of the new data, the current center line of the I chart, and the current control chart standard deviation used to calculate the control limits of the I chart (σR′) to calculate the t value according to formula (3). If all of the following conditions are met, it is permitted to recalculate and update the center line of the I chart to reduce its statistical uncertainty: (1) |t| ≤ 1.7; (2) the current EWMA value is on one side of the center line for fewer than 65% (8.6.2.2). Note: The value 1.7 is based on a one-sided t test with a significance level of 5% and degrees of freedom from 40 to 250, rounding the data to one decimal place (8.6.2.2 note).
  • Formula (3): t = (x̄newdata − Īcurrent) / [σR′ · √(1/n1 + 1/n2)]. Where Īcurrent is the current center line of the I chart (the arithmetic mean calculated using all controlled results without including the new test results described in 8.6.2); x̄newdata is the arithmetic mean of the new test results described in 8.6.2; n1 is the number of data used to calculate Īcurrent; n2 is the number of data used to calculate x̄newdata.
  • As a safeguard against slow drift in one direction that is below the recognition capability of control chart rules, when four consecutive rising or falling data points appear on the same side of the center line of the I chart, it is necessary to use a check standard material to verify the accuracy of the test system; according to ASTM D6617, determine the acceptable tolerance interval (8.6.2.2) for the difference between the obtained result and the accepted reference value (ARV) of the check standard material. Note: The standard deviation may be pooled or not pooled, depending on whether it is pooled in 8.6.2.1 (8.6.2.2 note).
• If the F test result is significant, investigate the assignable cause; if it is determined that the new variance represents the current system performance, then use the new sample variance to calculate the control limits of the current control chart (8.6.3).

