1、Designation: D6512 07 (Reapproved 2014)Standard Practice forInterlaboratory Quantitation Estimate1This standard is issued under the fixed designation D6512; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision.
2、 A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice establishes a uniform standard for com-puting the interlaboratory quantitation estimate associated withZ % relative st
3、andard deviation (referred to herein as IQEZ%),and provides guidance concerning the appropriate use andapplication. The calculations involved in this practice can beperformed with DQCALC, Microsoft Excel-based softwareavailable from ASTM.21.2 IQEZ%is computed to be the lowest concentration forwhich
4、a single measurement from a laboratory selected fromthe population of qualified laboratories represented in aninterlaboratory study will have an estimated Z % relativestandard deviation (Z % RSD, based on interlaboratory stan-dard deviation), where Z is typically an integer multiple of 10,such as 10
5、, 20, or 30, but Z can be less than 10. The IQE10 %is consistent with the quantitation approaches of Currie (1)3and Oppenheimer, et al. (2).1.3 The fundamental assumption of the collaborative studyis that the media tested, the concentrations tested, and theprotocol followed in the study provide a re
6、presentative and fairevaluation of the scope and applicability of the test method aswritten. Properly applied, the IQE procedure ensures that theIQE has the following properties:1.3.1 Routinely Achievable IQE ValueMost laboratoriesare able to attain the IQE quantitation performance in routineanalyse
7、s, using a standard measurement system, at reasonablecost. This property is needed for a quantitation limit to befeasible in practical situations. Representative laboratoriesmust be included in the data to calculate the IQE.1.3.2 Accounting for Routine Sources of ErrorThe IQEshould realistically inc
8、lude sources of bias and variation thatare common to the measurement process. These sourcesinclude, but are not limited to: intrinsic instrument noise, some“typical” amount of carryover error; plus differences inlaboratories, analysts, sample preparation, and instruments.1.3.3 Avoidable Sources of E
9、rror ExcludedThe IQEshould realistically exclude avoidable sources of bias andvariation; that is, those sources that can reasonably be avoidedin routine field measurements. Avoidable sources wouldinclude, but are not limited to: modifications to the sample;modifications to the measurement procedure;
10、 modifications tothe measurement equipment of the validated method, and grossand easily discernible transcription errors, provided there wasa way to detect and either correct or eliminate them.1.4 The IQE applies to measurement methods for whichcalibration error is minor relative to other sources, s
11、uch aswhen the dominant source of variation is one of the following:1.4.1 Sample Preparation, and calibration standards do nothave to go through sample preparation.1.4.2 Differences in Analysts, and analysts have little oppor-tunity to affect calibration results (as is the case with automatedcalibra
12、tion).1.4.3 Differences in Laboratories (for whatever reasons),perhaps difficult to identify and eliminate.1.4.4 Differences in Instruments (measurement equipment),such as differences in manufacturer, model, hardware,electronics, sampling rate, chemical processing rate, integra-tion time, software a
13、lgorithms, internal signal processing andthresholds, effective sample volume, and contamination level.1.5 Data Quality ObjectivesTypically, one would com-pute the lowest % RSD possible for any given dataset for aparticular method. Thus, if possible, IQE10 %would be com-puted. If the data indicated t
14、hat the method was too noisy, onemight have to compute instead IQE20 %, or possibly IQE30 %.In any case, an IQE with a higher % RSD level (such asIQE50 %) would not be considered, though an IQE with RSD0 (though this constraintis irrelevant for the Hybrid Model). A value ofg 0, there is sufficient s
15、tatistical evidence of curvature in therelationship between skand Tkto warrant the use of the Hybrid Model,Model C (Q 0 ensures that the increase in skwith respect to Tkis fasterthan linear). If these conditions do not hold, then the Straight-line Model(Model B) is the appropriate model to use. Proc
16、eed to 6.3.4(10) The Hybrid Model for the ILSD (Model C) can beused if there is evidence of curvature.(11) To evaluate the reasonableness of the Hybrid Model,Model C, the model must first be fitted using nonlinear leastsquares (NLLS), either by Newtons-Method iteration (pre-sented in the appendix),
17、or another NLLS method.TABLE 1 Bias-Correction Adjustment Factors for SampleStandard Deviations Based on n Measurements (at a particularconcentration)An2 3 4 5 6 7 8 910an1.253 1.128 1.085 1.064 1.051 1.042 1.036 1.031 1.028AFor each true concentration, Tk, the adjusted value sk=anskshould be modele
