# ASTM D6259-15

Designation D6259 − 15 An American National StandardStandard Practice forDetermination of a Pooled Limit of Quantitation for a Test1This standard is issued under the fixed designation D6259; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon ´ indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This practice covers the use of standard regressiontechniques and data from an interlaboratory study to determinea lower quantitative limit for a test . This determinedlower limit represents the numerical limit at or above which thetest results are considered to be quantitatively meaningful forcommerce or regulatory activities by this practice. It is definedby this standard as the pooled limit of quantitation PLOQ forthe test .1.2 This practice is applicable to test s that arecapable of producing numerical test results close to zero.Examples are those test s that determine quantitativelythe concentration of analytes near zero.2. Referenced Documents2.1 ASTM Standards2D6300 Practice for Determination of Precision and BiasData for Use in Test s for Petroleum Products andLubricantsE456 Terminology Relating to Quality and StatisticsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test 3. Terminology3.1 Definitions3.1.1 repeatability conditions, nconditions under whichtest results are obtained with the same test in the samelaboratory by the same operator with the same equipment in theshortest practical period of time using test units or testspecimens taken at random from a single quantity of materialthat is as nearly homogeneous as possible.NOTE 1By in the shortest practical period of time is meant that thetest results, at least for one material, are obtained in a time period not lessthan in normal testing and not so long as to permit significant change intest material, equipment, or environment. See Terminology E456.3.2 Definitions of Terms Specific to This Standard3.2.1 pooled limit of quantitation PLOQ, nlevel ofproperty or concentration for a test at which the ratio[10 pooled repeatability standard deviation of results for aconcentration level/concentration level] 1.3.2.1.1 DiscussionQuantitative test results obtained usinga test at or below its PLOQ is expected to have anuncertainty of 630 or greater at the 95 confidence level.3.2.2 pooled repeatability standard deviation, nthe statis-tically pooled standard deviation for results obtained underrepeatability conditions over multiple operators/laboratoriesfor a sample that is obtained in accordance with PracticeD6300 or other equivalent Interlaboratory Study ILS analysisfor example, Practice E691, ISO 4259.3.2.3 laboratory limit of quantitation LLOQ, nlevel ofproperty or concentration for a test at which the ratio[10 repeatability standard deviation of results for a concen-tration level determined in a single laboratory/concentrationlevel] 1.3.2.3.1 DiscussionQuantitative test results obtained bythis single laboratory at or below its LLOQ is expected to havean uncertainty of 630 or greater at the 95 confidencelevel.3.3 Acronyms3.3.1 ILS, ninterlaboratory study.3.3.2 LLOQ, nlaboratory limit of quanitation.3.3.3 PLOQ, npooled limit of quantitation.4. Summary of Practice4.1 Statistically pooled repeatability standard deviationsfrom multiple laboratories for at least seven samples meetingthe requirements in Section 6 are obtained.4.2 An empirical power function is fitted to the plot Y versusX whereY [10 pooled repeatability standard deviation/mean] foreach sample, andX [mean] of each sample.1This practice is under the jurisdiction of Committee D02 on PetroleumProducts, Liquid Fuels, and Lubricantsand is the direct responsibility of Subcom-mittee D02.94 on Coordinating Subcommittee on Quality Assurance and Statistics.Current edition approved July 1, 2015. Published August 2015. Originallyapproved in 1998. Last previous edition approved in 2010 as D6259 – 98 2010.DOI 10.1520/D6259-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume ination, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States14.3 The value of X at which the uated Y 1isdetermined using the function determined in 4.2. This value ofX is defined as the PLOQ for the .5. Significance and Use5.1 BackgroundIn a single laboratory, the limit ofquantitation, LOQ, equal to ten times the standard deviationobtained under repeatability conditions extrapolated to zeroconcentration s0 based on samples with close to zero concen-trations has been recommended.3A test result at this LOQ hasan uncertainty of 630 at the 99 confidence level.5.1.1 This practice uses a regression technique to determinea similar limit for a test PLOQ using statisticallypooled repeatability standard deviations over multipleoperators/laboratories/samples from ILS data. This PLOQ canbe used by industry to assess the reliability of a test , or,compare reliability of different test s, for quantitativemeasurement at concentrations near zero. Similarly, quantita-tive test results obtained using the test for levels at orbelow the PLOQ can be expected by industry to have anuncertainty of 630 or greater at the 95 confidence level.5.1.2 The regression technique described in this practice canalso be used to determine a limit of quantitation specific for asingle laboratory