Optimum schedule for preventive maintenance: A general solution for a partially specified time-to-failure distribution

The classic problem of determining an optimum schedule for preventive maintenance when the time-to-failure (TTF) is random has been previously addressed in the literature under various distributional assumptions. However, no general solution that requires only partial distributional information (in the form of the first few moments) has been suggested. In this paper we develop solution procedures characterized by four features: (1) The solutions are general in the sense that only the first few moments of the TTF distribution need to be specified. (2) The optimal solution is given explicitly in terms of the decision variables, thus allowing simple sensitivity analysis. (3) When the TTF moments are unknown, a new two-moment (partial and complete) distributional fitting procedure, used in the solution routine, ensures a better representation for the underlying TTF distribution relative to three-moment or four-moment distributional fitting. (4) When the TTF observations are truncated, simple routines to calculate maximum likelihood estimates are developed. We demonstrate that the partial distributional specification, required for the new solution procedures, does not detract meaningfully from the optimality of the solution.