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The most widely used approach for reliability estimation is the well-known stress-strength model,  θ  =  P ( X  &lt;  Y ), where  X  and  Y  are random variables. In this model, the reliability,  θ , of the system is the probability that the system is strong enough to overcome the stress imposed on it. In most cases,  X  and  Y  are assumed to be independent. Nevertheless, in reality, the strength variable  Y  could be highly dependent on the stress variable  X . In this paper, we discuss the kernel-based estimation of  θ  when  X  and  Y  are dependent random variables under progressive type II censored sample. The asymptotic properties of the kernel-based estimators of  θ  based on progressive type II censoring are proposed. An extensive computer simulation is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process.

Kernel-based estimation of P ( X < Y ) when X and Y are dependent random variables based on progressive type II censoring