ASTM E2554 for Estimating and Monitoring the Uncertainty of Test Results
ASTM E2554 Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method in a Single Laboratory Using a Control Sample Program
7. Overall Procedure - Control Charting Methods
7.1 General concepts of control charts are described elsewhere, such as in Manual 7A.
7.2 The general procedure involves two major phases: Preliminary and Monitoring.
7.2.1 Preliminary Phase:
7.2.1.1 This phase begins with an initial collection of test results.
7.2.1.2 Preliminary control charts are then prepared and examined. These charts are evaluated to determine if the process is in a state of statistical control. The usual principles of control charting utilize short-term variability to estimate the limits within which samples of test results should vary. For control sample programs this short-term variability is equivalent to repeatability precision. It is expected, however, that additional contributions to variation will be present over time and therefore additional variation, equivalent to intermediate precision, will be encountered.
7.2.1.3 An estimate of uncertainty standard deviation is developed.
7.2.1.4 An uncertainty control chart is then prepared to monitor future sample results.
7.2.2 Monitoring Phase:
7.2.2.1 The proposed uncertainty control chart is used to provide evidence that the estimate of uncertainty is not exceeding the estimated value.
7.2.2.2 The estimate of uncertainty should be periodically re-evaluated.
7.2.2.3 Where appropriate, it is recommended that a standard control chart also be maintained to determine whether the variation over time has been reduced to the level of short-term variation (repeatability).
7.3 Two types of control charting methods are recommended to develop estimates of uncertainty. These include:
7.3.1 Mean (Xbar) and range or standard deviation charts are used when multiple test results are conducted in each time period.
7.3.2 Individual charts (IndX) are used when single test results are obtained in each time period.
7.4 Variation Estimates:
7.4.1 Either a range chart or a standard deviation chart may be used to estimate the short-term variability when multiple assays are conducted under repeatability conditions per time period. An estimate from the control chart data can be compared to other estimates of repeatability (within laboratory, short-term variation) if available.
7.4.2 Sample averages are examined and may provide estimates of variation caused by other factors. Such factors may include environmental effects, operator factors, reagents, or instruments.
7.5 Systematic Procedures:
7.5.1 Specifically designed experiments can be used to ensure all known sources of variation, such as operators (analysts), equipment, reagents, or instruments are incorporated in the general study.
7.5.2 The data generated from this program is available for additional uses, such as control charting to evaluate trends, stratification by analysis, or stratification by equipment to identify training or maintenance needs or both.
8. Specific Procedures
8.1 Multiple Test Results Generated per Time Period:
8.1.1 A specified number of independent test results are taken during each time period. Generally this number is 5 or less. It is preferred that at least 25 sets of test results be obtained before developing the charts.
8.1.2 Either a range chart or a standard deviation chart is prepared. This is examined for special cause variation. If the variability appears random then an estimate of repeatability is computed. This may be done by pooling the sums of squares, using the average standard deviation, or using the average range.
NOTE 1 - If the ranges or standard deviations are zero in most of the samples, then this estimate of repeatability standard deviation is suspect and probably unusable. This is usually the result of insufficient resolution of the measurement system in use or severe rounding. An estimate based on the minimum interval size should be substituted for the zeros. As a rule of thumb, consider replacing the zeros when more than about 1/3 are zeros.
8.1.3 A means chart is used to examine variation among time periods. Limits on this chart permit comparison of variation between time periods using repeatability as the estimate of error.
8.1.3.1 If the control chart shows a state of statistical control then the uncertainty will be assumed approximately equivalent to the repeatability standard deviation.
8.1.3.2 In most cases it will be expected that the variability between means will show an "out of control" condition indicating that there are "special" causes of variation in addition to repeatability. The between means variation and within means repeatability estimates are then used to compute an estimate of uncertainty standard deviation.
8.1.4 Using the estimate of uncertainty standard deviation an Uncertainty Control Chart is prepared for future monitoring of the uncertainty. This chart may include control limits for means as a possible lower set of control limits along with the uncertainty control limits based on the estimate of uncertainty.
8.2 Individual Tests:
8.2.1 Single tests are generated at each time period. Variation among these results is evaluated.
8.2.2 In some cases, it is possible to incorporate external estimates of repeatability obtained from prior or concurrent studies.
