farlie-gumbel-morgenstern copula-based modeling of non-conforming rate in bivariate lifetime data

The lifetime performance index is a widely accepted measure for evaluating a process capability in terms of both its actual and expected performance‎. ‎in manufacturing contexts‎, ‎a product is typically considered acceptable if its lifetime exceeds a specified minimum threshold‎. ‎this study investigates statistical inference for the nonconforming rate of a two-component system‎, ‎in which the dependence between the two lifetime characteristics is modeled using the farlie-gumbel-morgenstern copula‎. ‎the marginal distributions of both components are assumed to follow weibull distributions‎. ‎a numerical example is presented to illustrate the practical application of the proposed approaches‎.