18、din place of sample standard deviation, sk. For n 10, use the formula, an=1+4(n1)1. See Johnson and Kotz (7).D6512 07 (2014)5(12) The fit from the Hybrid Model should be evaluated.Aplot of the residuals, in log form, should be constructed: plot rkversus Tk, where:rk5 lnsk2 lnsk, (8)and kis the predi
19、cted value of skusing the model. The plotshould show no systematic behavior (for example, curva-ture). If the fit satisfies both types of evaluation, go to 6.3.4.Otherwise, a different (and possibly more complex) modelmay be used, such as the exponential model: s = g exphT(1 + error). If there are e
20、nough true concentrations, amodel with more coefficients could be considered; possibili-ties include quadratic (strictly increasing with increasingconcentration), or even cubic.6.3.4 Fit the Mean-Recovery ModelThe mean-recoverymodel is a simple straight line,Model R:Y 5 a1bT1error. (9)The fitting pr
21、ocedure depends on the model selection from6.3.3. If the constant model, Model A, was selected for ILSD,then OLS can be used to fit Model R for mean recovery (see theleft column of Table 2, or Caulcutt and Boddy (5). If anonconstant ILSD model was selected, such as the Straight-line Model (Model B),
22、 or the Hybrid Model (Model C), thenweighted least squares (WLS) should be used to fit meanrecovery. The WLS approximately provides the minimum-variance unbiased linear estimate of the coefficients, a and b.The WLS procedure is described in 6.3.4.1.6.3.4.1 Weighted Least Squares Procedure, Using the
23、 Inter-laboratory Standard Deviation (ILSD) Model:(1) Using the ILSD model and coefficient estimates from6.3.3, compute the predicted interlaboratory standarddeviation, k, for each true concentration, Tk:Model B:sk5 g1hTk(10)Model C:sk5 g21hTk#2!1/2!(11)(2) Compute weights for WLS:wk5 sk!22. (12)Not
24、e that if WLS is carried out using computer software, thedefault setting for weights may be different. For example,instead of supplying the values, (k)2, as weights, the soft-ware may require the user to supply values (k)or(k)2asweights that are internally transformed by the software.(3) Carry out W
25、LS computations analogous to OLS com-putations. See Table 2 or Caulcutt and Boddy (5). The resultwill be coefficient estimates, a and b, for the mean-recoverymodel, Model R. Appendix II describes three approximateapproaches to WLS commonly practiced, but not acceptablefor this application.(4) After
26、fitting, the mean-recovery model should be evalu-ated for reasonableness and lack of fit. This evaluation shouldbe done by ensuring the following: (1) The fit is statisticallysignificant (overall p-value 5 %); (3)A plot of the residuals shows no obvious systematic curvature(for example, quadratic-li
27、ke behavior). If the mean-recoverymodel fails the evaluation, then the study supervisor will haveto determine if only a subset of the data should be analyzed(perhaps the model fails for the higher concentration(s), or ifmore data are needed.6.4 Compute the IQEThe IQE is computed using theILSD model
28、to estimate the interlaboratory standard deviation,and using the mean-recovery model to scale the standarddeviation. For any computed IQE to be valid, it must lie withinthe range of concentrations used in the study. The general formof the computation is to find the solution, LQ (within the rangeof c
29、oncentrations used in the study), to the following equation:T 5 100/Z!GT! (13)where function G(T) is the estimated interlaboratory stan-dard deviation (in concentration units) of true value, T, and Zis taken to be 10, 20, or 30, in increasing order. That is, the firstattempt is to compute IQE10 %.If
30、IQE10 %does not exist or isoutside the range of concentrations used in the study, thenIQE20 %is computed, if possible. If IQE20 %does not exist or isoutside the range of concentrations used in the study, thenIQE30 %is computed, if possible. If appropriate for a particularuse, IQEZ%can be computed fo
31、r any value of Z 30is not recommended. Thus, the IQE computation depends onthe form of the ILSD model, which is part of function G. Theratio, Z=100h/b, represents the limit of the %RSD achievable.Therefore the strictest IQE achievable by the analytical methodstudied is IQEZ %. For example, if Z = 10
32、00.17/1.0 = 17, thenthe strictest IQE achievable would be the IQE20 %(according tothe nearest higher multiple of 10).6.4.1 ILSD Constant Model (Model A)In this case, =g;hence G(T) = g/b and LQ = (100/Z)g/b. Thus,IQEZ %5 100/Z!g/b (14)6.4.2 ILSD “Straight-line” Model (Model B)In this case, =g+hT; hen
33、ce G(T) = (g + h T)/b. To find the IQE, onemust solve for T: T = (100/Z)(g+hT)/b. The solution is:IQEZ %5 g/bZ/100! 2 h!. (15)6.4.3 ILSD Hybrid Model (Model C)(additive and multi-plicative error, in accordance with Rocke and Lorenzato (3).TABLE 2 Ordinary Least Squares (OLS) and Weighted LeastSquare
