Estimation of P(Y < X) in Lindley distribution using progressively first failure censoring

The probability P(Y < X) plays an important role in reliability analysis as it represents reliability in a stress–strength model and availability when Y and X are stress and strength variables, respectively. In reliability theory Lindley distribution has been established as a useful lifetime model and inference procedures for its reliability characteristics are being developed in the literature. To develop these inferences, life testing experiments are conducted which are time consuming and costly in nature. To save time and money various types of censoring plans are used. One such censoring scheme called Progressive censoring has recently become very popular in reliability theory. Progressively first failure censoring is a generalization of progressive censoring scheme and is useful in various practical situations when testing material is inexpensive. In view of above in this paper, maximum likelihood and Bayes estimates for the parameter δ = P(Y < X) are studied when X and Y are Lindley random variables. The data are collected using progressively first failure censoring. A Monte Carlo simulation study is performed to compare different methods of estimation. Two examples, including a real data example, are also given to illustrate the proposed estimates in the paper. © 2014, The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.