On the mean remaining strength at the system level for some bivariate survival models based on exponential distribution

Abstract

a b s t r a c tIn this paper, we consider the mean remaining strength at the system level of twocomponent parallel and series systems in the case of possibly dependent components which are subject to a common stress. We assume that the strengths of the components have FGM, Freund's, Marshall-Olkin and Block-Basu's bivariate exponential models. A numerical study based on the generated data set is performed to obtain the maximum likelihood estimates of the mean remaining strength for two-component parallel system in the stress-strength setup.

The mean remaining strength of parallel systems in a stress-strength model based on exponential distribution

“…In this section, we consider the estimation problem of MRS. Although the estimation of the stress-strength reliability of di¤erent systems has been considered extensively, the similar problem for MRS has not been studied in the literature except for Gurler et al [18]. In our case, ML and Bayes estimations of the MRS are studied.…”

“…They obtained that the MRS of the k-out-of-n : F system, series and parallel systems for the exchangeable strength components under the common stress. The MRS of the two-component parallel and series systems were considered by Gurler et al [18] for the dependent strength components which are subject to a common stress.…”

Estimating the Dependence Parameter of Farlie–Gumbel– Morgenstern-Type Bivariate Gamma Distribution Using Ranked Set Sampling

“…The family was introduced by Morgenstern [1], Gumbel [2] and Farlie [3]. Several researchers have studied the FGM distribution family, see [4][5][6][7][8][9][10]. D'Este [11] and Gupta and Wong [12] discussed bivariate gamma distribution, which is derived from the FGM family.…”

Fuzzy Stress‐Strength Model and Mean Remaining Strength for Lindley Distribution: Estimation and Application in Cancer of Benign Endocrine

“…Also, there are many references for other distributions such as the beta Gompertz distribution, see Hassan [10], and the exponential Pareto distribution, see Al-Omari et al [11]. In the context of the mean remaining strength (MRS) of the component as the expected remaining strength under the stress, see Gurler [12], Gurler et al [13], Bairamove et al [14], and Kizilaslan [15]. Fuzziness is introduced in reliability by Huang [5].…”