Determining the optimal time policy model for the products with multiple failure states by considering a mixture distribution
Volume 15, Issue 2, Summer 2025, Pages 137-147
https://doi.org/10.48313/jqem.2025.522094.1522
Masoud Amini, Mohammad Saber Fallahnezhad, Mohammad Saleh Owlia, Mohammadali Vahdat, Shahaboddin Kharazmi
Abstract Purpose: This study aims to optimize warranty periods for complex products by examining the role of warranties in customer retention and cost management. The proposed model uses a mixed statistical distribution to simultaneously model minor and major failures, seeking to minimize the product's life-cycle cost while maintaining customer satisfaction.
Methodology: The mathematical model defines life-cycle costs, establishes an objective function to minimize total costs, and determines the optimal warranty period. A numerical example and sensitivity analysis are used for validation, and the model is solved using Maple 2024.
Findings: The optimal warranty period was identified as 3.5-4.5 time units, and the model achieved a 23% cost reduction compared to conventional methods. Sensitivity analysis showed that changes in failure probability and failure rate directly affect the optimal warranty length.
Originality/Value: Using a mixed statistical distribution to model different failure types simultaneously offers an innovative, more realistic approach. This model provides a practical tool for adjusting warranty policies and reducing life-cycle costs, with potential for further development by incorporating dependent failures and real-world data.