Reliability Estimation of Dependence Structure System For Huang-Kotz Iterated FGM With Lindley Marginal

Abstract

Huang and Kotz (1984) proposed a two-parameter extension of the original Fralie-Gumble-Morgenstern (FGM) family to model the higher association between the random variables. In this problem, we develop an iterated FGM (IFGM) based dependent stress-strength reliability model using Lindley marginals. Some important statistical and reliability properties of the proposed distribution are also derived. The prime goal of this study is to investigate the effect of stress-strength reliability parameters with respect to the variation in the dependence parameters α and β. Further, we compared the IFGM stress-strength reliability model with the original FGM using graphical representations to assess whether reliability was over or under-estimated. Finally, we investigated the performance of the proposed estimators through both Monte Carlo simulations as well as real data sets.

Keywords

• lindley distribution
• stress-strength reliability
• ifgm copula
• pseudo likelihood estimation
• monte-carlo simulation