Component and system level redundancy allocations in coherent systems of dependent components
摘要
This paper investigates the superiority of component level versus system level redundancy allocations in coherent systems with dependent components, analyzed through various stochastic orders. The well-known Barlow-Proschan (BP) principle asserts that, for a system of independent components, active redundancy allocation at the component level is superior (more reliable) than at the system level in terms of the usual stochastic order. However, the comparison results that hold for systems with independent components, including the BP principle, may not extend to systems with dependent components, even under the usual stochastic order. Existing works on generalization to dependent systems and alternative redundancy strategies, such as standby redundancy, remain limited, particularly under stronger stochastic orders. To address this gap, we study component versus system level redundancy allocations under several redundancy strategies in a unified manner using the concept of a redundancy distortion function. We also compare different redundancy mechanisms allocated at the component level to a system with dependent components, in the sense of some stochastic orderings. These results help identify the most appropriate redundancy strategy under component-level allocation for a given system with dependent components. Several examples are presented to illustrate the findings, considering both active and other types of redundancies.