On progressively censored competing risks data for Weibull distributions

In survival analysis, or in reliability study, an investigator is often interested in the assessment of a specific risk in the presence of other risk factors. It is well known as the competing risks problem in statistical literature. Moreover, censoring is inevitable in any life testing or reliability study. In this paper, we consider a very general censoring scheme, namely a progressive censoring scheme. It is further assumed that the lifetime distribution of the individual causes are independent and Weibull-distributed with the same shape parameters but different scale parameters.We obtain themaximum likelihood and approximate maximum likelihood estimates of the unknown parameters. We also compute the observed Fisher informationmatrix using the missing information principles, and use them to compute the asymptotic confidence intervals. Monte Carlo simulations are performed to compare the performances of the different methods, and one data set is analyzed for illustrative purposes.Wealso discuss different optimality criteria, and selected optimal progressive censoring plans are presented. © 2009 Elsevier B.V. All rights reserved.