Inference for two Weibull populations under joint generalized progressive type-I hybrid censoring with a simulation study and applications

The generalized progressive censoring scheme has been considered one of the most general cases of censoring schemes. In this study, we consider two Weibull populations under a jointly generalized progressive hybrid censoring scheme as a more flexible extension of the exponential distribution. The methods presented in this paper let experimenters evaluate life testing studies in the case of the most generalized censoring scheme based on a flexible distribution that has increasing, constant, and decreasing failure rates. The maximum likelihood method is used to obtain point estimates of the unknown parameters and the corresponding approximate confidence intervals by using asymptotic theory and bootstrap sampling. The Bayesian inferences are handled under informative and non-informative priors. The highest posterior density credible intervals are also obtained for the Bayesian estimations. We further obtained results with a challenging task an optimal censoring scheme using the A-optimality, D-optimality, and F-optimality criterion to let researchers determine the optimal censoring plan before conducting experiments or collecting data. Following the numerical results within this paper, A-optimality and D-optimality proposed the same scheme, while F-optimality proposed a scheme similar to them. In the last part of the study, we provide simulation studies under different censoring plans and use a numerical example to exemplify the theoretical outcomes. It is observed that the best estimation performances are obtained by informative Bayesian methods.