The analysis of redundant reliability systems with common-cause failures.

The reliability and income analyses of newly developed $k-out-of-(n + m):G$ (or $n, m, k$) type redundant systems subject to a combination of common-cause failures and independent failures are presented. The global goal was to evaluate the impacts of the standby activation policy and the system repair times on such relevant system performance indices as the reliability, long-run availability, mean time to failure, variance of time to failure and net income. To facilitate this investigation several possible repair policies are developed. Results obtained using typical and practical values of basic system variables indicate that the governing standby activation policy as well as the system repair time distribution affect profoundly the values of the afore-mentioned system performance indices. In addition, newly developed mathematical relationships that would enable the net incomes of $k-out-of-(n + m):G$ type systems to be maximized by the adoption of certain system repair rates are presented