8.6 Scheme for periodically updating control chart parameters2 (8.7)

• Scheme 2 applies to: control charts where the current QC sample is exhausted and the system undergoes an assignable cause change due to changing the QC sample (8.7.1). Different batches of QC samples may vary in properties to a greater or lesser extent; since the calculation of the control limits of the I chart requires an intermediate value determined by the test system, a specific conversion process is needed to ensure that the intermediate value of the new batch of QC samples is established using statistically controlled measurement results; this document lists two conversion procedures for the user to choose from.
• If any of the following conditions is met, the statistics (Īachieved, σachieved, MRachieved) of the I chart and MR chart established with similar QC samples may be used for the new batch QC sample conversion technique described in this chapter: (1) the reproducibility (Rpub) published by the test method does not change with level; (2) for a test method where reproducibility (Rpub) is expressed as a function, the ratio [Rpub@Ī_achieved / Rpub@1st new QC rest] is between 0.85 and 1.15, where Rpub@Ī_achieved is the reproducibility published by the test method at the level Īachieved, and Rpub@1st new QC rest is the reproducibility published by the test method at the level of the new batch of QC samples (8.7.1).
• Procedure 1: simultaneous testing (8.7.2).
  • When the current QC sample cannot satisfy the analytical sample amount for 20 times, collect and prepare a new batch of QC samples (8.7.2.1).
  • When testing the existing QC sample, simultaneously test and record the data of the new batch of QC samples; if the results of the existing QC sample prove that the process is in a controlled state, then the data of the new batch of QC samples are considered valid (8.7.2.2).
  • In order to indicate the status of the new batch of QC samples as early as possible, a run chart and a MR chart may be plotted immediately; after collecting 5 valid results of the new batch of QC samples, use the average of the 5 data as the trial control limit for the center line, use the σachieved of the previous control chart in 8.7.1 to calculate the trial control limit for the upper control limit, and convert the run chart into a I chart; similarly, MRachieved may also be used to calculate the trial control limits of the MR chart (8.7.2.3).
  • After collecting at least 20 controlled results of the new batch of QC samples, use the sample variance of the new data σ²newdata and the sample variance of the data in 8.7.1 σ²achieved to perform the F test; when the F test result is not significant and the reproducibility Rpub published by the test method is expressed in functional form, use the average of the new data set to evaluate R, thereby confirming that the ratio [Rpub@Ī_achieved / Rpub@1st new QC rest] is between 0.85 and 1.15; if the above ratio is confirmed to be between 0.85 and 1.15, and the number of data used to calculate σachieved is less than 100, then statistically pool the variance of the samples (formula A.31) and MR (formula A.30), use the square root of the pooled variance and MR as the new σR′, MR, and establish new I chart and MR chart as described in 8.7.2.7 (8.7.2.4).
  • If in 8.7.2.4 the F test result is not significant, the ratio is between 0.85 and 1.15, and the number of data points used to obtain the above ratio exceeds 100, it is recommended to perform statistical pooling according to 8.7.2.4, but the user may also consider whether to perform statistical pooling on their own; if statistical pooling is not performed, then σachieved and MRachieved are used as σR′, MR, and establish new I chart and MR chart as described in 8.7.2.7 (8.7.2.5).
  • If in 8.7.2.4 the F test result is significant, investigate the assignable cause; if it is determined that the new variance can represent the current system performance under the influence of random factors, then use σachieved and MRnewdata as the new σR′, MR, and establish new I chart and MR chart as described in 8.7.2.7 (8.7.2.6).
  • Complete the first-stage evaluation according to the methods from 8.4.1 to 8.4.4; according to 8.4.5, establish a new I chart and MR chart for the new batch of QC samples [may superimpose EWMA (rule 2)] (8.7.2.7).
  • When the existing QC sample is used up, switch to the new I chart and MR chart (8.7.2.8).
• Procedure 2-A: Q procedure (see A.9) (8.7.3).
  • The purpose of this process is to reduce the workload of simultaneously testing two kinds of QC samples; it requires predetermining the standard deviation of the test system (σknow); the σachieved that meets the requirements in 8.7.1 can be used as the σknow for this purpose; starting from the second result, for each new quality control result, calculate the Qr statistic and compare it with its theoretical average (0) and 3σ limit (±3); for details, see A.9 (8.7.3.1). Note: It is recommended that the standard deviation estimate be obtained from at least 50 data points (8.7.3.1 note).
  • When the Q procedure is running (at least 2 data points), it can provide quality assurance by jointly using the MRachieved of the MR and 8.7.1 established from observed values (8.7.3.2).
  • After accumulating 20 data points (Q procedure), execute the steps from 8.7.2.4 to 8.7.2.7; since the Q procedure is technically equivalent to the I control chart procedure, the user may follow the steps in 8.7.2.7 to establish a new I/MR control chart for the QC sample, or use the new QC sample to continue running the Q chart and MR chart separately to monitor the stability and precision of the measurement process (8.7.3.3).
  • Each new batch of QC samples must start a new Q chart (8.7.3.4).
  • Usually the Q chart and MR chart can be used for results preprocessed according to the situations in Chapter 8.2, situation 1 and situation 2; for situation 1, the standard deviation must be the standard deviation applicable to the check standard material; for situation 2, the standard deviation is 1, because formula (2) standardizes the data to a normal distribution (8.7.3.5).
• Procedure 2-B: The dynamically updated I/EWMA chart is essentially a I chart and EWMA chart with changing control limits, where the control limits are updated as each new result is obtained, and the control limits calculated from all previous results are used to judge whether the new result is controlled; the dynamic update combines the σknow of a single result with the changing standard error, which is related to the center line calculated from all previous results; as the number of results used for calculation increases, this standard error (for the I chart) steadily decreases, while for EWMA, the standard error usually first decreases and then increases toward its asymptotic value; for details, see A.10 (8.7.4).
• Run program 2-B in conjunction with the MR chart of 8.7.3.2; after accumulating at least 20 controlled data points, execute the steps from 8.7.2.4 to 8.7.2.7; since program 2-B is technically equivalent to the steps of the I chart, the user may follow the instructions of 8.7.2.7 to establish a new I/MR control chart for a new batch of QC samples, or continue to use the new batch of QC samples to execute program 2-B and run the MR chart to monitor the stability and precision of the testing process (8.7.5).

8.7 Short-term operation phase (8.8)

The procedures described in 8.7.3 and 8.7.4 can also be used to address short-term operation situations, when a single batch of QC samples can only provide a limited number (fewer than 20) of QC test results, and completely replacing them with identical QC samples is infeasible or impossible; in this case, because there is insufficient data to properly characterize the batch mean, these procedures can only be used to monitor the stability and precision of the measurement process.

8.8 After instrument replacement or repair (8.9)

Use the procedures described in 8.7.3 and 8.7.4 to address the following situations: when an instrument is taken out of service and replaced by another qualified instrument, or when an instrument is returned to service after major modification (such as replacement of critical components or factory recalibration). For these situations, it is assumed that the existing precision data remain valid; use the existing precision data together with the MR chart to monitor the stability and precision after update or overhaul, respectively. After accumulating sufficient data, a statistical evaluation should be conducted to confirm that the above assumption holds, or to update the system precision parameters. Using the existing precision data allows the test system to be put into use immediately, while providing a quality assurance to prevent the performance of the updated or overhauled test system from being statistically worse than the previous system. The use of these procedures is supplementary to the means required for qualification confirmation of the updated instrument, such as calibration and running check reference materials.

