Optimal-maintenance modeling on finite time with technology replacement and changing repair costs

Abstract

The authors explore maintenance models for finite time missions. Motivated by real world applications, and models which are lacking in literature, they include exponential cost forms that allow for net present value analysis, and explore replacing obsolete equipment with new. In this paper, they demonstrate through mathematical modeling that: by using simple search methods, one can find optimal replacement intervals for systems under a general finite time mission; under Weibull hazard functions, one can express the optimal replacement rate simply; by allowing for special exponential cost function forms, one can find local cost minima for exponentially growing costs, or include the time value of money; for systems in use, one can monitor the marginal cost, and replace the system when this marginal cost equals the expected average cost for the replacing system; when replacing one technology with a new, there are conditions under which the optimal replacement cycles are completely interrelated, and other conditions where one can calculate one from an independent calculation of another; and in budget constrained times, use present value estimates such as the ones we provide. To apply optimal replacement planning in industry, one must consider finite time missions, net present value of costs, and replacing obsolete equipment with new technology.