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MATHEMATICAL MODEL OF ACCELERATED LIFE TESTING USING GEOMETRIC PROCESS FOR MARSHALLOLKIN EXTENDED EXPONENTIAL DISTRIBUTION

Abstract

In accelerated life testing researcher generally use a life stress relationship between life characteristic and stress to estimate the parameters of failure time distributions at use condition which is just a re-parameterization of original parameters but from statistical point of view it is easy and reasonable to deal with original parameters of the distribution directly instead of developing inference for the parameters of the life stress relationship. By assuming that the lifetimes at increasing stress levels forms a geometric process one can easily handle the original parameters of life distribution directly in accelerated life testing. In this paper a mathematical model for the analysis of constant stress accelerated life testing by using geometric process for Marshall-Olkin Extended Exponential distribution is developed. The estimates of parameters are obtained by using the maximum likelihood method for complete data. In order to get the asymptotic variance of the ML estimator, the Fisher information matrix is constructed. The asymptotic interval estimates of the parameters are then obtained by using this asymptotic variance. In the last a simulation study is performed to illustrate the statistical properties of the parameters and the confidence intervals

Sadia Anwar, Mustafa Kamal, Arif-Ul-Islam

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