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

•A generalized Freund bivariate model for two-component load-sharing systems is posed.•New bivariate distributions can be generated by combining baseline distributions.•Maximum likelihood estimation of this model is implemented by a genetic algorithm.•A procedure to generate synthetic two-dimensional data from this model is described.•The proposed model is applied to three real engineering data sets evidencing the load-sharing effect. 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.