
High system reliability can be achieved by redundancy and maintenance. The most typical model is a standard parallel system which consists of \(n\) identical units in parallel. It was originally shown that the system can operate for a specified mean time by either changing the replacement time or increasing the number of units [1, p. 65]. There liabilities of many redundant systems were computed and summarized [2]. A variety of redundant systems with multiple failure modes and their optimization problems were discussed [3]. Reliabilities of parallel and parallel-series systems with dependent failures of components were derived [4]. Some optimization methods of redundancy allocation for series-parallel systems were studied [5]. A good survey of multistate and consecutive \(k\)-out-of-\(n\) systems was done [6, 7].
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