Inference of Competing Risks Model with Partially Observed Failure Causes Based on Minimum Ranked Set Sampling

Ranked set sampling (RSS) provides an efficient and flexible approach to collect failure information from perspectives of saving time and cost. In this paper, inference of a competing risks model is proposed based on a popular RSS named minimum ranked set sampling with unequal samples setting. When the lifetimes of competing risks follow exponential distributions and the associated failure causes are partially observed, classical and Bayesian inference are investigated, respectively. Maximum likelihood estimators along with the existence and uniqueness are established and approximate confidence intervals are constructed in consequence by using asymptotic theory. Under general flexible priors, Bayesian estimators and highest posterior density credible intervals are established as well. In addition, when there is extra information available, likelihood and Bayesian estimations are also discussed based on extra order restriction information. Finally, extensive simulation studies and a real-life example are presented for illustrations.