Optimal allocation of reliability improvement target under dependent component failures

We study the problem of apportioning the reliability improvement target of a series system to components by considering the failure risk and improvement cost when both common cause and cascading failures exist. To solve this problem, previous research has developed different allocation weights in which every component is improved independently in proportion to the allocation weight. In practice, however, allocation weights are not independent among components because several components improve simultaneously when the occurrences of common cause failures are reduced. Therefore, in this study, we partition dependent component failures into mutually exclusive sub-failures to express the system risk in terms of the risk of component sub-failures, where the common cause failures, and cascading failures are incorporated into occurrence and severity evaluations, respectively. Then, an optimization problem is considered to maximize the effectiveness of the system improvement, which is measured as the difference between the decreased failure risk and the increased improvement cost. Finally, a numerical example is presented to illustrate that a component selected for improvement at a low budget would not necessarily be selected at a high budget if different marginal improvement costs were associated with different component failures. In other words, components are selected for improvement only if the reduction in the risk is sufficiently large to offset the improvement cost.