An integral-equation approach for replacement modelling over finite time horizons

An integral-equation approach to calculating the exact and asymptotic estimates of expected costs in stochastic replacement problems is advocated. The method is based upon the known solution to the generalized renewal integral equation and upon the key renewal theorem. The basic failure-based and age-based replacement policies are taken as illustrative examples for the method, and the relationship to more conventional methods of calculation is highlighted. The benefit of the integral-equation format is that it provides a relatively clear procedure for evaluating more complex stochastic replacement situations.