Optimal preventive replacement policy for repairable products with multiple repair attempts under personalized warranty

This paper investigates an optimal preventive replacement policy for repairable products subject to multiple repair attempts under a personalized free-repair warranty (FRW). Under the FRW policy, which specifies a tailored warranty period provided by the manufacturer, the product is preventively replaced at periodic intervals. Upon unexpected failure between consecutive replacement cycles, repairs are performed free of charge to the customer within the warranty period. Accounting for realistic imperfections in repairs, e.g. component degradation or environmental stresses, the model incorporates successful repairs that are worse than minimal repair modeled via a Generalized Polya Process (GPP) or unsuccessful repair attempts described with a compound counting process. Using stochastic process theory and cost optimization modeling frameworks, the optimal replacement cycles are derived analytically to minimize expected cost rates, both with and without warranty coverage, and compared to demonstrate the cost advantages of warranty inclusion. Numerical examples and sensitivity analyses illustrate the model’s applicability, offering practical insights for operational research (OR) applications in industries such as manufacturing, transportation, and energy, where warranty-driven maintenance strategies enhance operational efficiency.