Minimum–Maximum regret redundancy allocation with the choice of redundancy strategy and multiple choice of component type under uncertainty

• In this paper a robust redundancy allocation problem with choice of redundancy strategy and component type is presented.
• The time to failure of components follows Erlang distribution whose scale parameters are uncertain in terms of interval data.
• The problem is formulated through Min–Max regret criterion and a benders decomposition technique is proposed to deal with the problem.
• The effectiveness of the proposed benders decomposition is compared with an enumeration method.
• The robust solution includes redundancy level, redundancy strategy and component type which are useful for designers who are risk-averse.

This paper deals with a redundancy allocation problem in series–parallel systems with the choice of redundancy strategy, including active and cold standby strategies in which component’s time to failure follows an Erlang distribution. The scale parameter of Erlang distribution and consequently the reliability of each component are imprecise in terms of interval data, and only the lower and upper bounds are known. This problem, for the first time, is formulated through Min–Max regret criterion, which is commonly used to define robust solutions. The resulting problem formulation contains an unlimited number of constraints, and a Benders’ decomposition method is implemented to deal with the given problem. This method is compared with an enumeration method to show its effectiveness. The performance of the proposed model using the Benders’ decomposition method is examined over different problem sizes, and the associated results are analyzed.