عادله فلاح

‎In this paper‎, ‎non-parametric inference is considered for $k$-component coherent systems‎, ‎when the‎ ‎system lifetime data is progressively type-II censored‎. ‎In these coherent systems‎, ‎it is assumed that the‎ ‎system structure and system signature are known‎. ‎Based on the observed progressively type-II censored‎, ‎non-parametric confidence intervals are calculated for the quantiles of component lifetime distribution‎. ‎Also‎, ‎tolerance limits for component lifetime distribution are obtained‎. ‎Non-parametric confidence intervals for quantiles and tolerance limits are obtained based on two methods‎, ‎distribution function method and W mixed matrix method‎. ‎Two numerical‎ ‎example is used to illustrate the methodologies developed in this paper‎.

In this paper, statistical inference is considered for k-component coherent systems, when the system lifetime data is progressively type-II censored. In these coherent systems, it is assumed that the system structure and system signature are known and the component lifetime distribution is exponential. Pivotal and Bayesian methods are introduced for point estimation of the component lifetime parameter, and these methods are compared with the maximum likelihood and the least squares methods existing in the literature. Pivotal confidence interval, Bayesian confidence interval and confidence interval based on the likelihood ratio test are computed. Using Monte Carlo simulations, different point and interval estimates are compared and it is observed that pivotal and Bayesian methods perform better than other existing estimation methods.