1、Designation: D7783 13Standard Practice forWithin-laboratory Quantitation Estimation (WQE)1This standard is issued under the fixed designation D7783; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A numbe
2、r in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.NoteBalloted information was included and the year date changed on March 28, 2013.1. Scope1.1 This practice establishes a uniform standard for com-putin
3、g the within-laboratory quantitation estimate associatedwith Z % relative standard deviation (referred to herein asWQEZ%), and provides guidance concerning the appropriateuse and application.1.2 WQEZ%is computed to be the lowest concentration forwhich a single measurement from the laboratory will ha
4、ve anestimated Z % relative standard deviation (Z % RSD, based onwithin-laboratory standard deviation), where Z is typically aninteger multiple of 10, such as 10, 20, or 30. Z can be less than10 but not more than 30. The WQE10 %is consistent with thequantitation approaches of Currie (1)2and Oppenhei
5、mer, et al(2).1.3 The fundamental assumption of the WQE is that themedia tested, the concentrations tested, and the protocolfollowed in the developing the study data provide a represen-tative and fair evaluation of the scope and applicability of thetest method, as written. Properly applied, the WQE
6、procedureensures that the WQE value has the following properties:1.3.1 Routinely Achievable WQE ValueThe laboratoryshould be able to attain the WQE in routine analyses, using thelaboratorys standard measurement system(s), at reasonablecost. This property is needed for a quantitation limit to befeasi
7、ble in practical situations. Representative data must beused in the calculation of the WQE.1.3.2 Accounting for Routine Sources of ErrorThe WQEshould realistically include sources of bias and variation thatare common to the measurement process and the measuredmaterials. These sources include, but ar
8、e not limited to intrinsicinstrument noise, some typical amount of carryover error,bottling, preservation, sample handling and storage, analysts,sample preparation, instruments, and matrix.1.3.3 Avoidable Sources of Error ExcludedThe WQEshould realistically exclude avoidable sources of bias andvaria
9、tion (that is, those sources that can reasonably be avoidedin routine sample measurements). Avoidable sources wouldinclude, but are not limited to, modifications to the sample,modifications to the measurement procedure, modifications tothe measurement equipment of the validated method, and grossand
10、easily discernible transcription errors (provided there wasa way to detect and either correct or eliminate these errors inroutine processing of samples).1.4 The WQE applies to measurement methods for whichinstrument calibration error is minor relative to other sources,because this practice does not
11、model or account for instrumentcalibration error, as is true of quantiation estimates in general.Therefore, the WQE procedure is appropriate when the domi-nant source of variation is not instrument calibration, but isperhaps one or more of the following:1.4.1 Sample Preparation, and especially when
12、calibrationstandards do not go through sample preparation.1.4.2 Differences in Analysts, and especially when analystshave little opportunity to affect instrument calibration results(as is the case with automated calibration).1.4.3 Differences in Instruments (measurement equipment),such as difference
13、s in manufacturer, model, hardware,electronics, sampling rate, chemical-processing rate, integra-tion time, software algorithms, internal signal processing andthresholds, effective sample volume, and contamination level.1.5 Data Quality ObjectivesFor a given method, onetypically would compute the lo
14、west % RSD possible for anygiven data set. Thus, if possible, WQE10 %would be computed.If the data indicated that the method was too noisy, one mighthave to compute instead WQE20 %, or possibly WQE30 %.Inany case, a WQE with a higher % RSD level (such asWQE50 %) would not be considered, though a WQE
15、 with RSD20), thedistribution may be distorted by the random nature of samplingalone. As a general rule, if there were no bias, then on averageand over a large sampling, a truly uncensored set of zero-concentration (blank) data would have a mean of zero withapproximately half of the results being ne
16、gative values and halfpositive, and be Normally distributed. If some positive ornegative bias were present, the percentages would shift.However, in general the frequency should be higher near themean of the values and should decline as the concentrationsmove away from the mean, with approximately ha
17、lf of thenon-mean data above and half below the mean.(1) Blank data are considered suspect if: (1) there is novariation in these data, (2) there are an inordinate number ofzero values (and no negative values) relative to the frequenciesof positive values (6.2.3 above), (3) if there is a high frequen
