The life-span prediction of a system connected in series

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−1exp⁡(−x/θ)I(x>0)f(x;θ)=θ−1exp⁡(−x/θ)I(x>0). Employing the Bayes method, a prior distribution G(θ)G(θ) is used to describe the variability of θθ but the form of G(θ)G(θ) 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.