The life-span prediction of a system connected in series

The life-span prediction of a system connected in series

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Article ID: iaor201527023
Volume: 79
Issue: 5
Start Page Number: 1770
End Page Number: 1777
Publication Date: Jan 2009
Journal: Mathematics and Computers in Simulation
Authors: ,
Keywords: Bayesian analysis, life expectancy, partial differential equations (PDE)
Abstract:

This article considers the prediction problem of the life‐span of a system whose components connected in series and the lifetime of the components follows the exponential distribution with probability density f ( x ; θ ) = θ 1 exp θ ( x / θ ) I ( x > 0 ) equ1. Employing the Bayes method, a prior distribution G ( θ ) equ2 is used to describe the variability of θ equ3 but the form of G ( θ ) equ4 is not specified and only one moment condition is assumed. Suppose the observed lifetimes of components are rightly censored, we define a prediction statistic to predict the life‐span of the series‐wound system which consists of some untested components, firstly, under the condition that the censoring distribution is known and secondly, that it is unknown. For several different priors, we investigate the coverage frequencies of the proposed prediction intervals as the sample size and the censorship proportion change. The simulation study shows that our predictions are efficient and applicable.

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