Confidence intervals for the two-parameter exponential reliability with Type II censored data

摘要

Purpose:To construct confidence intervals for the reliability based on two-parameter exponential distribution with Type II censored data.Summary:While exponential distribution plays an important role in reliability theory and practice that involve with life testing experiments, such experiments often experience to deal with Type II censored data. The interval estimation of the reliability of the two-parameter exponential distribution is considered when Type II censored available. The fiducial interval, the Engelhardt-Bain interval and asymptotic interval are studied. The case of constructing confidence intervals using the relationship between reliability and quantiles is also considered. Further, the intervals based on the inverse cumulative distribution function transform, the percentile intervals, the bootstrap intervals and Bayesian intervals are studied. The intervals based on generalized variables are presented. In order to illustrate the confidence intervals, both simulation and real time examples are given. The coverage probabilities and expected lengths based for the confidence intervals are obtained to make comparisons.Results:The role played by exponential distribution in reliability theory and practice as well as in other fields is examined. In reliability studies, the life testing experiments often involve Type II censored data in which a total number of units is placed on test and then the test is terminated as soon as a prefixed number of failures are observed. There are many reliability studies involving Type II censored data with different failure time distributions. There are such studies using two-parameter exponential distribution as well. Highlighting the importance of two-parameter exponential distribution to study the confidence intervals for two-parameter exponential distribution with Type II censored data is proposed.Several confidence intervals that are suggested in the literature for the exponential reliability are presented.