Applications of the Lambert W Function in the Calculation of Optimal Replacement Time

The Lambert [Formula: see text] function has been applied in several branches of science, since it allows the exact solution of a wide family of transcendental equations commonly present in engineering and applied mathematics. This paper introduces its use for the computation of the optimal replacement time in three maintenance policies: operation and maintenance costs increasing through time, age replacement and periodic replacement. For each case, analytical expressions are derived in closed form, validity ranges are established and an industrial application is presented. The proposed approach avoids the need to employ computationally expensive numerical methods, providing an accurate and efficient tool for decision making in asset management.