Abstract
In the present study, we consider a two-component parallel system. We do not know the probability distributions of the lifetimes of each component that characterize their behavior. Using the conventional nonparametric kernel estimate, we introduce three different approaches to estimate nonparametrically the cumulative distribution function or reliability function of the parallel system. In addition to the analytical formulation of these estimates, we utilize the criteria of mean integrated squared error to evaluate and compare each of the proposed estimates. A numerical simulation illustrates and compares three proposed methods of estimating nonparametrically the reliability behavior of a two-component parallel system.
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