A generalized Freund bivariate model for a two-component load sharing system

Abstract

Motivated by reliability systems whose components fail one by one and share a common load, this work provides a generalized Freund bivariate class of distributions for modeling the two component lifetimes of a parallel redundant system. When a component fails, such load-sharing systems can be repaired meanwhile the surviving one endures the total load, modifying its two-dimensional lifetime model, which is of interest in maintenance and stress-strength reliability modeling. The proposed model is based on the overload of the surviving component after the first failure, causing both the proportional failure rate parameters and the baseline distribution of the component to change. A genetic algorithm is employed to find the maximum likelihood estimation, and a simulation study illustrates its implementation and efficiency. Applications in three real engineering data sets are carried out, revealing the usefulness of the proposed class for modeling the load-sharing effect.