Reliability estimation of k-unit series system based on progressiverly censored data

In this article, we consider a k-unit series system with component lifetime distribution to be a member of the scale family of distributions. We discuss estimation of the scale parameter and estimation of reliability function of the family based on progressively Type-II censored sample. The maximum likelihood estimator (MLE) of the scale parameter is derived using Expectation-Maximization (EM) algorithm and is used to estimate reliability function. Confidence intervals are constructed using asymptotic distribution of MLE. β-expectation tolerance interval for lifetime of the system is obtained. We consider half-logistic distribution as a member of the scale family and study performance of the MLE, reliability estimate and confidence interval using simulation experiments