Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures

In this paper, we develop exact nonparametric statistical inference for some characteristics of the component lifetime distribution based on the lifetimes of coherent systems with known signatures. Distribution-free confidence limits for population quantiles of component lifetime distributions are derived. Computational formulas as well as a procedure for choosing suitable confidence limits are presented. Construction of tolerance limits for the component lifetime distribution is also described. Finally, some examples are presented to illustrate the methods of inference developed here.