Meta-analysis of exponential lifetime data from Type-I hybrid censored samples

In this study, in order to do a life testing experiment, sampled units are divided into a prefixed number of groups with equal number of units. Units in all the groups are tested simultaneously and independently and, in each group the experiment is terminated as soon as a prefixed time elapses or a prefixed number of failures occurs. We provide the meta-analysis of an exponential lifetime data from Type-I hybrid censored samples. The main goal of this study is to obtain optimal schemes based on some optimality criteria by minimizing certain cost function that is based on a maximum likelihood estimator of mean lifetime. We provide the maximum likelihood estimator of mean lifetime and its probability density function under this set-up. Various optimal schemes have been provided by minimizing expected total cost incurred during the experiment as the raw moments can be obtained explicitly. Numerical results on bias and mean squared error of the maximum likelihood estimator have been reported. We also provide confidence intervals of the unknown parameter. For illustration, meta-analysis for a real data set of three groups is presented.