18、cyof the lowest value in the data set (for example, whereminimum-peak-area rejection has been used) relative to thefrequency of higher concentration values, and few or no lowervalues, or (4) a frequency graphic does not begin to approxi-mate a bell curve (when there are 20 or more samples).(2) If th
19、e distribution of the data is suspect, the literature,plus instrument-software and equipment manuals, should beconsulted. These documents can provide an understanding of:(1) the theory of operation of the detection system, (2) thesignal processing, calibration, etc., and (3) other aspects of theconv
20、ersion of response to reported values. Judgment will beneeded to determine whether to use some or all of thetrue-concentration-zero (blank) data, or to exclude the datafrom the calculations. In general, if less than 10 % of thezero-concentration data are: (1) censored, (2) suspect, or (3)false-zeros
21、, then these “problem” data should be removed.Only the remaining blank data are used in the WQE calcula-tions; there must be at least six replicates. Where the zeroD7783 134concentration is excluded or is not possible to obtain, it isimportant to include a true concentration as close as possible toz
22、ero in the study design.(3) Where 75 % or less of the data are censored orsmoothed, and there are at least six remaining values, it isreasonable to use statistical procedures to simulate the distri-bution that is missing or smoothed. Software procedures arecommercially available. Additionally, proce
23、dures such as log-normal transformation may be used to accommodate data thatare not normally distributed. The presence of zero-concentration in the study data and in theWQE is not as criticalas inclusion of such data in the WDE calculations. Therefore,the decision about inclusion or exclusion of zer
24、o-concentrationdata in a WQE data set should weigh: (1) the number of otherconcentrations available, (2) the range of the otherconcentrations, and (3) the risk of extrapolation of the WQEoutside the data-set concentration range against the quality ofthe zero-concentration data.6.2.3.2 True Concentra
25、tions Near ZeroAs with concen-tration zero, true concentrations very near to zero may alsohave been censored, smoothed, and contain false-zeros. Ex-amination of these very low concentrations, as above for zeroconcentration, is important. The likelihood of occurrence andthe percentage of data affecte
26、d decreases with increasingconcentration.6.3 Data Screening, Outlier Identification, and Outlier Re-moval:6.3.1 Data that are to be the input to the WQE calculationshould be screened for compliance with this practicesconditions, appropriateness for the intended use of the WDE,obvious errors, and ind
27、ividual outliers. Graphing of the data(true versus measured) is recommended as an assistive visualtool. This graphic is available in the DQCALC software.6.3.2 Outlying individual measurements must be evaluated;if determined to be erroneous, they should be eliminated usingscientifically-based reasoni
28、ng. Identification of potential outli-ers for data evaluation and validation may be accomplishedusing statistical procedures, such as the optional one providedin the DQCALC software, or through visual examination of agraphical representation of the data. WQE computations mustbe based on retained dat
29、a from at least six independentmeasurements at each of at least five concentration levels. Thedata removed and the percentage of data removed must berecorded and retained to document the WQE calculations.6.4 Modeling Standard Deviation versus TrueConcentrationThe purpose is to characterize the intra
30、labora-tory measurement standard deviation (ILSD) as a function oftrue concentration, = G (T). The relationship is used for twopurposes: (1) to provide weights (if needed) for fitting themean-recovery model and (2) to provide the within-laboratorystandard deviation estimates crucial to determining t
31、he WQEs.NOTE 3See Caulcutt and Boddy (5) for more discussion of standarddeviation modeling and weighted least squares (WLS) in analyticalchemistry.6.4.1 This practice utilizes four models as potential fits forthe IntraLaboratory Standard Deviation (ILSD) model. Theidentification process considers (t
32、hat is, fits and evaluates) eachmodel in turn, from simplest to most complex, until a suitablemodel is found. See Carroll and Ruppert (6) for furtherdiscussion of standard-deviation modeling. The model order isas follows:Model A Constant ILSD Model!:s 5 g1error (1)where:g = a fitted constant.Under M
33、odel A, standard deviation does not change withconcentration, resulting in a relative standard deviation thatdeclines with increasing T.Model B Straight 2 line ILSD Model!:s 5 g1h 3 T1error (2)where:g and h = fitted constants.Under Model B, standard deviation increases linearly withconcentration, re
