Optimal maintenance of a system of machines with weakest-link-dependent performance

This paper considers the maintenance policy of a system of machines whose deterioration is dependent on the machines’ quality states and maintenance efforts. The return of the system of machines, however, is dependent only on the machine with the lowest quality state. This becomes a realistic feature when the machines are arranged in series as part of an assembly line production. This feature also gives rise to an unconventional optimization problem with an interesting theoretical challenge. The problem is subsequently formulated as a constrained optimal control problem. It is first shown that the problem admits an optimal control. Then by using the control parametrization approach, an efficient computational scheme is devised for solving the problem.