Bivariate general exponential models with stress-strength reliability application

Abstract

In this paper, we introduce two families of general bivariate distributions. We refer to these families as general bivariate exponential family and general bivariate inverse exponential family. Many bivariate distributions in the literature are members of the proposed families. Some properties of the proposed families are discussed, as well as a characterization associated with the stress-strength reliability parameter, R, is presented. Concerning R, the maximum likelihood estimators and a simple estimator with an explicit form depending on some marginal distributions are obtained in case of complete sampling. When the stress is censored at the strength, an explicit estimator of R is also obtained. The results obtained can be applied to a variety of bivariate distributions in the literature. A numerical illustration is applied on some well-known distributions. Finally a real data example is presented to fit one of the proposed models.

Stress-Strength Reliability and Randomly Censored Model of Two-Parameter Power Function Distribution

“…Many authors explore the stress-strength model for different probability distributions. For example, Khames and Mokhlis [19] introduced a bivariate general exponential model for the stress-strength reliability model. Saber et al [18] suggested a remained stress-strength model for the generalized exponential model.…”

Reliability assessment of the standby system with dependent components by bivariate exponential distributions

“…For example, Refs. 9,15–17 established the stress-strength models with exponential bivariate distributions. However, the main emphasis of this research is to investigate the system reliability in which the components follow exponential bivariate distributions.…”