Bayesian optimum life testing plans under progressive Type-I interval censoring scheme

In many industrial applications, it is not always feasible to continuously monitor the life testing experiments to collect lifetime data. Moreover, intermediate removals of the test units from the life testing experiment are sometimes essential. Progressive Type-I interval censoring schemes are useful in these scenarios. Optimal planning of such progressive Type-I interval censoring schemes is an important issue to the experimenter, as the optimal plans can achieve the desired objectives using much lesser resources. This article provides Bayesian D-optimal progressive Type-I interval censoring schemes, assuming that the lifetime follows a log-normal distribution. An algorithm is provided to find the optimal censoring schemes and the number of inspections. The algorithm is then used to obtain the optimal Bayesian progressive Type-I interval censoring schemes in 2 different contexts. The resulting optimal Bayesian censoring schemes are compared with the corresponding locally optimal censoring schemes. A detailed sensitivity analysis is performed to investigate the effect of prior information. The sampling variation associated with the optimal censoring schemes is visualized through a simulation study.