A study of interval analysis for cold-standby system reliability optimization under parameter uncertainty

• We use interval analysis theory to deal with the uncertain parameters.
• We incorporate interval analysis into cold-standby system optimization problem.
• A new interval order relation reflecting decision maker’s preference is defined.
• We propose the evaluation procedure of interval-valued system reliability and cost.
• A genetic algorithm involving dual mutation and random keys technique is developed.

This paper presents a study of interval analysis for solving cold-standby system reliability optimization problems with considering parameter uncertainty. Most works reported in existing literature have been based on the assumption that the probabilistic properties and statistical parameters have a known functional form, which is usually not the case. Very often the parameters are presented in form of an interval-valued number or bounds/tolerance from the engineering design. In this paper, interval analysis is used to incorporate this in the system optimization problems. A definition of interval order relation reflecting decision makers’ preference is proposed for comparing interval numbers. A computational algorithm is developed to evaluate the system reliability and expected mission cost, in which a discrete approximation approach and a technique of interval universal generating function are used. For illustration, an application to sequencing optimization for heterogeneous cold-standby system is given; a modified genetic algorithm is developed to solve the proposed optimization problem with interval-valued objective. The results indicate that the interval analysis exhibits a good performance for dealing with parameter uncertainty of cold-standby system optimization problems.