Consideration of dependent failures in redundancy optimization problems with multiple constraints

System reliability is often improved by introducing multiple redundancies in critical subsystems. However, redundancy introduces problems, such as increased costs, weight, and power requirements, which must be constrained within available resources. Hence, in order to maximize system reliability the use of redundancy should be optimized with respect to these constraints. A number of optimization techniques been applied to solve this class have of problems. However, most do not consider dependent failures, such as common-cause and sympathetic-cause failures, which play an important role in redundancy optimization problems. Furthermore, the fraction of dependent failures to total failures may be different among subsystems, and this difference changes the optimal allocation of redundancy. In this paper, an algorithm is developed, which effectively considers dependent failures by using the well-known beta and alpha factors. In developing formulae, a Markovian model is used, which is suitable for handling dependent failures. An example application is also included