Fuzzy Bayesian system reliability assessment based on Pascal distribution

Ramin Gholizadeh

doi:10.1007/s00158-009-0396-y

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Fuzzy Bayesian system reliability assessment based on Pascal distribution

2009-05-19

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Ramin Gholizadeh *

Aliakbar Mastani Shirazi

Bahram Sadeghpour Gildeh

Deiri, Eynollah

DOI：10.1007/s00158-009-0396-y

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Abstract

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The main purpose of this paper is to provide a methodology for discussing the fuzzy. Bayesian system reliability from the fuzzy component reliabilities, actually we discuss on the Fuzzy Bayesian system reliability assessment based on Pascal distribution, because the data sometimes cannot be measured and recorded precisely. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayes estimation method will be used to create the fuzzy Bayes point estimator of system reliability by invoking the well-known theorem called 'Resolution Identity' in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four sub-problems for the purpose of simplifying computation. Finally, the sub problems can be solved by using any commercial optimizers, e.g. GAMS or LINGO.

Keywords:

Bayes point estimators

Confidence degree

Fuzzy real numbers

Nonlinear programming

System reliability

Pascal distribution