Inference for log‐location‐scale family of distributions under competing risks with progressive type‐I interval censored data

In this article, we present statistical inference of unknown lifetime parameters based on a progressive Type‐I interval censored dataset in presence of independent competing risks. A progressive Type‐I interval censoring scheme is a generalization of an interval censoring scheme, allowing intermediate withdrawals of test units at the inspection points. We assume that the lifetime distribution corresponding to a failure mode belongs to a log‐location‐scale family of distributions. Subsequently, we present the maximum likelihood analysis for unknown model parameters. We observe that the numerical computation of the maximum likelihood estimates can be significantly eased by developing an expectation‐maximization algorithm. We demonstrate the same for three popular choices of the log‐location‐scale family of distributions. We then provide Bayesian inference of the unknown lifetime parameters via Gibbs Sampling and a related data augmentation scheme. We compare the performance of the maximum likelihood estimators and Bayesian estimators using a detailed simulation study. We also illustrate the developed methods using a progressive Type‐I interval censored dataset.