Optimal cost-effective design of triple-modular-redundancy-with-spares systems

The design issue for the optimal number of spare units in a triple-modular-redundancy system with spare units, including fault coverage and common-cause failure, is addressed. Two aspects of the problem are shown: (1) how to minimize the average total system cost, and how to minimize the average total system cost subject to an acceptance designed reliability level; and (2) how to maximize the system reliability with imperfect coverage, including common-cause failures. Application and numerical examples illustrate the results