Multi-component stress–strength parameter estimation of a non-identical-component strengths system under the adaptive hybrid progressive censoring samples

Abstract

To produce more flexible models in reliability theory field, statistical inference of stress–strength parameter was studied in a multi-component system with the non-identical-component strengths based on bathtub-shaped distribution under adaptive Type-II hybrid progressive censoring samples. The problem is considered in three cases. First, with assuming that common first parameter is unknown for strengths and stress variables, the maximum likelihood estimation (MLE) and two Bayes approximations are obtained. Also, asymptotic, two bootstrap, and highest posterior density (HPD) intervals are derived. Second, with assuming that common first parameter is known, MLE, exact Bayes estimation, uniformly minimum variance unbiased estimator (UMVUE), and different confidence intervals are provided. Finally, in the third case, with assuming that all parameters are different and unknown, MLE and Bayesian estimation are studied. For comparing different estimates, the Monte Carlo simulation is used and one real data set is employed to implement theoretical methods.