Bivariate Exponentiated Generalized Linear Exponential Distribution with Applications in Reliability Analysis

Abstract: The aim of this paper, is to define a bivariate exponentiated generalized linear exponential distribution based on Marshall-Olkin shock model. Statistical and reliability properties of this distribution are discussed. This includes quantiles, moments, stress-strength reliability, joint reliability function, joint reversed (hazard) rates functions and joint mean waiting time function. Moreover, the hazard rate, the availability and the mean residual lifetime functions for a parallel system, are established. One data set is analyzed, and it is observed that, the proposed distribution provides a better fit than Marshall-Olkin bivariate exponential, bivariate generalized exponential and bivariate generalized linear failure rate distributions. Simulation studies are presented to estimate both the relative absolute bias, and the relative mean square error for the distribution parameters based on complete data.