1、Designation: D6617 13D6617 17 An American National StandardStandard Practice forLaboratory Bias Detection Using Single Test Result fromStandard Material1This standard is issued under the fixed designation D6617; the number immediately following the designation indicates the year oforiginal adoption
2、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.INTRODUCTIONDue to the inherent imprecision in all test methods, a laboratory cannot expe
3、ct to obtain thenumerically exact accepted reference value (ARV) of a check standard (CS) material every time oneis tested. Results that are reasonably close to the ARV should provide assurance that the laboratory isperforming the test method either without bias, or with a bias that is of no practic
4、al concern, hencerequiring no intervention. Results differing from the ARV by more than a certain amount, however,should lead the laboratory to take corrective action.1. Scope*1.1 This practice covers a methodology for establishing an acceptable tolerance zone for the difference between the resultob
5、tained from a single implementation of a test method on a Check Standard (CS) and itsARV, based on user-specifiedType I error,the user-established test method precision, the standard error of the ARV, and a presumed hypothesis that the laboratory isperforming the test method without bias.NOTE 1Throu
6、ghout this practice, the term user“user” refers to the user of this practice;practice, and the term laboratory“laboratory” (see 1.1) refersto the organization or entity that is performing the test method.1.2 For the tolerance zone established in 1.1, a methodology is presented to estimate the probab
7、ility that the single test resultwill fall outside the zone, in the event that the presumed hypothesis is not true and there is a bias (positive or negative) of auser-specified magnitude that is deemed to be of practical concern (that is, the presumed hypothesis is not true).concern.1.3 This practic
8、e is intended for ASTM Committee D02 test methods that produce results on a continuous numerical scale.1.4 This practice assumes that the normal (Gaussian) model is adequate for the description and prediction of measurementsystem behavior when it is in a state of statistical control.NOTE 2While this
9、 practice does not cover scenarios in which multiple results are obtained on the same CS under site precision or repeatabilityconditions, the statistical concepts presented are applicable. Users wishing to apply these concepts for the scenarios described are advised to consult astatistician and to r
10、eference the CS methodology described in Practice D6299.1.5 This international standard was developed in accordance with internationally recognized principles on standardizationestablished in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
11、by the World Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2D2699 Test Method for Research Octane Number of Spark-Ignition Engine FuelD6299 Practice for Applying Statistical Quality Assurance and Control Charting Techniques to Evaluate Analy
12、tical Measure-ment System Performance1 This practice is under the jurisdiction of ASTM Committee D02 on Petroleum Products Products, Liquid Fuels, and Lubricantsand is the direct responsibility ofSubcommittee D02.94 on Coordinating Subcommittee on Quality Assurance and Statistics.Current edition app
13、roved June 15, 2013May 1, 2017. Published July 2013May 2017. Originally approved in 2000. Last previous edition approved in 20082013 asD6617 08.D6617 13. DOI: 10.1520/D6617-13.10.1520/D6617-17.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at ser
14、viceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version.
