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Bayes estimation of reliability under a random environment governed by a Dirichlet prior

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2 Author(s)
S. Kumar ; North Carolina Univ., Charlotte, NC, USA ; R. C. Tiwari

The reliability function of a component whose lifetime is exponentially distributed with a known parameter λ>0 is R (t|λ)=exp (-λt). If an environmental effect multiplies the parameter by a positive factor η, then the reliability function becomes R(t|η,λ)=exp(-ηλt). The authors assume that η itself is random, and its uncertainty is described by a Dirichlet process prior D(α) with parameter α=MG0, where M>O represents an intensity of assurance in the prior guess, G0, of the (unknown) distribution of η. Under squared error loss, the Bayes estimator of R(t|η,λ) is derived both for the no-sample problem and for a sample of size n. Using Monte Carlo simulation, the effects of n, M, G0 on the estimator are studied. These examples show that: (a) large values of n lead to estimates where the data outweigh the prior, and (b) large values of M increase the contribution of the prior to the estimates. These simulation results support intuitive ideas about the effect of environment and lifetime parameters on reliability

Published in:

IEEE Transactions on Reliability  (Volume:38 ,  Issue: 2 )