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The competing risks model plays an important role in the statistical analysis of engineering, econometric, biological and other fields. A tested product may fail from different causes. Therefore, these failure causes as if competing with each other to bring about the failure of tested products (an experimental unit). Hence, in the statistical literature, this is known as the competing risk problem and it has been studied quite extensively by several researchers when the lifetime of the product is the latent failure time of the first failure cause among all the possible failure causes. In this paper, a competing risks model based on a generalized progressive hybrid type-I (GPH type-I) censoring is considered when the latent lifetime distributions of failure causes are inverse Weibull (IW) distributed and partially observed. We established various estimation methods including Maximum likelihood estimates (MLEs) and Bayes estimates (BEs). MLEs with the corresponding asymptotic confidence intervals are obtained. Bayes estimates of the parameters are obtained based on squared error loss (SEL) function under the assumption of independent gamma priors. Furthermore, we applied Markov Chain Monte Carlo (MCMC) techniques to compute BEs and to calculate the credible intervals. Finally, simulation studies and real data set are used for illustrative purpose. [ABSTRACT FROM AUTHOR]

There are many situations in reliability or medical studies, where items may fail due to one of several causes. Further, censoring is unavoidable in any life testing. In this paper attempts to estimate problem for the competing risks model where the data are adaptive type-II progressive hybrid censored scheme and follow the inverse Weibull distribution. In this regards, we obtain the maximum likelihood estimation of the parameters and the asymptotic confidence intervals for the unknown parameters. Further, Bayes estimates of the parameters which obtained based on squared error and LINEX loss functions under the assumptions of independent gamma priors. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques by applying the Metropolis-Hasting algorithm under the square error and LINEX loss function to derive Bayesian estimators. Finally, two data sets with a Monte Carlo simulation study and a real data set of the electronic applications are analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]