15、 Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.*A Summary of Changes section
16、appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E178D7915 Practice for Dealing With Outlying ObservationsApplication of Generalized Extreme Studentized Deviate (GESD)Technique to Simultaneously Ident
17、ify Multiple Outliers in a Data Set3. Terminology3.1 Definitions for accepted reference value (ARV), accuracy, bias, check standard (CS), in statistical control, site precision, siteprecision standard deviation (SITE), site precision conditions, repeatability conditions, and reproducibility conditio
18、ns can be foundin Practice D6299.3.2 Definitions of Terms Specific to This Standard:3.2.1 acceptable tolerance zone, na numerical zone bounded inclusively by zero 6 k (k is a value based on a user-specifiedType I error; is defined in 3.2.7) such that if the difference between the result obtained fro
19、m a single implementation of a testmethod for a CS and its ARV falls inside this zone, the presumed hypothesis that the laboratory or testing organization isperforming the test method without bias is accepted, and the difference is attributed to normal random variation of the test method.Conversely,
20、 if the difference falls outside this zone, the presumed hypothesis is rejected.3.2.2 consensus check standard (CCS), n a special type of CS in which the ARV is assigned as the arithmetic average of atleast 16 non-outlying (see Practice E178D7915 or equivalent) test results obtained under reproducib
21、ility conditions, and the resultspass the Anderson-Darling normality test in Practice D6299, or other statistical normality test at the 95 % confidence level.3.2.2.1 DiscussionThese may be production materials with unspecified composition, but are compositionally representative of material routinely
22、tested by the test method, or materials with specified compositions that are reproducible, but may not be representative of routinelytested materials.3.2.3 delta (), na sign-less quantity, to be specified by the user as the minimum magnitude of bias in either direction (eitherpositive or negative) t
23、hat is of practical concern.3.2.4 power of bias detection, nin applying the methodology of this practice, this refers to the long run probability of beingable to correctly detect a bias of a magnitude of at least in the correct direction, using the acceptance tolerance zone set underthe presumed hyp
24、othesis, and is defined as (1 Type II error), for a user-specified .3.2.4.1 DiscussionThe quantity (1 Type II error), commonly known as the power of the test in classical statistical hypothesis testing, refers to theprobability of correctly rejecting the null hypothesis, given that the alternate hyp
25、othesis is true. In applying this standard practice,the power refers to the probability of correctly detecting a positive or negative bias of at least .3.2.5 standardized delta (S) , n, expressed in units of total uncertainty () per the equation:S!5/ (1)3.2.6 standard error of ARV (SEARV) , na stati
26、stic quantifying the uncertainty associated with the ARV in which the latter isused as an estimate for the true value of the property of interest. For a CCS, this is defined as:CCS/=N (2)where:N = total number of non-outlying results used to establish the ARV, collected under reproducibility conditi
27、ons, andCCS = the standard deviation of all the non-outlying results.3.2.6.1 DiscussionAssuming a normal model, a 95 % confidence interval that would contain the true value of the property of interest can beconstructed as follows:ARV21.96 SEARVtoARV11.96 SEARV (3)3.2.7 total uncertainty (), ncombine
28、d quantity of test method SITE and SEARV as follows:5=2SITE1SE2ARV (4)3.2.8 type I error, nin applying the methodology of this practice, this refers to the theoretical long run long-run probabilityof rejecting the presumed hypothesis that the test method is performed without bias when in fact the hy
29、pothesis is true, hence,committing an error in decision.D6617 1723.2.8.1 DiscussionType I error, commonly known as alpha () error in classical statistical hypothesis testing, refers to the probability of incorrectlyrejecting a presumed, or null hypothesis based on statistics generated from relevant
30、data. In applying this practice, the nullhypothesis is stated as: The test method is being performed without bias; or it can be equivalently stated as: H0: bias = 0.3.2.9 type II error, nin applying the methodology of this practice, this refers to the long run long-run probability of accepting(that
31、is, not rejecting) the presumed hypothesis that the method is performed without bias, when in fact the presumed hypothesisis not true,true and the test method is biased by a magnitude of at least , performed with a bias, hence, committing an error indecision.3.2.9.1 DiscussionType II error, commonly
32、 known as beta () error in classical statistical hypothesis testing, refers to the probability of failure toreject the null hypothesis when it is not true, based on statistics generated from relevant data. To quantify Type II error, the useris required to declare a specific alternate hypothesis that
