A comparative study of probability estimation methods for reliability analysis

Authors:
Zhimin Xi;Chao Hu;Byeng D. Youn
Affiliations:
Department of Industrial and Manufacturing Systems Engineering, University of Michigan, Dearborn, USA 48168;Department of Mechanical Engineering, University of Maryland, College Park, USA 20742;School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, South Korea
Venue:
Structural and Multidisciplinary Optimization
Year:
2012

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Abstract

In this paper we investigate the performance of probability estimation methods for reliability analysis. The probability estimation methods typically construct the probability density function (PDF) of a system response using estimated statistical moments, and then perform reliability analysis based on the approximate PDF. In recent years, a number of probability estimation methods have been proposed, such as the Pearson system, saddlepoint approximation, Maximum Entropy Principle (MEP), and Johnson system. However, no general guideline to suggest a most appropriate probability estimation method has yet been proposed. In this study, we carry out a comparative study of the four probability estimation methods so as to derive the general guidelines. Several comparison metrics are proposed to quantify the accuracy in the PDF approximation, cumulative density function (CDF) approximation and tail probability estimations (or reliability analysis). This comparative study gives an insightful guidance for selecting the most appropriate probability estimation method for reliability analysis. The four probability estimation methods are extensively tested with one mathematical and two engineering examples, each of which considers eight different combinations of the system response characteristics in terms of response boundness, skewness, and kurtosis.