Analysis of Reliability Characteristics of Bathtub-Shaped Distribution Under Adaptive Type-I Progressive Hybrid Censoring

In reliability and life testing experiments, obtaining complete data still consumes lots of time, financial and human supports. A censoring scheme which can have balance between the total testing time, the used number of units and cost in life tests is desirable. Nevertheless, with short product development times, life testing experiments must be performed with severe time constraints, which makes failure-censored schemes such as type-II censoring and progressive type-II censoring schemes are no longer applicable in many real life scenarios. Therefore, an adaptive type-I progressive hybrid censoring scheme has been shown to be useful in this case, which assures the termination of the life testing experiment at a predetermined time and results in a higher efficiency estimations. In this paper we consider the estimation problem of parameters, reliability and hazard rate functions of a two-parameter bathtub-shaped distribution under adaptive type-I progressive hybrid censoring scheme using the maximum likelihood and Bayesian estimation methods. Lindley's approximation and an importance sampling procedure under the assumption of independent gamma priors are used to obtain the Bayes estimators. Approximate confidence, two parametric bootstrap and highest posterior density intervals are also obtained for the unknown parameters, reliability and hazard rate functions. The approximate confidence intervals of the reliability and hazard rate functions are obtained by estimating their variances using delta method. A simulation study is conducted to compare the performance of the different estimators in terms of their mean squared errors and interval lengths. Finally, two real data sets are analyzed to show the applicability of the different estimations. The data analysis showed that the adaptive type-I progressive hybrid censoring scheme is flexible and very useful in terminating the experiment when the time is the main concern to the experimenter.