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Nonparametric Estimation of the Probability of Detection of Flaws in an Industrial Component, from Destructive and Nondestructive Testing Data, Using Approximate Bayesian Computation
Author(s) -
Keller Merlin,
Popelin AnneLaure,
Bousquet Nicolas,
Remy Emmanuel
Publication year - 2015
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/risa.12484
Subject(s) - markov chain monte carlo , parametric statistics , nonparametric statistics , bayesian probability , context (archaeology) , computation , computer science , component (thermodynamics) , monte carlo method , algorithm , mathematics , statistics , paleontology , physics , biology , thermodynamics
We consider the problem of estimating the probability of detection (POD) of flaws in an industrial steel component. Modeled as an increasing function of the flaw height, the POD characterizes the detection process; it is also involved in the estimation of the flaw size distribution, a key input parameter of physical models describing the behavior of the steel component when submitted to extreme thermodynamic loads. Such models are used to assess the resistance of highly reliable systems whose failures are seldom observed in practice. We develop a Bayesian method to estimate the flaw size distribution and the POD function, using flaw height measures from periodic in‐service inspections conducted with an ultrasonic detection device, together with measures from destructive lab experiments. Our approach, based on approximate Bayesian computation (ABC) techniques, is applied to a real data set and compared to maximum likelihood estimation (MLE) and a more classical approach based on Markov Chain Monte Carlo (MCMC) techniques. In particular, we show that the parametric model describing the POD as the cumulative distribution function (cdf) of a log‐normal distribution, though often used in this context, can be invalidated by the data at hand. We propose an alternative nonparametric model, which assumes no predefined shape, and extend the ABC framework to this setting. Experimental results demonstrate the ability of this method to provide a flexible estimation of the POD function and describe its uncertainty accurately.