“Optimal” Policy in a Maintenance Cost Problem

Abstract

This paper is concerned with estimating the “optimal” policy when the (unknown) cost function C(x) is nonlinear with a single minimum, and can be approximated in the neighborhood of the minimum by a polynomial regression. The value x0, at which C(x) attains minimum, is approximated by ◯0 obtained from the regression function, and the expected value of the difference between the actual cost, Ŷ0 = C(◯0), and the true minimum cost, Y0 = C(x0), is evaluated. The Central Limit Theorem and Taylor series expansion of the multivariable function is applied in this procedure.