Computational Statistics https://doi.org/10.1007/s00180-020-01021-y ORIGINAL PAPER Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution Junru Ren 1 · Wenhao Gui 1 Received: 10 April 2020 / Accepted: 27 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract This paper considers the statistical inference for the competing risks model from generalized Rayleigh distribution based on progressive Type-II censoring when the parameters of the latent lifetime distributions are different or common. Maximum like- lihood estimates are obtained, where the existence of the point estimators are proved, and the confidence intervals are established via the observed Fisher information matrix as well. Bayesian estimates of unknown parameters and reliability characteristics are derived under symmetric and asymmetric loss functions, and Monte Carlo Markov Chain sampling method is used to compute the Bayesian point estimates and the highest posterior density credible intervals. In addition, Bootstrap methods are also considered to obtain bias-corrected point estimates and approximate confidence inter- vals. Then we carry out hypothesis test using likelihood ratio test statistics. Monte Carlo simulation and a set of real data are presented to assess the performance of our proposed methods. Finally, the optimal censoring scheme issue is studied. Keywords Maximum likelihood estimation · Monte Carlo Markov Chain · Bootstrap method · Likelihood ratio test · Optimal progressive censoring plan 1 Introduction In real life testing, there are often more than one cause of product failure, and only the smallest failure time can be observed when multiple modes of failure work together. It is called competing risks model for various modes of failure are considered to be competing in a sense. In electronic engineering, social sciences or medical statistics, competing risks data are quite common, which consist of a time to failure and associ- ated failure mode. Therefore, it is necessary to do the precise inference of each failure B Wenhao Gui whgui@bjtu.edu.cn 1 Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China 123