Estimations and optimal censoring schemes for the unified progressive hybrid gamma-mixed Rayleigh distribution

Censoring is a common occurrence in reliability engineering tests. This article considers estimation of the model parameters and the reliability characteristics of the gamma-mixed Rayleigh distribution based on a novel unified progressive hybrid censoring scheme (UPrgHyCS), where experimenters are allowed more flexibility in designing the test and higher efficiency. The maximum likelihood estimates of the model parameters and reliability are provided using the stochastic expectation–maximization algorithm based on the UPrgHyCS. Further, the Bayesian inference associated with any parametric function of the model parameters is considered using the Markov chain Monte Carlo method with the Metropolis-Hastings (M-H) algorithm. Asymptotic confidence and credible intervals of the proposed quantities are also created. The maximum a posteriori estimates of the model parameters are acquired. Due to the importance of determining the optimal censoring scheme for reliability problems, different optimality criteria are proposed and derived to find it. This method can help to design experiments and get more information about unknown parameters for a given sample size. Finally, comprehensive simulation experiments are provided to investigate the performances of the considered estimates, and a real dataset is analyzed to elucidate the practical application and the optimality criterion work in real life scenarios. The Bayes estimates using the M-H technique show the best performance in terms of error values.