Parameter Estimation of Type-I and Type-II Hybrid Censored Data from the Log-Logistic Distribution

Abstract

In experiments on product lifetime and reliability testing, there are many practical situations in which researchers terminate the experiment and report the results before all items of the experiment fail because of time or cost consideration. The most common and popular censoring schemes are type-I and type-II censoring. In type-I censoring scheme, the termination time is pre-fixed, but the number of observed failures is a random variable. However, if the mean lifetime of experimental units is somewhat larger than the pre-fixed termination time, then far fewer failures would be observed and this is a significant disadvantage on the efficiency of inferential procedures. In type-II censoring scheme, however, the number of observed failures is pre-fixed, but the experiment time is a random variable. In this case, at least pre-specified number of failure are obtained, but the termination time is clearly a disadvantage from the experimenter’s point of view. To overcome some of the drawbacks in those schemes, the hybrid censoring scheme, which is a mixture of the conventional type-I and type-II censoring schemes, has received much attention in recent years. In this paper, we consider the analysis of type-I and type-II hybrid censored data where the lifetimes of items follow two-parameter log-logistic distribution. We present the maximum likelihood estimators of unknown parameters and asymptotic confidence intervals, and a simulation study is conducted to evaluate the proposed methods.