Statistical inference of adaptive type II progressive hybrid censored data with dependent competing risks under bivariate exponential distribution

Marshall-Olkin bivariate exponential distribution is used to statistically infer the adaptive type II progressive hybrid censored data under dependent competition risk model. For complex censored data with only partial failure reasons observed, maximum likelihood estimation and approximate confidence interval based on Fisher information are established. At the same time, Bayesian estimation is performed under the highly flexible Gamma-Dirichlet prior distribution and the highest posterior density interval using Gibbs sampling and Metropolis-Hastings algorithm is obtained. Then the performance of two methods is compared through several indexes. In addition, the Monte Carlo method is used for data simulation of multiple sets of variables to give experimental suggestions. Finally, a practical example is given to illustrate the operability and applicability of the proposed algorithm to efficiently carry out reliability test.