Family of Kumaraswamy generalized distribution in estimation of multi-component reliability under the adaptive hybrid progressive censoring schemes

ABSTRACTIn this paper, the statistical inference on multi-component stress-strength parameter with non-identical-component strengths, based on Kumaraswamy generalized distribution under adaptive hybrid progressive censoring samples, is considered. The problem is solved in three cases. First, when one parameter is unknown, the maximum likelihood estimation (MLE), Bayes approximations, asymptotic and highest posterior density intervals are obtained. Second, when the common parameter is known, MLE, approximation Bayes estimations, uniformly minimum variance unbiased estimator and different confidence intervals are provided. Third, when all parameters are different and unknown, MLE and Bayesian estimation are studied. The Monte Carlo simulation is employed to compare the estimations. Based on the simulation results, it is observed that the Bayesian estimates perform better than MLEs. Also, the highest posterior density intervals have better performance than asymptotic intervals. Moreover, it is observed that the performance of uniformly minimum variance unbiased estimators is worse than MLEs. To implement the theoretical method, two real data sets are analyzed.