Application of Bayesian techniques to reliability prediction of the structural elements of the electronic apparatus

Abstract

In the clause are examined means for using of Bayesian method of approach to calculate of non-parametric empirical Bayes estimation of probability for flawless work of electronic apparatus. Existence of field of study of insensibility is fixed, e.g. existence of this field of study in the prior definition, corrections within of which don't lead to corrections in estimations of probability for failure less work. .Using a classical approach, the parameter the failure rate λ is assumed constant, but unknown and an estimate of λ computed by an estimation technique such as maximum likelihood or matching moments. Based on the statistical properties of the estimator, inferences regarding the true parameter λ are subsequently made. This means that classical interval estimation and hypothesis testing are based on inductive reasoning. Using the Bayesian approach, however, it is assumed that one has some prior knowledge regarding the parameter λ. Uncertainly regarding the true value of λ is treated by assuming that the true value of λ can be described by a probability distribution. Combination of observed data (or evidence) with a prior distribution (prior distribution relates to the knowledge or belief one has regarding λ) results in an updated posterior distribution for λ. Since a posterior distribution for the parameter λ is now available, the construction of probability intervals and hypothesis testing is necessarily based on deductive reasoning and consequently eliminates the need for constructing confidence limits. The Bayesian approach has often been a subject of controversy ever since it was first proposed by Bayes. Bouissou, Martin and Ourghanlian considered estimation of a safety­ critical system including software: a Bayesian belief network for evidence sources. Tran, Murdock and Pohl accomplished Bayesian analysis for system