Instantaneous failure analysis on Lindley distribution under progressive type II censoring

This paper deals with the analysis of the occurrence of instantaneous failures in Lindley distribution using progressive type-II censored samples. The test items that fail at a time are called instantaneous failures. Such failures are naturally experienced in life testing experiments, clinical trials, weather predictions, geographic information systems, athlete performance analysis, and many other real fields. These occurrences may be due to the inferior quality of a product or service, faulty construction, or alignment of events/objects, or due to no response to the treatments. Such failures usually discard the assumption of a single-mode distribution and hence the usual method of modeling and inference procedures may not be accurate in practice. To tackle this problem, one must use a non-standard mixture of degenerate distribution degenerated at zero and a standard distribution of a continuous or discrete variable. In this paper, we have considered a non-standard mixture model with continuous Lindley failure distribution for positive components under a progressive type-II censoring scheme. We obtained the maximum likelihood estimators of the proposed distribution and its asymptotic, bootstrap-p (boot-p), and bootstrap-t (boot-t) confidence intervals are derived. The Bayes estimators for the proposed distribution parameters, reliability function, and hazard rate function with their highest posterior density credible intervals using informative priors and non-informative priors under different loss functions are obtained. The performances of different estimators are studied using the MCMC simulation technique. Two real-life data sets have been analyzed for illustration purposes.