Nonparametric Inference for Component Lifetime Distribution of Coherent Systems Based on Progressively Censored

‎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.