Modeling for reliability optimization of system design and maintenance based on Markov chain theory.

•MINLP model that represents the stochastic process of system failures and repairs as a continuous-time Markov chain.•Model optimizes the selection of redundancy and the frequency of inspection and maintenance tasks for maximum profit.•Effective decomposition and scenario reduction methods are also proposed t handle large number of states.•Proposed model applied to small and medium scale examples, as well as to air separation process.