Optimal Inspection and Repair Schedules for Multicomponent Systems

An engineering approach to the solution of multicomponeint inspection and repair problems is introduced. This approach utilizes the practical fact that in realistic situations failure and wear processes in individual components are mutually independent. A stochastic model comprising a number of independent Markov chains is developed and operating and maintenance costs are expressed in terms of the failure and maintenance actions for the individual components. While this approach has the advantage that the problem size grows linearly rather than exponentially with the number of system components, it does increase the complexity of the objective function. For systems with a series structure, the objective function is concave, and concave programming techniques are employed to generate maintenance schedules. The computational experience gained from a number of practical examples, which is summarized in this paper, confirms the expectation that the feasibility of the solution is dependent primarily on the structure of the cost function rather than on the problem size (number of variables). These numerical examples illustrate the feasibility of the proposed approach.