PROGRESSIVE TYPE-II RANDOM CENSORING SCHEME WITH LINDLEY FAILURE AND CENSORING TIME DISTRIBUTIONS

The random censoring scheme has been studied in detail in medical studies, especially in clinical trials to deal with unintentional removals or dropouts. The formal or conventional random censoring scheme has been discussed in the literature by numerous researchers for various statistical distribution models. The progressive censoring scheme has become prevalent in life testing experiments in the last few years, to increase the efficiency and the performance of the estimators. In progressive censoring, a large number of objects or units are placed on a lifetime experiment and intentional progressive removals of live units at epochs other than termination point are considered. But, no one has studied so far, the intentional or progressive removals in the random censoring scenario. The present research paper deals with the progressive type-II random censoring scheme, which has the positive aspects of progressive type-II censoring scheme as well as random censoring scheme. Here, we consider both the failure and censoring time distributions as the Lindley distribution. The maximum likelihood estimators of the unknown parameters with their associated asymptotic confidence intervals are derived with progressively type-II randomly censored data. To evaluate the impact of prior information, Bayes estimates are calculated under the squared error loss function. The expected time on test is also computed. A Monte Carlo simulation study is conducted here, to evaluate the performance of different estimators. A real data set is given for an illustrative purpose. In the end, the criteria for an optimum censoring scheme are given.