“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 x 0 , 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, Ŷ 0 = C ( ◯ 0 ), and the true minimum cost, Y 0 = C ( x 0 ), is evaluated. The Central Limit Theorem and Taylor series expansion of the multivariable function is applied in this procedure.