Prediction for the future system failures based on Type-II censored coherent systems data under a proportional hazard model

In this paper‎, ‎we consider a k-component coherent system while the system lifetimes are observed‎, ‎the system structure is known and the component lifetime follows the proportional hazard rate model‎. ‎We discuss the prediction problem based on Type-II censored coherent system lifetime data‎. ‎For predicting the future system failures‎, ‎we obtain the maximum likelihood predictor‎, ‎the best unbiased predictor‎, ‎the conditional median predictor and the Bayesian predictors‎. ‎As it seems that the integrals of the Bayes prediction do not possess closed forms‎, ‎the Metropolis-Hastings method is applied to approximating these integrals‎. ‎Different interval predictors based on classical and Bayesian approaches are derived‎. ‎A numerical example is presented to illustrate the prediction methods used in this paper‎. ‎A Monte Carlo simulation study is performed to evaluate and compare the performances of different prediction methods.