Inference on P(Y < X) in Bivariate Rayleigh Distribution |
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Authors: | A Pak N B Khoolenjani A A Jafari |
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Institution: | 1. Department of Statistics, Shahid Chamran University, Ahvaz, Iran;2. Department of Statistics, Shiraz University, Shiraz, Iran;3. Department of Statistics, Yazd University, Yazd, Iran |
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Abstract: | This paper deals with the estimation of reliability R = P(Y < X) when X is a random strength of a component subjected to a random stress Y, and (X, Y) follows a bivariate Rayleigh distribution. The maximum likelihood estimator of R and its asymptotic distribution are obtained. An asymptotic confidence interval of R is constructed using the asymptotic distribution. Also, two confidence intervals are proposed based on Bootstrap method and a computational approach. Testing of the reliability based on asymptotic distribution of R is discussed. Simulation study to investigate performance of the confidence intervals and tests has been carried out. Also, a numerical example is given to illustrate the proposed approaches. |
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Keywords: | Bivariate Rayleigh distribution Fisher information matrix Maximum likelihood estimator Stress-Strength model System reliability |
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