MS-QA_06-2019 rev5

MS-QA 2019 2 Companion Guidance Section B— Development of Performance Criteria MS-QA Companion Guidance Section B Development of Quality System-Specific Performance Criteria The limits in MS-QA are based upon a conservative estimate of industry performance. Most measurement systems will exhibit smaller imprecision and bias errors. It is possible to use more restrictive limits that can be more helpful. To make the control charts useful for specific measurement systems, the default warning and control limits can be updated using the results of QC checks following statistically defensible control limit generation algorithms. One way to set the "in control" precision error level is to initially use a level prescribed in MS-QA that is recognized by industry and EPA as a goal for precision. It is based on a 10 percent COV (corresponding to a 14 percent RPD). After at least 20 pairs of measurements are plotted, it will become apparent whether the 10 percent COV (or 14 percent RPD) is appropriate for your system. If it is not, a new control chart should be prepared so that the warning and control limits are set at the correct probability limits for your system. It can be shown (Iglewicz and Myers 1970, EPA 600/9-76-005; U.S. EPA 1984) that when the expected precision is a constant function of the mean, control limits can be expressed in terms of the COV. COV=S/Xm; where S is the variance or the square of the standard deviation, and Xm is the mean or average of the two measurements. One method for obtaining percentiles for the distribution of the COV is to apply a chi-squared (X2) test: X2n-1 ≈ B[(n-1)COVn2/(n+(n-1)COVn2)] (Equation 1) where: B = n[1 + (1/COV2)]; COVn = the observed COV of the nth pair (the pair that is to be evaluated); and COV = the "in control" COV (e.g., 10 percent at levels greater than 4 pCi/L). For duplicates, where n=2, Equation 1 becomes X2 = [2 + (2/COV2)][COVn2/(2 + COVn2)] (Equation 2) To illustrate using the chi-squared (X2) test, we will use example data provided in the MS-QA Companion Guidance Section A for Time Sequence Control Charts . 1 st One calculates “B”: B = n[1 + (1/COV2)] Using the example data that produced a “COV” based on a series of duplicates, t his spreadsheet formula “2*(1+(1/(COV*COV))) = B” produced a “B” value of 847.8063125. 2 nd For calculating the warning level, use chi-squared=3.84 This spreadsheet formula “SQRT((2*3.84)/(“B”-3.84))” using chi-squared=3.84 produced the value 0.09539334 as a COV. This value times 1.414 converted to an RDP warning level of 13% 3 rd For calculating the control limit, use chi-squared=6.64 This similar formula “SQRT((2*6.64)/(“B”-6.64))” using chi-squared=6.64 produced the value 0.12564873 as a COV. This value times 1.414 converted to an RDP control limit of 18%