8.9 Evaluating system performance using precision and bias (Chapter 9)

• Evaluate laboratory intermediate precision from test results of QC samples (9.1): use the σR′ estimated by the root-mean-square (rms) formula in the currently valid I chart (see 8.6, 8.7) to estimate the intermediate precision of the test system for a specific sample type and measurement level: R′ = 2.77 × σR′ (Formula 4) (9.1.1).
  • In addition, when the data have no autocorrelation (see A.4), R′ can be estimated by multiplying 2.46 by the MR on the MR chart of QC samples, according to Formula (5): R′ = 2.46 × MR (9.1.1.1). Note: The standard deviation of laboratory intermediate precision (σR′) is estimated from the MR chart: σR′ = MR / 2.77 = MR / 1.128 (9.1.1.1 Note).
  • To estimate the standard deviation of laboratory intermediate precision (σR′) using retained results, first calculate the differences between the original values and the re-measured values of samples with the same nominal value, apply the root-mean-square formula (Formula 6) to the differences to obtain the standard deviation of the differences; if the precision of the test system is independent of the sample level, the differences obtained from samples with different measurement values can be used directly; otherwise, use pairs of samples with the same nominal value (generally within 2R) to estimate the standard deviation at that value; divide the standard deviation of the differences by 1.414 to obtain the estimated standard deviation of laboratory intermediate precision (σR′) (Formula 7) (9.1.1.2).
    • Formula (6): ds = √[Σ(did − d̄)² / n]. Where ds is the standard deviation of the differences; did is an individual difference; i is the index of the difference; n is the total number of differences.
    • Formula (7): σR′ = ds / 1.414. Where ds is the standard deviation of the differences.
  • If possible, compare R′ with the reproducibility at the same level in the method; R′ should be less than or equal to this value; use the χ² test described in A.7 (9.1.2).
• Estimate the bias of the test system from multiple test results of a single check reference material (9.2): calculate the bias of the test system using multiple data obtained from the same check reference material; after collecting at least 20 results of the same check reference material under intermediate precision conditions, calculate the mean of all individual differences that are controlled and plotted on the I chart; perform a t test to determine whether the mean is statistically different from 0 (see A.6) (9.2.1). If the t test result shows that the mean is statistically not different from 0, then the bias of the test system can be ignored (9.2.2). If the t test result shows that the mean is statistically different from 0, then the best estimate of the bias of the test system at the check reference material level is the mean; if the user considers the bias to be of practical significance, investigate the root cause and take corrective action (9.2.3).
• Estimate the bias of the test system from test results of multiple check reference materials (9.3): when multiple check reference materials are used, determine whether there is a relationship between the test result level and the bias (9.3.1); plot the pretreated results obtained as described in Chapter 8 against the corresponding ARV, and check from the plot whether the bias depends on the test value (9.3.2); if the bias does not depend on the test value, perform a t test as in 9.2 to determine whether the mean of the pretreated differences in the I chart is statistically different from 0 (9.3.3). If the t test result shows that the mean is statistically not different from 0, then the bias of the test system can be ignored (9.3.3.1); if the t test result shows that the mean is statistically different from 0, then the test system has bias; the bias may depend on the test value; however, statistical methods for estimating the relationship between bias and test value are beyond the scope of this document (9.3.3.2). If 9.3.2 shows that the bias depends on the test value, then the bias of the test system is related to the magnitude of the test value; statistical methods for estimating the relationship between bias and test value are beyond the scope of this document (9.3.4). If 9.3.3.2 shows bias, or 9.3.4 shows that the bias depends on the test value, find the root cause; if there is evidence of correlation between bias and level, or the user wishes to rigorously determine the relationship between bias and level for multiple check reference materials, it is recommended to use the ASTM D6708 method under the guidance of a statistical expert (9.3.5).
• Evaluate measurement uncertainty from the laboratory intermediate precision of the test system (9.4): obtain the laboratory intermediate precision σR′ of the test system according to the method of clause 9.1 (9.4.1); under laboratory intermediate precision conditions, estimate the bias of the test system according to the method of clause 9.2 or 9.3; if the test results of the test system pass the t test, it indicates that the bias of the test system is not statistically significant compared with 0, so the laboratory intermediate precision can be used to evaluate the measurement uncertainty of the test system; for detailed steps, see the example in Appendix B, and refer to ASTM D6792 (9.4.2).

8.10 Verifying the effectiveness of system operation using VA samples (Chapter 10)

• If the user decides to use VA samples in the quality assurance program, it is necessary to periodically evaluate the test results of VA samples; the purpose of the evaluation is to determine whether the system operation status described in Chapter 9 is applicable to the analysis of routine samples (10.1).
• The testing of VA samples shall be conducted in the form of internal or external supervision, and