34、sulting in an asymptotically constant relativestandard deviation as T increases.Model C Hybrid ILSD Model!:s 5 $g21 h 3 T!2%121error (3)where:g and h = fitted constants.Under Model D, within-laboratory standard deviation in-creases with concentration in such a way that the relativestandard deviation
35、 declines as T increases, approaching anasymptote of h.Model D Exponential ILSD Model!:s 5 g 3 exp$h 3 T%1error(4)where:g and h = fitted constants.Under Model D, within-laboratory standard deviation in-creases exponentially with concentration, resulting in a relativestandard deviation that may initi
36、ally decline as T increases, buteventually increases as T increases.6.4.1.1 In all cases, it is assumed that g 0. A value of g s1, where smaxis themaximum sample standard deviation of measurements,made at concentration,Tmax. Otherwise, set h0=0.X2.1.1.3 Compute the natural log of the estimated stand
37、arddeviation, lssk, for each Tk, using the current estimates, gjandhj:lssk5 f Tk! (X2.1)where we definef Tk! 5 ln=gj21hj2Tk2X2.1.1.4 Compute the difference (residual), rk, between thelog sample standard deviation and estimated log standarddeviation for each k:rk5 lsk2 lssk(X2.2)Note that rkis the na
38、tural log of the ratio of the samplestandard deviation to the estimated standard deviation, so rkrepresents log-proportional error, and is ideally equal to zero.X2.1.1.5 Compute fgk, the slope (that is, numerical deriva-tive) of f(T) with respect to g, for each k:fgk5 gj/exp$2 lssk% (X2.3)X2.1.1.6 C
39、ompute fhk, the slope of f(T) with respect to h, foreach Tk:fhk5 hjTk!2/exp$2 lssk% (X2.4)X2.1.1.7 Compute the following intermediate statistics:u=k(fgk)2v=k(fhk)2c=k(fgkfhk)d = 1/uvc2p=k(fgkrk)q=k(fhkrk)X2.1.1.8 Compute the jth step changes to g and h (made toreduce the sum of squared residuals), a
40、nd % relative changes:g=d(vpcq) dg%=100|g/gj|h=d(uqcp) dhT% = 100 | h/ hj|TmaxX2.1.1.9 Compute new g and h estimates:gj115 gj1g (X2.5)D7783 139X2.1.1.10 If dg% 0, so there is sufficient evidence ofcurvature to warrant using the Hybrid Model (Model C).FIG. X4.1 Reported Concentration Measurement (ppb
41、) Versus True Concentration (ppb); Each Concentration With Weighted LeastSquare-Line Fit (above) and (below) ResidualsTABLE X4.2 Bias-Correction Adjustment Factors for SampleStandard Deviations Based on n Measurements (at a particularconcentration)An 2345678910aprimen1.2 1.1 1.0 1.064 1.0 1.0 1.036
42、1.0 1.053 28 85 51 42 31 28AFor each true concentration, Tk, the adjusted value sk= aprimensprimekshouldbe modeled in place of sample standard deviation, sprimek. For n 10, use theformula, aprimen=1+4(n-1)-1. See Johnson and Kotz (7).TABLE X4.3 Straight-Line OLS Fit of s on TStandard Deviation = s =
43、 g + hT = 0.06498 + 0.12678 TSummary of FitRSquare 0.896432RSquare 0.875719AdjRoot Mean Square Error 0.212178Parameter EstimatesTerm Estimate StandardErrort-Ratio Prob |t|g 0.064976 0.110288 0.59 0.5814D7783 1311X4.1.8 Model C, the Hybrid Model, is used to fit the samplestandard deviation data in Ta
44、ble X4.1, using NLLS solved byNewtons-method iteration, as presented in the appendix. Thesteps are as follows:X4.1.8.1 Compute the natural log sample standarddeviation, lsk, for each true concentration, Tk. See Table X4.1.X4.1.8.2 Let j be the index of iteration, and set j=0.Compute initial values,
45、g0and h0, as follows:g05 s15 0.173 (X4.1)h05 smax2 s1!/Tmax2 T1! 5 0.140 (X4.2)See Table X4.5.X4.1.8.3 Compute the natural log of the estimated standarddeviation, lssk, for each k, using the current values of gjand hj(not shown).X4.1.8.4 Compute the residuals rk= lsklsskfor each k (notshown).X4.1.8.
46、5 Compute fgk= gj/exp2 lssk for each k (notshown).X4.1.8.6 Compute fhk=hj(Tk)2/ exp2 lssk for each k (notshown).X4.1.8.7 Compute intermediate statistics: u, v, c, d, p, and q.See Table X4.5.X4.1.8.8 Compute the jth-step changes to g and h (see TableX4.5):g=d(Vpcq) dg%=100|g/gj|h=d(Uqcp) dhT% = 100 |
47、 hj|TmaxX4.1.8.9 Compute the new g and h (see Table X4.5):gj+1=gj+ ghj+1=hj+ hX4.1.8.10 Iterate (increase j by 1, and return to X4.1.8.3)until dg%|t|g (Intercept) 0.0649765 0.048621 1.34 0.2524h (slope w.r.t. T) 0.1267813 0.008496 14.92 0.0001Q (coefficient of q) 0.0129282 0.002774 4.66 0.0096TABLE
48、X4.5 Summary Statistics from Newtons Method Fit of Hybrid Modelj ghuvcdpqg h dg% dh T%0 0.173 0.1400 73.11 176.87 27.77 8.22E05 0.0634 4.3765 0.0109 0.0265 6.3 2271 0.183 0.1135 74.99 238.43 32.28 5.96E05 0.0540 0.2681 0.0002 0.0011 0.1 11.52 0.184 0.1146 74.47 234.83 32.89 6.10E05 0.0016 0.0037 3E0
49、5 2E05 0.02 0.2D7783 1312REFERENCES(1) Currie, L., “Nomenclature in Evaluation of Analytical MethodsIncluding Detection and Quantification Capabilities,” Pure and Ap-plied Chemistry, Vol 67, 1995, pp. 16991723.(2) Oppenheimer, L., Capizzi, T.P., Weppelman, R.M., and Mehta, H.,“Determining the Lowest Limit of Reliable Assay Measurements,”Analytical Chemistry, Vol 55, 1983, pp. 638643.(3) Rocke, D.M. and Lorenzato, S., “A Two-Component Model forMeasurement Error in Analytical Chemistry,” Technometrics,
