1、Designation: E2862 12E2862 18Standard Practice forProbability of Detection Analysis for Hit/Miss Data1This standard is issued under the fixed designation E2862; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revis
2、ion. 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 defines the procedure for performing a statistical analysis on nondestructive testing hit/miss data to determineth
3、e demonstrated probability of detection (POD) for a specific set of examination parameters. Topics covered include the standardhit/miss POD curve formulation, validation techniques, and correct interpretation of results.1.2 The values stated in inch-pound units are to be regarded as standard. The va
4、lues given in parentheses are mathematicalconversions to SI units that are provided for information only and are not considered standard.1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to
5、establish appropriate safety safety, health, and healthenvironmental practices and determine theapplicability of regulatory limitations prior to use.1.4 This international standard was developed in accordance with internationally recognized principles on standardizationestablished in the Decision on
6、 Principles for the Development of International Standards, Guides and Recommendations issuedby the World Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E178 Practice for Dealing With Outlying ObservationsE456 Terminology Relating to Quality
7、 and StatisticsE1316 Terminology for Nondestructive ExaminationsE2586 Practice for Calculating and Using Basic StatisticsE3023 Practice for Probability of Detection Analysis for Versus a DataE3080 Practice for Regression Analysis2.2 Department of Defense Handbook:MIL-HDBK-1823A Nondestructive Evalua
8、tion System Reliability Assessment33. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 analyst, nthe person responsible for performing a POD analysis on hit/miss data resulting from a POD examination.3.1.2 demonstrated probability of detection, nthe calculated POD value resulting
9、from the statistical analysis on the hit misshit/miss data.3.1.3 false call, nthe perceived detection of a discontinuity that is identified as a find during a POD examination when nodiscontinuity actually exists at the inspection site.3.1.4 hit, nan existing discontinuity that is identified as a fin
10、d during a POD demonstration examination.3.1.5 miss, nan existing discontinuity that is missed during a POD examination.3.1.6 probability of detection, detection (POD), nthe fraction of nominal discontinuity sizes expected to be found given theirexistence.1 This practice is under the jurisdiction of
11、 ASTM Committee E07 on Nondestructive Testing and is the direct responsibility of Subcommittee E07.10 on Specialized NDTMethods.Current edition approved Jan. 15, 2012Feb. 1, 2018. Published February 2012April 2018. DOI:10.1520/E2862-12.Originally approved in 2012. Last previous editionapproved in 20
12、12 as E2862 12. DOI:10.1520/E2862-18.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.3 Available from Standar
13、dization Documents Order Desk, DODSSP, Bldg. 4, Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http:/dodssp.daps.dla.mil.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.
14、 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.Copyright ASTM International,
15、100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2 Symbols:3.2.1 adiscontinuity size.3.2.2 apthe discontinuity size that can be detected with probability p.3.2.2.1 DiscussionEach discontinuity size has an independent probability of being detected and correspondin
16、g probability of being missed. Forexample, being able to detect a specific discontinuity size with probability p does not guarantee that a larger size discontinuity willbe found.3.2.3 ap/cthe discontinuity size that can be detected with probability p with a statistical confidence level of c.3.2.3.1
17、DiscussionAccording to the formula in MIL-HDBK-1823A, ap/c is calculated by applying a statistical uncertainty bound toa one-sided upperconfidence bound on ap. The, uncertainty bound is ap/c function the amount of data, the scatter in the data, and the specified levelof statistical confidence. The r
18、esulting value represents how large the discontinuitytrue withap POD equal tocould be given pthecould be when uncertainty associated with estimatingstatistical uncertainty associated with limited sample data. ap is accounted for.Hence ap/c ap. Note that POD is equal to p for both ap/c and ap. ap is
19、based solely on the hit/miss data resulting from theexamination and represents a snapshot in time, whereas ap/c accounts for the uncertainty associated with limited sample data.4. Summary of Practice4.1 This practice In general, the POD examination process is comprised of specimen set design, study
20、design, examinationadministration, statistical analysis of examination data, documentation of analysis results, and specimen set maintenance. Thispractice is focused only on and describes step-by-step the process for analyzing nondestructive testing hit/miss data resulting froma POD examination, inc
21、luding examination and includes minimum requirements for validating the resulting POD curve.curve anddocumenting the results.4.2 This practice also includes definitions and discussions for results of interest (for example, a90/95) to provide for correctinterpretation of results.4.3 Definitions of st
22、atistical terminology used in the body of this practice can be found in Annex A1.4.4 A more general discussion of the POD analysis process can be found in Appendix X1.4.5 An example POD analysis using simulated data can be found in Appendix X2.4.6 A mathematical overview of the underlying model comm
23、only used with hit/miss data resulting from a POD examinationcan be found in Appendix X3.5. Significance and Use5.1 The POD analysis method described herein is based on a well-known and well established statistical method. It shall be usedto quantify the demonstrated POD for a specific set of examin
24、ation parameters and known range of discontinuity sizes when theinitial response from a nondestructive evaluation inspection system is ultimately binary in nature (that is, hit or miss). This methodrequires that a relationship between discontinuity size and POD exists and is best described by a gene
25、ralized linear model with theappropriate link function for binary outcomes.under the following conditions.5.1.1 The initial response from a nondestructive evaluation inspection system is ultimately binary in nature (that is, hit or miss).5.1.2 Discontinuity size is the predictor variable and can be
26、accurately quantified.5.1.3 A relationship between discontinuity size and POD exists and is best described by a generalized linear model with theappropriate link function for binary outcomes.5.2 This practice does not limit the use of a generalized linear model with more than one predictor variable
27、or other types ofstatistical models if justified as more appropriate for the hit/miss data.5.3 If the initial response from a nondestructive evaluation inspection system is measurable and can be classified as a continuousvariable (for example, data collected from an Eddy Current inspection system),
