ASTM E2862-18
(Practice)Standard Practice for Probability of Detection Analysis for Hit/Miss Data
Standard Practice for Probability of Detection Analysis for Hit/Miss Data
SIGNIFICANCE AND USE
5.1 The POD analysis method described herein is based on a well-known and well established statistical method. It shall be used to quantify the demonstrated POD for a specific set of examination parameters and known range of discontinuity sizes 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 accurately quantified.
5.1.3 A relationship between discontinuity size and POD exists and is best described by a generalized linear model with the appropriate 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 or other types of statistical 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 continuous variable (for example, data collected from an Eddy Current inspection system), 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 distribution of induced discontinuity sizes in the POD specimen set is known and well-documented; discontinuities in the POD specimen set are unobstructed; and the POD examination administration procedure (including data collection method) is well-designed, well-defined, under control, and unbiased. The analysis results are only valid if convergence is achieved and the model adequately represents the data.
5.5 The POD analysis method described herein is consistent with the analysis method for binary data described in MIL-HDBK-1823A, and is included in several widely utilized POD software packages to perform a POD analysis on hit/miss data. It is also found in statistical software packages that have generalized linear modeling...
SCOPE
1.1 This practice defines the procedure for performing a statistical analysis on nondestructive testing hit/miss data to determine the demonstrated probability of detection (POD) for a specific set of examination parameters. Topics covered include the standard hit/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 values given in parentheses are mathematical conversions 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 responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
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Designation: E2862 − 18
Standard Practice for
1
Probability of Detection Analysis for Hit/Miss Data
This standard is issued under the fixed designation E2862; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2.2 Department of Defense Handbook:
MIL-HDBK-1823A Nondestructive Evaluation System Re-
1.1 This practice defines the procedure for performing a
3
liability Assessment
statistical analysis on nondestructive testing hit/miss data to
determine the demonstrated probability of detection (POD) for
3. Terminology
a specific set of examination parameters. Topics covered
3.1 Definitions of Terms Specific to This Standard:
include the standard hit/miss POD curve formulation, valida-
3.1.1 analyst, n—the person responsible for performing a
tion techniques, and correct interpretation of results.
POD analysis on hit/miss data resulting from a POD examina-
1.2 The values stated in inch-pound units are to be regarded
tion.
as standard. The values given in parentheses are mathematical
3.1.2 demonstrated probability of detection, n—the calcu-
conversions to SI units that are provided for information only
lated POD value resulting from the statistical analysis on the
and are not considered standard.
hit/miss data.
1.3 This standard does not purport to address all of the
3.1.3 false call, n—the perceived detection of a discontinu-
safety concerns, if any, associated with its use. It is the
ity that is identified as a find during a POD examination when
responsibility of the user of this standard to establish appro-
no discontinuity actually exists at the inspection site.
priate safety, health, and environmental practices and deter-
3.1.4 hit, n—an existing discontinuity that is identified as a
mine the applicability of regulatory limitations prior to use.
find during a POD demonstration examination.
1.4 This international standard was developed in accor-
3.1.5 miss, n—an existing discontinuity that is missed dur-
dance with internationally recognized principles on standard-
ing a POD examination.
ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
3.1.6 probability of detection (POD), n—the fraction of
mendations issued by the World Trade Organization Technical nominal discontinuity sizes expected to be found given their
Barriers to Trade (TBT) Committee. existence.
3.2 Symbols:
2. Referenced Documents
3.2.1 a—discontinuity size.
2
2.1 ASTM Standards:
3.2.2 a —the discontinuity size that can be detected with
p
E178 Practice for Dealing With Outlying Observations
probability p.
E456 Terminology Relating to Quality and Statistics
3.2.2.1 Discussion—Each discontinuity size has an indepen-
E1316 Terminology for Nondestructive Examinations
dent probability of being detected and corresponding probabil-
E2586 Practice for Calculating and Using Basic Statistics
ity of being missed. For example, being able to detect a specific
E3023 Practice for Probability of Detection Analysis for â
discontinuity size with probability p does not guarantee that a
Versus a Data
larger size discontinuity will be found.
