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Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure
Authors:Soumya Roy  Chiranjit Mukhopadhyay
Institution:1. Department of Management Studies, Indian Institute of Science, Bangalore, Indiasoumya@mgmt.iisc.ernet.in;3. Department of Management Studies, Indian Institute of Science, Bangalore, India
Abstract:Consider a J-component series system which is put on Accelerated Life Test (ALT) involving K stress variables. First, a general formulation of ALT is provided for log-location-scale family of distributions. A general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, log-linear model, etc., as special cases. Later, the component lives are assumed to be independent Weibull random variables with a common shape parameter. A full Bayesian methodology is then developed by letting only the scale parameters of the Weibull component lives depend on the stress variables through the general stress translation function. Priors on all the parameters, namely the stress coefficients and the Weibull shape parameter, are assumed to be log-concave and independent of each other. This assumption is to facilitate Gibbs sampling from the joint posterior. The samples thus generated from the joint posterior is then used to obtain the Bayesian point and interval estimates of the system reliability at usage condition.
Keywords:Series system  Common shape parameter  Stress translation function  Gibbs sampling  Log-concavity
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