28、then Practice E3023 may be more appropriate.5.4 Prior to performing the analysis it is assumed that the discontinuity of interest is clearly defined; the number and distributionof induced discontinuity sizes in the POD specimen set is known and well-documented; discontinuities in the POD specimen se
29、tare unobstructed; and the POD examination administration procedure (including data collection method) is well-designed,well-defined, under control, and unbiased; and the initial response is ultimately binary in nature (that is, hit or miss). unbiased. Theanalysis results are only valid if convergen
30、ce is achieved and the model adequately represents the data.E2862 1825.5 The POD analysis method described herein is consistent with the analysis method for binary data described inMIL-HDBK-1823A, whichand is included in several widely utilized POD software packages to perform a POD analysis onhit/m
31、iss data. It is also found in statistical software packages that have generalized linear modeling capability. This practicerequires that the analyst has access to either POD software or other software with generalized linear modeling capability.6. Procedure6.1 The POD analysis objective shall be cle
32、arly defined by the responsible engineer or by the customer.6.2 The POD analysis objective shall be clearly defined by the responsible engineer or by the customer.analyst shall obtain thehit/miss data resulting from the POD examination, which shall include at a minimum the documented known induced d
33、iscontinuitysizes, whether or not the discontinuity was found, and any false calls.6.1.1 The analyst shall obtain the hit/miss data resulting from the POD examination, which shall include at a minimum thedocumented known induced discontinuity sizes, whether or not the discontinuity was found, and an
34、y false calls.6.3 The analyst shall also obtain specific information about the POD examination, which shall include at a minimum thespecimen standard geometry (for example, flat panels), specimen standard material (for example, Nickel), examination date,number of inspectors, type of inspection metho
35、d (for example, line-of-site Level 3 Fluorescent Penetrant Inspection), and pertinentcomments from the inspector(s) and test administrator.6.3.1 In general, the results of an experiment apply to the conditions under which the experiment was conducted. Hence, thePOD analysis results apply to the cond
36、itions under which the POD examination was conducted.6.4 Prior to performing the analysis, the analyst shall conduct a preliminary review of the POD examination procedure andresulting hit/miss data to identify any examination administration or data issues. The analyst shall identify and attempt to r
37、esolveany issues prior to conducting the POD analysis. Examples of examination administration or data issues Identified issues and theirresolution shall be documented in the report. Examples of issues that could arise and possible resolutions are:are outlined in thefollowing subsections:6.4.1 If the
38、 examination procedure was poorly designed or executed, or both, the validity of the resulting data is questionable.In this case, the examination procedure design and execution should be reevaluated. For design guidelines see MIL-HDBK-1823A.6.4.2 If the examination procedure was properly designed bu
39、t problems or interruptions occurred during the POD examinationthat may bias the results, the POD examination should be re-administered. If this occurs, it shall be documented in the report.6.4.3 If a discontinuity was missed because it was obstructed (such as a clogged discontinuity), the discontin
40、uity shall beremoved from the POD analysis since there was not an opportunity for the discontinuity to be found. If a discontinuity is removedfrom the analysis, the specific discontinuity and rationale for removal shall be documented in the final report.Data that appear tobe outlying (for example, a
41、n early hit in the small size range or a late miss in the large size range) should be identified andinvestigated.6.4.3.1 If a discontinuity was missed because it was obstructed (such as a clogged discontinuity), the discontinuity shall beremoved from the POD analysis since there was not an opportuni
42、ty for the discontinuity to be found.6.4.3.2 If a discontinuity is removed from the analysis, the specific discontinuity and rationale for removal shall be documentedin the final report.6.4.4 POD cannot be modeled as a continuous function of discontinuity size if there is a complete separation of mi
43、sses and hitsas crack size increases. If a complete separation of misses and hits is present in the data, the POD examination may bere-administered. If this occurs, it shall be documented in the report. If a complete separation of misses and hits occurs on a regularbasis, the specimen set should be
44、examined for suitability as a POD examination specimen set.6.4.5 POD cannot be modeled as a continuous function of discontinuity size if all the discontinuities are found or if all thediscontinuities are missed. If this occurs, the specimen set is inadequate for the POD examination.6.5 The analyst s
45、hall use a generalized linear model with the appropriate link function to establish the relationship between PODand discontinuity size. For application to POD, the generalized linear model with discontinuity size as the single predictor variableis typically expressed as g(y)g(p) = b0 + b1a or g(y)g(
46、p) = b0 + b1ln(a), where a or ln(a) is the continuous predictor variable,b0 is the intercept, b1 is the slope, yp is the binary response variable, probability of a response (that is, p=POD), and g()g is thefunction that “links” the binary response with the predictor variable.a function (commonly ref
47、erred to as the “link” function) thatmaps 0, 1 onto the real number line. If predictor variables other than discontinuity size are quantifiable factors, a generalizedlinear model with more than one predictor may be used. (For more detail on GLMs, see Appendix X3.)6.6 The analyst shall choose the app
48、ropriate link function based on how well the model fits the observed data. MIL-HDBK-1823A discusses four different link functions (Logit, Probit, Log-Log, Complementary-LogLog) and describes methods forselecting the appropriate one. In general, the logit and probit link functions have worked well in
49、 practice for modeling hit/missdata. (For more detail on the logit and probit link functions, see Appendix X3.)6.6.1 In general, the appropriateness of a selected model is determined by the significance of the predictor variable(s), how wellthe model fits the observed data, and how well the underlying assumptions are met. Hence, model selection may be an iterativeprocess as the appropriateness of the link function, the significance of the predictor variable(s), goodness-of-fit, and otherunderlying assumptions are typically assessed after the model has been devel
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