LLOQ. The limit thus quantified for onelaboratory is defined by this standard as the laboratory limit ofquantitation LLOQ.5.1.3 It should be noted that since differences in repeatabil-ity testing capabilities between different laboratories can exist,therefore, LLOQ determined at a single laboratory can bedifferent than the PLOQ determined for the test .5.2 Values below the PLOQ are deemed by this practice tobe too uncertain for meaningful use in commerce, or inregulatory activities.6. Procedure6.1 Make the preparations outlined in 6.2, then carry out theprocedures described in Section 7.6.2 Preparations6.2.1 Select Test LevelsDecide the objective of the test, the range of typical samples it is expected to cover.Determine a set of at least seven test levels intended to be usedto estimate the PLOQ see Note 2. The ILS can include morethan seven test levels. However, for use of regression forPLOQ only, use results from samples meeting the followingrequirements6.2.1.1 At least four shall have Y values see Section 4,Summary of Practice greater than 0.5,6.2.1.2 At least one shall have a Y value less than 0.5,6.2.1.3 At least one shall have a Y value between 0.5 and 1,6.2.1.4 At least two, but preferable three of the sevensamples shall have a Y value greater than 1.2, and6.2.1.5 No sample should exceed 4 times the estimatedPLOQ.6.2.1.6 See Table 1 for an example.NOTE 2Mean and standard deviation data from experiencedlaboratories, archived research reports, and known limitations of the test or equipment can give a preliminary notion of the PLOQ.6.2.2 Select Sample MaterialsUse sample materials thatare typical of those to which the test is applied. Inspecial cases, the of standard additions spiking can benecessary to achieve the selected test levels. Synthetic blendsmay be required because of cost or other practical consider-ations.6.2.2.1 For a multi-analyte test , an analyte-specificplan is required to determine the PLOQ of each analyte ofinterest. PLOQs determined for one analyte cannot be extrapo-lated to another.6.2.3 Select Number of LaboratoriesPractice D6300 re-quires at least six laboratories be used in the ILS study.6.2.4 Determine Number of Runs Per SampleFor thispractice, the required minimum degrees of freedom for therepeatability standard deviation for each sample is six.Therefore, for determination of PLOQ using an ILS involvingsix laboratories, the minimum number of runs per sample istwo.6.2.4.1 For determination of LLOQ at a single laboratory,the minimum number of runs per sample is seven.6.2.4.2 If a blank measurement is required to calculate themeasured level of analyte, the analyst must obtain a separateblank measurement for each sample aliquot analyzed.7. Calculation7.1 Arrange the averages and corresponding pooled repeat-ability standard deviations in ascending order of the averagesfor each sample.7.2 Calculate the ratio Y [10 pooled repeatabilitystandard deviation/average] for each sample.7.3 Plot Y versus X where X average of each sample.7.4 Fit a power function for Y versus X using standardregression software.NOTE 3Step 7.4 can be easily achieved by utilizing the “attrendline” option in Excel and select the “power” function option.7.5 Solve for the value of X for which the value of Y 1using the fitted function in 7.4. The value of X for which Y 1 is the PLOQ.7.6 For LLOQ, replace pooled repeatability standard devia-tions in this section by repeatability standard deviations deter-mined at a single laboratory meeting the requirement of 6.2.4.3Taylor, J. K., Quality Assurance of Chemical Measurements, Lewis Publishers,Michigan, 1987.TABLE 1 Example Data from an Interlaboratory StudySample Mean XWithin LaboratoriesY 10 StandardDeviation/MeanStandardDeviationDegrees ofFreedomS8 110 44.72 10 4.065S1 640 100 10 1.563S3 870 89.44 10 1.028S6 1180 94.87 10 0.804S2 1272 78.17 9 0.615S7 2505 136 10 0.543S4 3165 125 8 0.395S5 3338 112.4 10 0.337D6259 − 1528. Reporting Low-level Data8.1 Should a test result be reported that is below the PLOQof the test , it is recommended that the PLOQ for thetest be reported in parentheses after the data, forexample, chlorine content 110 mg/kg PLOQ1000 mg/kg.8.2 A statement about the PLOQ should appear in the test in the Scope section of the test .9. Example of PLOQ Calculation9.1 Example of data from an interlaboratory study used tocute this practice are provided in Table 1.9.1.1 The fitted power function and PLOQ solved using thefitted function is provided in Fig. 1.10. Keywords10.1 limit of quantitation; pooled limit of quantitationD6259 − 153SUMMARY OF CHANGESSubcommittee D02.94 has identified the location of selected changes to this standard since the last issueD6259 – 98 2010 that may impact the use of this standard. Approved July 1, 2015.1 Revised entire standard.ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints single or multiple copies of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 phone, 610-832-9555 fax, or serviceastm.org e-mail; or through the ASTM websitewww.astm.org. Permission rights to photocopy the standard may also be secured from the Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, Tel 978 646-2600; http// 1 Fitted Function and Solution for PLOQ Data from Table 1D6259 − 154