Stress-Strength Reliability of a Two-Parameter Bathtub-shaped Lifetime Distribution Based on Progressively Censored Samples |
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Authors: | Shirin Shoaee |
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Affiliation: | Faculty of Mathematics and Computer Science, Department of Statistics, Amirkabir University of Technology, Tehran, Iran |
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Abstract: | Based on progressively Type-II censored samples, this article deals with inference for the stress-strength reliability R = P(Y < X) when X and Y are two independent two-parameter bathtub-shape lifetime distributions with different scale parameters, but having the same shape parameter. Different methods for estimating the reliability are applied. The maximum likelihood estimate of R is derived. Also, its asymptotic distribution is used to construct an asymptotic confidence interval for R. Assuming that the shape parameter is known, the maximum likelihood estimator of R is obtained. Based on the exact distribution of the maximum likelihood estimator of R an exact confidence interval of that has been obtained. The uniformly minimum variance unbiased estimator are calculated for R. Bayes estimate of R and the associated credible interval are also got under the assumption of independent gamma priors. Monte Carlo simulations are performed to compare the performances of the proposed estimators. One data analysis has been performed for illustrative purpose. Finally, we will generalize this distribution to the proportional hazard family with two parameters and derive various estimators in this family. |
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Keywords: | Asymptotic distributions Bathtub-shape lifetime distribution Bayesian estimator Maximum likelihood estimator Proportional hazard family Progressive Type-II Censoring Stress-strength model Uniformly minimum variance unbiased estimator |
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