## ASTM-E3023 › Standard Practice for Probability of Detection Analysis for â Versus a Data

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### Scope

1.1 This practice defines the procedure for performing a statistical analysis on Nondestructive Testing (NDT) â versus a data to determine the demonstrated probability of detection (POD) for a specific set of examination parameters. Topics covered include the standard â versus a regression methodology, 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 and health practices and determine the applicability of regulatory limitations prior to use.*

### Significance and Use

5.1 The POD analysis method described herein is based on well-known and well-established statistical methods. 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 measurable and can be classified as a continuous variable.

5.1.2 The relationship between discontinuity size (a) and measured signal response (â) exists and is best described by a linear regression model with an error structure that is normally distributed with mean zero and constant variance, σ^{2}. (Note that “linear” refers to linear with respect to the model coefficients. For example, a quadratic model is a linear model.)

5.2 This practice does not limit the use of other statistical models if justified as more appropriate for the â versus a data.

5.3 This practice is not appropriate for data resulting from a POD examination on nondestructive evaluation systems that generate an initial response that is binary in nature (for example, hit/miss). Practice E2862 is appropriate for systems that generate a hit/miss-type response (for example, fluorescent penetrant).

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; the POD examination administration procedure (including data collection method) is well designed, well defined, under control, and unbiased; the initial inspection system response is measurable and continuous in nature; the inspection system is calibrated; and the measurement error has been evaluated and deemed acceptable. The analysis results are only valid if the â versus a data are accurate and precise and the linear model adequately represents the â versus a data.

5.5 The POD analysis method described herein is consistent with the analysis method for â versus a data described in MIL-HDBK-1823A and is included in several widely utilized POD software packages to perform a POD analysis on â versus a data. It is also found in statistical software packages that have linear regression capability. This practice requires that the analyst has access to either POD software or other software with linear regression capability.

### Keywords

a-hat vs. a; ahat vs. a; eddy current inspection; eddy current POD; Linear Regression; POD; POD analysis; probability of detection; regression;; ICS Number Code 19.100 (Non-destructive testing)

### To find similar documents by ASTM Volume:

03.03 (Nondestructive Testing)

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### Document Number

ASTM-E3023-15

### Revision Level

2015 EDITION

### Status

Current

### Modification Type

New

### Publication Date

Aug. 1, 2015

### Document Type

Practice

### Page Count

12 pages

### Committee Number

E07.10