Abstract: The author considered a k-out-of-n system with covariates. The conditional hazard functions of the residual life of the normally operating variables in the system were assumed to be a proportional hazards model. The author discussed the maximum likelihood estimation of the model parameters, the reliability function and the quantile function of the system, and the asymptotic normality of these estimates. The author gave the confidence intervals of the model and studied the performances of the point and interval estimators by Monte Carlo simulation. The results show that the mean square errors (MSEs) of the estimates decrease with the increases of the sample size.

Key words: hazard； maximum likelihood estimation； Monte Carlo method, sequential k-out-of-n system； conditional