An approximate renewal function-based method for investment cost-warranty cost-reliability allocation in mechanical systems

To address the challenge of simultaneously optimizing investment costs and warranty expenditures in reliability allocation for mechanical systems, a reliability–economy quantitative mapping model with a bidirectional transmission mechanism is developed by incorporating the dynamic relationship between lifetime distribution and warranty periods. An approximate renewal function-based optimization method for cost–warranty–reliability allocation in mechanical systems is subsequently proposed. An exponential feasibility-reconstructed cost function model is formulated by taking into account subsystem technical boundaries. By integrating Weibull renewal process approximation theory, a three-stage warranty cost prediction strategy is introduced, comprising first-failure dominance for short time scales, mixed-distribution approximation for medium time scales, and steady-state approximation for long time scales. Furthermore, a nonlinear phased adaptive optimization framework is established, utilizing the particle swarm optimization (PSO) algorithm to solve the nonlinear programming problem. Case studies involving no-till planters are conducted to verify the effectiveness of the proposed method. The results indicate that the method accurately captures the bidirectional influence of reliability enhancement on life cycle economics, and the resulting allocation scheme achieves reduced total costs.