34、s (WLS) Computations to Estimate Straight-line ModelCoefficients(Computations shown for convenience and contrast)OLS WLST51noi51nTi, Tw5oi5lnwiTi/oi5lnwiy 51noi51nyiyw5oi5lnwiyi/oi5lnwiSTT5oi5lnsTi2 Td2SwTT5oi51nwisTi2 Td2STY5oi5lnsTi2 Tdsyi2 yd SwTY5oi5lnwisTi2 Tdsyi2 ydslope5 b 5 STY/STTslope5 b 5
35、 SwTY/SwTTintercept5 a 5 y 2 bTintercept5 a 5 yw2 bTwD6512 07 (2014)6In this case, =(g2+hT2)(1/2); hence G(T) =(g2+hT2)(1/2)/b. To find the IQE, one must solveT 5 100/Z!/b!g21hT#2!1/2!(16)This solution is derived by squaring each side of the equationand solving to get: IQEZ%= g/(bZ/100)2 h21/2, wher
36、e thepositive square root is taken.6.5 Non-Trivial Amount of Censored DataMore than10 % of the data for at least one true concentration may havebeen reported as nondetects or less-thans. Despite the attemptin 6.2.3.1 to reduce or eliminate reported nondetects orless-thans, they may still occur at a
37、level that disrupts the dataanalysis presented in 6.3 and 6.4. If there is excessivecensoring, the study supervisor should contact laboratorieswith such measurements to see whether the data can beextracted in uncensored form from data archives. If this effortis not a sufficient remedy, serious consi
38、deration should begiven to augmenting the IQE study with measurements ofsamples at new and different concentrations (generally, higher).7. Data Analysis7.1 The data analysis for eliminating data is given in Section10 of Practice D2777.7.2 The data analysis involved in computing an IQE isshown by exa
39、mple in Section 10 of this practice.8. Report8.1 The analysis report should be structured as in AnnexA1.8.1.1 The report should be given a second-party review toverify that:8.1.1.1 The data transcription and reporting have beenperformed correctly,8.1.1.2 The analysis of the data has been performedco
40、rrectly, and8.1.1.3 The results of the analysis have been usedappropriately, including assessment of assumptions necessaryto compute an IQE.8.1.2 A statement of the review and the results shouldaccompany the report. Reviewer(s) should be qualified in oneor both of the following areas: (1) applied st
41、atistics, and (2)analytical chemistry.9. Rationale9.1 The basic rationale for the IQE is contained in Currie(1). The IQE is a performance characteristic of an analyticalmethod, to paraphrase Currie. As with the InterlaboratoryDetection Estimate (IDE) (described in Practice D6091), theIQE is vital fo
42、r the planning and use of chemical analyses. TheIQE is another benchmark indicating whether the method canadequately meet measurement needs.9.2 The idealized definition of IQEZ%is that it is the lowestconcentration, LQ, that satisfies: T = (100/Z) (where Tisthe actual standard deviation of interlabo
43、ratory measurementsat concentration T), which is equivalent to satisfying, %RSD =/T = Z %. In other words, IQEZ%is the lowest concentrationwith Z % RSD (assuming such a concentration exists). If, as iscommonly the case, %RSD declines with increasing trueconcentration, then the relative uncertainty o
44、f any measure-ment of a true concentration greater than the IQE will notexceed 6Z %. The range, 63LQ, is an approximate predictionor confidence interval very likely to contain the measurement,which is assumed to be Normally distributed. This assertion isbased on critical values from the Normal distr
45、ibution (or fromthe Students t distribution if is estimated rather than known).Then, with high confidence, the relative error of any measure-ment of a true concentration greater than the IQE will notexceed 63Z %. For example, a measurement above theIQE10 %(and assumed to have true concentration abov
46、e theIQE) could be reported as 6 ppb (630%)=6(62) ppb, witha high degree of certainty.9.3 There are several real-world complications to this ide-alized situation. See Maddalone et al. (8), Gibbons (9), andColeman et al. (10). Some of these complications are listed asfollows:9.3.1 Analyte recovery is
47、 not perfect; the relationship be-tween measured values of concentrations and true concentra-tions cannot be assumed to be trivial. There is bias betweentrue and measured values. Recovery can and should bemodeled. Usually a straight line will suffice.9.3.2 Variation is introduced by different labora
48、tories,analysts, models and pieces of equipment; environmentalfactors; flexibility/ambiguity in a test method; contamination;carryover; matrix influence; and other factors. It is intractableto model these factors individually, but their collective contri-butions to measurement ILSD can be observed,
49、if thesecontributions are part of how a study is designed and con-ducted.9.3.3 The interlaboratory standard deviation of measure-ments is generally unknown, and may change with trueconcentration, possibly because of the physical principle of thetest method. To ensure that a particular %RSD is attained at orabove the IQE, there must be a way to predict the ILSD atdifferent true concentrations. Short of severely restricting therange of concentrations for a study, prediction is accomplishedb
