Inference and Prediction for the Burr XII Distribution Under A Generalized Type‐III Hybrid Censoring Scheme

ABSTRACT This paper introduces a generalized Type‐III hybrid censoring scheme for reliability data analysis. The scheme combines two failure‐number thresholds with two time limits, so that more failure information can be retained while the testing duration remains controlled. Under this censoring scheme, classical and Bayesian inference procedures are developed for the Burr XII distribution. The unknown parameters, survival function and hazard rate function are estimated, and Bayesian estimates are obtained by a Markov chain Monte Carlo method. The analysis is also extended to series and parallel system reliability, future ordered failure times and remaining useful life prediction. Bootstrap confidence intervals are constructed to assess estimation uncertainty. Monte Carlo simulations are used to compare the mean squared errors, coverage probabilities and average lengths of the proposed estimators and intervals. The results show that the estimates become more stable as the sample size increases, and the Bayesian estimates often improve on the maximum likelihood estimates. A real electronic‐component lifetime dataset is finally analyzed to illustrate the implementation of the proposed methods.