Inference on the stress-strength reliability of multi-component systems based on progressive first failure censored samples

Abstract

This paper studies the statistical estimation of the stress-strength reliability of multi-component systems under the progressive first failure censoring samples, where the lifetime distribution of each component follows the modified Kumaraswamy distribution. Both the point and interval estimations of the parameters in the reliability function are considered. To this aim, some estimations such as maximum likelihood estimation (MLE), asymptotic confidence intervals, uniformly minimum variance unbiased estimation (UMVUE), approximate Bayes estimation, and highest posterior density (HPD) intervals are obtained. By employing the Monte Carlo simulation, comparison of the performance between different estimates is provided. The paper then analyzes a case study for illustration of the proposed method.