Reliability properties of systems with exchangeable components and exponential conditional distributions

Abstract

Reliability, failure rate, hazard, mean residual life, ordering, series and parallel systems, Primary 62N05, Secondary 90B25,

Some properties of hazard rate functions of systems with two components

“…Navarro and Lai (2007) discussed the usual stochastic ordering st Ն for systems with some bivariate exponential distributions. Other ordering results for particular models of dependency were obtained in Navarro et al (2006aNavarro et al ( , 2006bNavarro et al ( , 2008a. In Section 3, we will assume that the two components follow either the Marshall-Olkin bivariate exponential (MOBVE) distribution or standard type II Gumbel bivariate exponential (GBVE) distribution.…”

Bivariate distributions with conditionals satisfying the proportional generalized odds rate model

“…The basic properties of the new models are obtained. Similar studies of other bivariate models are given in Gupta (2001), Gupta and Gupta (2012), Gupta et al (2013), Navarro et al (2006).…”

Reliability properties of bivariate conditional proportional hazard rate models

“…The classes of bivariate distributions with the second-kind beta conditionals and the Pearson type VII conditionals were also studied in [15,16]. Navarro and Shaked [27], Navarro et al [25] and Kotz et al [22] have studied reliability properties of systems with exchangeable components and characterization problems for distributions with exponential conditionals (see also Balakrishnan et al [9]). The hazard gradient function defined by Johnson and Kotz [20] is a key tool for studying these properties.…”