Statistical inference for the non-conforming rate of FGM Copula-Based bivariate exponential lifetime

Lifetime performance index is widely used as process capability index to evaluate the performance and potential of a process. In manufacturing industries, the lifetime of a product is considered to be conforming if it exceeds a given lower threshold value, so nonconforming products are those that fail to exceed this value. Nonconformities are so important that affect the safe or efiective use of the products. This article deals with the processes that the products lifetime is related to a two-component system, distributed as Farlie-Gumbel-Morgenstern (FGM) copula-based bivariate exponential and presents the probability of non-conforming products. Also, bootstrap upper con dence bounds are constructed and their performance are investigated in simulation study. In addition, Monte Carlo scheme is applied to do hypothesis testing on it. Finally, two example sets are presented to demonstrate the application of the proposed index.