E3080 Practice for Regression Analysis
3.2.3 a —the discontinuity size that can be detected with
p/c
probability p with a statistical confidence level of c.
3.2.3.1 Discussion—According to the formula in MIL-
1
This practice is under the jurisdiction of ASTM Committee E07 on Nonde- HDBK-1823A, a is a one-sided upper confidence bound on
p/c
structive Testing and is the direct responsibility of Subcommittee E07.10 on
a , a represents how large the true a could be given the
p p/c p
Specialized NDT Methods.
statistical uncertainty associated with limited sample data.
Current edition approved Feb. 1, 2018. Published April 2018. Originally
Hence a > a . Note that POD is equal to p for both a and
approved in 2012. Last previous edition approved in 2012 as E2862 – 12. p/c p p/c
DOI:10.1520/E2862-18.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
3
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Available from Standardization Documents Order Desk, DODSSP, Bldg. 4,
Standards volume information, refer to the standard’s Document Summary page on Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http://
the ASTM website. dodssp.daps.dla.mil.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2862 − 18
a . a is based solely on the hit/miss data resulting from the administration proce
...
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. Because
it 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 version
of the standard as published by ASTM is to be considered the official document.
Designation: E2862 − 12 E2862 − 18
Standard Practice for
1
Probability of Detection Analysis for Hit/Miss Data
This standard is issued under the fixed designation E2862; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice defines the procedure for performing a statistical analysis on nondestructive testing hit/miss data to determine
the demonstrated probability of detection (POD) for a specific set of examination parameters. Topics covered include the standard
hit/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 values given in parentheses are mathematical
conversions 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 responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2
2.1 ASTM Standards:
E178 Practice for Dealing With Outlying Observations
E456 Terminology Relating to Quality and Statistics
E1316 Terminology for Nondestructive Examinations
E2586 Practice for Calculating and Using Basic Statistics
E3023 Practice for Probability of Detection Analysis for â Versus a Data
E3080 Practice for Regression Analysis
2.2 Department of Defense Handbook:
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MIL-HDBK-1823A Nondestructive Evaluation System Reliability Assessment
3. Terminology
3.1 Definitions of Terms Specific to This Standard:
3.1.1 analyst, n—the person responsible for performing a POD analysis on hit/miss data resulting from a POD examination.
3.1.2 demonstrated probability of detection, n—the calculated POD value resulting from the statistical analysis on the hit miss
hit/miss data.
3.1.3 false call, n—the perceived detection of a discontinuity that is identified as a find during a POD examination when no
discontinuity actually exists at the inspection site.
3.1.4 hit, n—an existing discontinuity that is identified as a find during a POD demonstration examination.
3.1.5 miss, n—an existing discontinuity that is missed during a POD examination.
3.1.6 probability of detection, detection (POD), n—the fraction of nominal discontinuity sizes expected to be found given their
existence.
1
This practice is under the jurisdiction of ASTM Committee E07 on Nondestructive Testing and is the direct responsibility of Subcommittee E07.10 on Specialized NDT
Methods.
Current edition approved Jan. 15, 2012Feb. 1, 2018. Published February 2012April 2018. DOI:10.1520/E2862-12.Originally approved in 2012. Last previous edition
approved in 2012 as E2862 – 12. DOI:10.1520/E2862-18.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
3
Available from Standardization Documents Order Desk, DODSSP, Bldg. 4, Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http://dodssp.daps.dla.mil.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
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E2862 − 18
3.2 Symbols:
3.2.1 a—discontinuity size.
3.2.2 a —the discontinuity size that can be detected with probability p.
p
3.2.2.1 Discussion—
Each discontinuity size has an independent probability of being detected and corresponding probability of being missed. For
example, being able to detect a specific discontinuity size with probability p does not guarantee that a larger size discontinuity will
be found.
3.2.3 a —the discontinuity size that can be detected with probability p with a statistical confidence level of c.
p/c
3.2.3.1 Discussion—
According to the formula in MIL-HDB
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