33、 is believed to be true. In applying this practice, the alternate hypothesiswill take the form: “The test method is biased by at least ”,” where is a priori decided by the user as the minimum amountof bias in either direction (positive or negative) that is of practical concern. The alternate hypothe
34、sis can be equivalently stated as:H1: |bias| .4. Significance and Use4.1 Laboratories performing petroleum test methods can use this practice to set an acceptable tolerance zone for infrequenttesting of CS or CCS material, based on , and a desired Type I error, for the purpose of ascertaining if the
35、 test method is beingperformed without bias.4.2 This practice can be used to estimate the power of correctly detecting bias of different magnitudes, usinggiven the acceptabletolerance zone set in 4.1, and hence, gain insight into the limitation of the true bias detection capability associated with t
36、hisacceptable tolerance zone. With this insight, trade-offs can be made between desired Type I error versus desired bias detectioncapability to suit specific business needs.4.3 The CS testing activities described in this practice are intended to augment and not replace the regular statistical monito
37、ringof test method performance as described in Practice D6299.5. General Requirement5.1 Application of the methodology in this practice requires the following:5.1.1 The standard material has an ARV and associated standard error (SEARV).NOTE 3For a given power of detection, the magnitude of the assoc
38、iated bias detectable is directly proportional to 5=SE2ARV1 2SITE . Therefore,efforts should be made to keep the ratio (SEARV SITE) to as low a value as practical. A ratio of 0.5 or less is considered useful.5.1.2 The user has a SITE for the test method that is reasonably suited for the standard mat
39、erial.D6617 173NOTE 4It is recognized that there will be situations in which the CS may not be compositionally similar to or have property level similar to, or both,the materials regularly tested. For those situations, the site precision standard deviation (SITE) estimated using regularly tested mat
40、erial at a property levelclosest to the check standard should be used.5.1.3 User-specified Type I error and the minimum magnitude of bias that is of practical concern ().5.1.4 The test method is in statistical control.NOTE 5Within the context of this practice, a test method can be in statistical con
41、trol (that is, mean is stable, under common cause variations), butcan be biased.NOTE 6Generally, sites with site nominally less than 0.25 R, or equivalently, site precision (2.77 site) less than 0.69 R (R is the published testmethod reproducibility, if available) are considered to be reasonably prof
42、icient in controlling the common cause or random variations associated with theexecution of the test method.6. Procedure6.1 Confirm the usefulness of the CS by assessing the ratio SEARV / SITE#.NOTE 7A ratio of less than or equal to 0.5 is considered useful.6.2 Calculate 5=2SITE1SE2 ARV.6.3 Specify
43、the required Type I error rate.NOTE 8A suggested starting value is 0.05.6.4 Specify required .NOTE 9The magnitude of is usually specified based on nonstatistical considerations such as business risks or operational issues, or both.6.5 Calculate S5/.6.6 See Table 1.6.7 Look across the row with the S
44、values and identify the column with a S value closest to the S calculated in 6.5.6.8 Look down the column identified in 6.7 and locate the row with the value in Column A closest to the required Type I error.The value in the cell where the row and column intersect is the power of detection.6.9 If the
45、 power of detection is not acceptable (typically it will be too low), iteratively change one or all of the following untilall requirements are met.6.9.1 Type I error.6.9.2 Delta ().6.9.3 Power of bias detection.NOTE 10For a single implementation of the test method, the power of bias detection will d
46、epend on the magnitude of specified, the total uncertainty, and the specified Type I error rate. For a fixed magnitude of , power of bias detection (of magnitude ) can be increased at the expense of an increasein Type I error rate. For a fixed Type I error, power of detection bias will increase as t
47、he magnitude of increases.6.10 Use the appropriate k value from Column B of Table 1 that met the specified Type I error and power of bias detection tocalculate the boundaries of the acceptable tolerance zone.6.11 Construct the acceptable tolerance zone: 0 6 k.6.12 When a single test result X for a C
48、S is obtained, calculate the quantity (X ARV).6.13 If X ARV falls inside the acceptable tolerance zone inclusively, accept the presumed hypothesis that the laboratory isperforming the test method without bias.TABLE 1 Type I Error and Associated Power of Bias Detection for Various s Valuess=Magnitude
49、 of bias expressed as (s) = see 6.50.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 4(Column A) (Column B)Type I Error k Power of correctly detecting (s) in either direction = that is, either + or 0.01 2.58 0.019 0.034 0.058 0.092 0.141 0.204 0.282 0.372 0.470 0.569 0.664 0.750 0.822 0.9230.025 2.24 0.041 0.068 0.107 0.161 0.229 0.312 0.405 0.503 0.602 0.694 0.776 0.843 0.896 0.9610.05 1.96 0.072 0.113 0.169 0.239 0.323 0.417 0.516 0.614 0.705 0.785 0.851 0.901 0.938 0
