Reliability and Mission Cost of 1-Out-of-<formula formulatype="inline"><tex Notation="TeX">$N$</tex></formula>:G Systems With State-Dependent Standby Mode Transfers

Abstract

The paper proposes a new fault tolerant system design model, in particular a 1-out-of- $N$ :G hybrid redundant system with standby elements subject to state-dependent standby mode transfers. Specifically, in such systems, one standby element always resides in the hot standby mode, and thus is ready to replace the failed online element at any time to make the system dependable. If the online operating element or the hot standby element fails, one of the warm standby elements is immediately transferred to the hot standby mode. A numerical algorithm is first suggested for evaluating the reliability and the expected mission cost of the considered system. The algorithm is based on a discrete approximation of element time-to-failure distributions, and can work with any type of distribution. Furthermore, based on the suggested algorithm, the problem of optimal sequencing of standby elements initiation is formulated and solved. The objective of this optimization problem is to minimize the expected mission cost associated with elements' standby and operation expenses, as well as the mode transfer expenses, while meeting a certain system reliability constraint. Illustrative examples are provided.