Interval programming for the redundancy allocation with choices of redundancy strategy and component type under uncertainty: Erlang time to failure distribution

Engineering design problems involve meeting system’s performance requirements such as reliability which is in close relation to appropriate selection of components and determination of a system level architecture. In this paper a new nonlinear redundancy allocation model with the choice of redundancy strategy and component types is presented. The redundancy strategies can be in forms of active and cold standby. Also there is a choice for no redundancy strategy. We assume that time to failure follows Erlang distribution which is parameterized in terms of shape and scale parameters which are usually determined deterministically. In this paper we release the deterministic assumption of the scale parameter since in reality the estimation of this parameter accompanies with uncertainty. Also, the cost and weights are not known exactly due to estimation uncertainties and fluctuations. The uncertain proposed model maximizes the system’s reliability, which is converted into a deterministic multi-objective model maximizing left bound and center of intervals. Finally, a numerical example is presented to show the performance of the proposed method.