In the past, redundancy, inventory and maintenance are often considered separately to improve the system availability. Recently, a few joint optimization papers have emerged, but they only considered hot-standby redundancy, one-for-one-ordering inventory policy and the case of single repairman. In order to deepen the previous research, this article formulates a joint optimization model of components redundancy, spares inventory and repairmen allocation for a standby series system with an objective of maximizing system availability. As to the components redundancy, hot-standby, warm-standby and cold-standby are considered, respectively. A more general batching ordering inventory policy is adopted and the number of repairmen is added as a new element. By continuous time Markov process, related reliability probability indices are derived. Then the mathematical model is constructed and branch-and-bound method is employed to solve the optimal solution. Finally, we conduct analysis and comparison for different numerical examples and obtain the following results: cold-standby and warm-standby redundancy yield higher availabilities compared to hot-standby under the same conditions. The optimal batch ordering inventory policy is better than optimal one-for-one-ordering inventory policy if the spares replenishment rate is not high enough. Moreover, an optimal number of repairmen, which is always more than one, can be achieved to enhance the efficiency of maintenance.
Reliability properties of k-out-of-n systems with one cold standby unit
