# Optimal length of warranty and burn-in periods considering different types of repair

Document Type : Research Paper

Author

Industrial Engineering Department, Engineering Faculty, Islamic Azad University (West-Tehran Branch), Tehran, Iran

Abstract

Failure rate curve based on the failure rate function of many electrical and mechanical systems shows a bathtub-shape form. In the first phase of this curve, where the failure rate has a decreasing form with a high slope, manufacturers use the burn-in method to eliminate defective products before reaching the market. In this phase most of the failures are minor (since the component is completely new, this type of error generally takes happen because of bad assembling, displacement of a socket, and so on) or major type failures (for example because of wrong design, selecting unsuitable raw materials, and so on). In the second phase, where the failure rate curve shows a constant value, manufacturers offer warranty services to their customers to ensure them about the quality and performance of their products. In this paper, we investigate the total cost incurred during the burn-in and warranty periods from the manufacturer's point of view. We consider different types of repair services and obtain the expected total cost in each phase. We present an optimization example to illustrate the efficacy of the proposed model in finding optimal values for burn-in and warranty periods.

Keywords

Main Subjects

#### References

Brezavscek, A. (2013). A simple discrete approximation for the renewal function. Business System Research, 4 (1), 65-75.
Cha,  J.H. (2000). On a better burn-in procedure. Journal of applied probability, 37(4), 1099-1103.
Cha, J.H. (2003). A further extension of the generalized burn-in model. Journal of applied probability, 40(1), 264-270.
Dhillon, B. (1979). A hazard rate model. IEEE transactions on reliability, 28(2), 150.
Jiao, C., & Zhu, X. (2018). Optimal design of sales and maintenance under the renewable warranty. RAIRO operations research, 52(2), 529-542.
Kijima, M. (1989). Some results for repairable systems with general repair. Journal of applied probability, 26(1), 89-102.
Kwon, Y.M., Wilson, R., & Na, M.H. (2010). Optimal burn-in with random repair cost. Journal of the Korean statistical society, 39(2), 245-249.
Mi, J. (1999). Comparisons of renewable warranties. Naval research logistics, 46(1), 91-106.
MoghimiHadji, E., & Rangan,  A. (2012). Optimal burn-in, warranty and maintenance decisions in system design. International journal of modeling in operations management, 2(3), 266-278.
Monga, A., & Zuo, M.J. (1998). Optimal system design considering maintenance and warranty. Computers and operations research, 25(9), 691-705.
Park, M., Jung, K.M., & Park, D.H. (2013). Optimal post-warranty maintenance policy with repair time threshold for minimal repair. Journal of reliability engineering and system safety, 111 (C), 147-153.
Park, M., Jung, K.M., & Park, D.H. (2020). Warranty cost analysis for second-hand products under a two-stage repair-or-full refund policy, Journal of reliability engineering and system safety, 193 (C), 106596.
Podilyakina, N. (2016). Product reliability and warranty period as a cost-forming factors. Business: Theory and Practice, 17(4), 361-369.
Rangan, A., & Khajoui, S. (2007). Optimal system design based on burn-in, warranty and maintenance. 1st annual RFID Eurasia conference, Istanbul, Turkey.
Rangan, A., & MoghimiHadji, E. (2011). Approximation to g-renewal functions. International journal of quality and reliability management ,28(7), 773-780.
Shafiee, M. (2013). Optimal burn-in and preventive maintenance warranty strategies with time dependent maintenance costs. IIE transactions, 45(9), 1024-1033.
Shafiee, M., Chukova, S., & Yun, W.Y. (2014). Optimal burn-in and warranty for a product with post-warranty failure penalty. International journal of advanced manufacturing technology, 70(1-4), 297-307.
Wang,  J., Ye, J., & Xie, P. (2019). New repairable system model with two types repair based on extended geometric process.  Journal of systems engineering and electronics, 30(3), 613-623.

### History

• Receive Date: 18 June 2020
• Revise Date: 07 August 2020
• Accept Date: 12 August 2020
• First Publish Date: 01 November 2020