An integrated model for maintenance policies and production scheduling based on immune–culture algorithm

The development of integrated modelling for maintenance policies of multi-component repairable system and production scheduling is challenging for two reasons. First, capturing dependency of this multi-component repairable system is difficult because different failure types associated with different components are under competing risks and their complicated relationships may lead to overall system dependency. Second, the integrated model is difficult to optimize because it is an NP-hard problem that exact optimization methods are intractable. For coping with these two difficulties, we propose a parametric statistical model using copula function to capture the overall system dependency. Under partially perfect maintenance policy at component-level, the likelihood functions for observed failures are derived and maximum likelihood method is used to estimate unknown parameters. Then relying on this parametric statistical model, the system hazard function is derived to depict the reliability-based imperfect preventive maintenance policy at system-level. Finally, to obtain the optimal solution(s) of the integrated model, we design an adaptive immune clone selection–culture algorithm, which is inspired from immune clone selection algorithm and culture algorithm. Results of the case study validate that our proposed maintenance policies and methodology have great advantages over the component-level or system-level maintenance policy and immune clone selection algorithm.