Optimizing a joint reliability-redundancy allocation problem with common cause multi-state failures using immune algorithm

Redundancy-reliability allocation problem (RRAP) is a well-known problem in reliability area. In general, this problem aims to maximize a system's reliability or minimize a system's costs under some constraints. In this paper, we develop a RRAP for a series-parallel system with multi-state components. Thus, the subsystems' components, the system's subsystems, and the system have different working states with corresponding working probabilities. The RAP in the paper is a RAP with mix components (RAPMC). We consider the choice of allocating non-identical components to each sub-system. Moreover, we consider the common cause failure (CCF) for the components, which causes simultaneous failure of all identical components of a subsystem. We assume the component's failure state probability is reduced by conducting technical activities, and the reduced probability is added to the component's working states' probabilities. The model's objective function is to minimize the system's costs under a minimum reliability level and other constraints by allocating the optimal set of components to each subsystem and determining each component's technical activities level. Since the RRAP belongs to the Np-Hard category of problems, an immune algorithm is used to solve the developed problem. The results indicate considering the technical activities decreases the system's costs.