The well-known Marshall–Olkin model is known for its extension of exponential distribution preserving lack of memory property. Based on shock models, a new generalization of the bivariate Marshall–Olkin exponential distribution is given. The proposed model allows wider range tail dependence which is appealing in modeling risky events. Moreover, a stochastic comparison according to this shock model and also some properties, such as association measures, tail dependence and Kendall distribution, are presented. The new shock model is analytically quite tractable, and it can be used quite effectively, to analyze discrete–continuous data. This has been shown on real data. Finally, we propose the multivariate extension of the Marshall–Olkin model that has some intersection with the well-known multivariate Archimax copulas.

This paper compares the reliability functions of the cold standby, hot standby, and load-sharing redundancy configurations, each of which is composed of two identical components for meeting a given system requirement. Thus far, no research has been done into the conditions that make one configuration more reliable than another because their reliability functions have no closed forms even when the component follows a Weibull lifetime distribution. In this paper, two analytical results are obtained given that the reliability of each configuration is expressed in terms of the design and operational loads of the component. First, higher reliability can be achieved in a cold standby configuration than in a load-sharing configuration if the increase in the component reliability obtained from the reduction in the operational load is not significant. Second, a cold standby configuration exhibits better reliability and carries a higher load than a hot standby configuration if the design load can be increased with a less decrease in the component reliability.