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

Document Type : Research Paper

Authors

1 Khorasan Razavi Agricultural and Natural Resources Research and Education Center, AREEO, Mashhad, Iran

2 Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

3 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

10.22103/jmmrc.2021.17947.1156

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


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