“Optimal” Policy in a Maintenance Cost Problem

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.