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

Abstract

‎‎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 effective 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 confidence 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.‎

Keywords

• lifetime performance index‎
• ‎farlie-gumbel-morgenstern copula‎
• ‎non-conforming rate‎
• ‎bootstrap upper confidence bound‎
• ‎monte carlo procedure