Robust series–parallel systems design under combined interval–ellipsoidal uncertainty sets

•The paper presents binary and integer models for the redundancy allocation problem in series-parallel systems under uncertainty of components’ reliabilities.•Multiple component types and also component mixing are considered in the proposed models.•The robust counterpart optimization approach is employed to tackle the uncertainty.•The proposed robust models are useful in designing robust systems which are immune against different realizations of uncertainty.

System reliability is an important requirement in design stage of systems, which depends on some parameters such as components’ reliabilities which are estimated in advance. Due to some factors, the estimated reliabilities for components may vary during and prior to implementation. Therefore, it is important to consider various controllable and uncontrollable factors, which influence the system reliability, in the design phase of systems. Consequently, the need for presenting robust designs, which are insensitive or less sensitive to these variations, is necessary in the area of system engineering. In most cases especially for new and evolving systems, or for strategic design of systems, less or no historical data are available. Therefore, stochastic, fuzzy or interval programming approaches are no longer applicable to consider the uncertainty. In this paper, for the first time an uncertainty set in the form of combined interval–ellipsoidal is considered to study the behavior of variations. A robust optimization approach is employed to deal with this kind of uncertainty in reliability optimization problems. The findings indicate that applying the proposed robust reliability models, results in robust and reliable designs in practice which is crucial for many systems such as medical systems, nuclear systems and the like.