A Modified Constrained Optimal Replacement Model for Nonlinearly Deteriorating Systems under Limited Resources

Abstract

Optimal replacement of failing systems is a classical problem in asset management, operation research and reliability engeeniring. The assumption of classical replacement model such as linear deterioration and unconstrained decision contexts rarely hold in real industrial practice. A modified restricted optimal replacement model is proposed in this study to explicitly incorporate operational and financial restrictions into the replacement decision making. System performance deteriorates following a nonlinear dynamic process. Replacemnt actions are represented as binary cost variables for a continuous-time optimal control optimal control system. Convex operating and maintenance costs are introduced to penalize extreme deterioration. The existence and uniqueness of solutions, positively invariance, global asymptotic stability of the degradation dynamics, and boundedness of the cost functional are among the rigrous theoretical properties of the model that are established. Sensitivity analysis shows how the curve of maintenance cost, replacement cost, and degradation intensity affect the best time to replace. Numerical simulation validate the suggested framework’s practical applicability. The model offers a tool for restricted replacement planning in industrial systems that is both realistically implemenatable and mathematically sound.