Abstract
Based on failures of a parallel-series system, a new distribution called geometric-Poisson-Rayleigh distribution is proposed. Some properties of the distribution are discussed. A real data set is used to compare the new distribution with other 6 distributions. The progressive-stress accelerated life tests are considered when the lifetime of an item under use condition is assumed to follow the geometric-Poisson-Rayleigh distribution. It is assumed that the scale parameter of the geometric-Poisson-Rayleigh distribution satisfies the inverse power law such that the stress is a nonlinear increasing function of time and the cumulative exposure model for the effect of changing stress holds. Based on type-I progressive hybrid censoring with binomial removals, the maximum likelihood and Bayes (using linear-exponential and general entropy loss functions) estimation methods are considered to estimate the involved parameters. Some point predictors such as the maximum likelihood, conditional median, best unbiased, and Bayes point predictors for future order statistics are obtained. The Bayes estimates are obtained using Markov chain Monte Carlo algorithm. Finally, a simulation study is performed, and numerical computations are performed to compare the performance of the implemented methods of estimation and prediction.