Designing a Model for Estimating the Cost of Pro-Rata Warranty with limitation of Each Failure Rectification Cost under Inflationary Conditions 

Document Type : Original Article

Authors

1   Assistant Professor of Industrial management, Imam Khomeini International University (IKIU), Qazvin, Iran 

2   Assistant Professor, College of Farabi, University of Tehran, Iran 

Abstract
In this paper, a mathematical model for predicting expected costs to the manufacturer and buyer in pro-rata warranty policy under inflationary conditions is developed. In this model, the cost of individual claims to the manufacturer is limited to fixed cost 𝐶𝐼 whereby the manufacturer carries out all rectification action with a portion of the cost to the customer if the cost of rectification is below a limit 𝐶𝐼. If the cost of rectification exceeds 𝐶𝐼 then the customer pays the difference between the costs of rectification and 𝐶𝐼.based on this model we analyze respectively the expected warranty costs from the perspectives of the manufacturer and the consumer. A real data are executed to demonstrate the applicability of the model. It is proved that, inflation rate, warranty period length and failure parameters impacts the manufacturer and the consumer expected costs. 
 
 

Keywords


[1]    Wang, Y., Liu, Z., & Liu, Y. (2015). Optimal preventive maintenance strategy for repairable items under two-dimensional warranty. Reliability Engineering and System Safety, 142, 326–333. https://doi.org/10.1016/j.ress.2015.06.003
[2]    نصراللهی، م. (1396). مدل تعیین قیمت وارانتی PRW با تولید کنندگان ریسک گریز. مطالعات مدیریت صنعتی، 15(45)، 75–96.
[3]    Shang, L., Cai, Z., Chen, H., & Zhang, S. (2018). Post-warranty maintenance optimization for products with deterioration depending on aging and shock. Quality Technology and Quantitative Management, 00(00), 1–21. https://doi.org/10.1080/16843703.2018.1509431
[4]    افصحی، م.، حسین زاده کاشان، ع.، استادی، ب. و ذگردی، ح. ا. (1397). بهینه‌سازی یکپارچه قیمت، سیاست‌های وارانتی پایه و تمدید وارانتی با در نظر گرفتن محصولات از وارانتی خارج‌شده. مهندسی و مدیریت کیفیت، 8(1)، 63–74.
[5]    Murthy, D. N. P. (2007). Product reliability and warranty: an overview and future research. Production, 17(3), 426–434.
[6]    Thomas, M. U., & Rao, S. S. (1999). Warranty Economic Decision Models_ A Summary and some suggested Directions for Future Research. Operations Research, 47(6), 807–820.
[7]    نصراللهی، م.، اصغری زاده، ع.، جعفرنژاد، ا. و صنیعی منفرد، م. (1393). توسعه سیاست جدید وارانتی PRW برای برآورد هزینه‌ها. مدیریت صنعتی، 6(1)، 137–150.
[8]    Menke, W. W. (1969). Determination of Warranty Reserves. Management Science, 15(10), 542–549. https://doi.org/10.1287/mnsc.15.10.b542
[9]    Jain, M., & Maheshwari, S. (2006). Discounted costs for repairable units under hybrid warranty. Applied Mathematics and Computation, 173(2), 887–901. https://doi.org/10.1016/j.amc.2005.04.022
[10]    Tsai, P.-C., & Fang, C.-C. (2015). A Bayesian Analysis in Determining Pro-rata Warranty Decision with Two-Dimensional Deterioration. International Journal of Knowledge Engineering-IACSIT, 1(2), 160–164. https://doi.org/10.7763/ijke.2015.v1.28
[11]     Alqahtani, A. Y., & Gupta, S. M. (2017). Warranty as a marketing strategy for remanufactured products. Journal of Cleaner Production, 161, 1294–1307. https://doi.org/10.1016/j.jclepro.2017.06.193
[12]     Alqahtani, A. Y., & Gupta, S. M. (2017a). Optimizing two-dimensional renewable warranty policies for sensor embedded remanufactured products. Journal of Industrial Engineering and Management, 10(2), 145. https://doi.org/10.3926/jiem.2187
[13]    Chen, Z., Zhao, T., Luo, S., & Sun, Y. (2017). Warranty Cost Modeling and Warranty Length Optimization under Two Types of Failure and Combination Free Replacement and Pro-Rata Warranty. IEEE Access, 5, 11528–11539. https://doi.org/10.1109/ACCESS.2017.2715840
[14]    Wang, X., Xie, W., Ye, Z. S., & Tang, L. C. (2017). Aggregate discounted warranty cost forecasting considering the failed-but-not-reported events. Reliability Engineering and System Safety, 168(April), 355–364. https://doi.org/10.1016/j.ress.2017.04.009
[15]    Ahmed, E. A., Mabrouk, I. S., & Mahran, B. A. (2018). Hybrid repair warranty cost model for repairable products based on generalized exponential distribution with simulation study. International Journal of Contemporary Mathematical Sciences, 13(6), 263–278. https://doi.org/10.12988/ijcms.2018.81031
[16]    Taleizadeh, A. A., Pourrezaie Khaligh, P., & Moon, I. (2019). Hybrid NSGA-II for an imperfect production system considering product quality and returns under two warranty policies. Applied Soft Computing Journal, 75, 333–348. https://doi.org/10.1016/j.asoc.2018.11.013
[17]    Babbie, E. R. (2012). The Practice of Social Research (13th ed.). Wadsworth Publishing.
[18]    Wacker, J. G. (1998). A definition of theory: research guidelines for different theory-building research methods in operations management. Journal of Operations Management, (16), 361–385.
[19]    اصغری زاده, ع. ا. (1379). مقدمه‌ای بر خط مشی‌ها و مدل‌های وارانتی: مولود تازه مدیریت مهندسی و تولید. دانش مدیریت, (51), 61–87.
[20]    Blischke, W. R., Karim, M. R., & Murthy, D. N. P. (2011). Warranty Data Collection and Analysis. Thermoplastics and Thermoplastic Composites. Springer Science & Business Media. https://doi.org/10.1007/978-1-4471-4588-2
[21] Murthy, D. N. P., & Blischke, W. R. (2006). Warranty Management and Product Manufacture. Springer Science & Business Media.
[22] Chen, J.-A., & Chien, Y.-H. (2007). Renewing Warranty and Preventive Maintenance for Products with Failure Penalty Post-Warranty. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, 23, 107–121.  https://doi.org/10.1002/qre
[23]    Matti Kurvinen, Töyrylä, I., & Murthy, D. N. P. (2016). Warranty Fraud Management Reducing Fraud and Other Excess Costs in Warranty and Service Operations. John Wiley & Sons.
[24]    Popovic, V., Stamenkovic, D., & Rakicevic, B. (2013). Choosing the Right Warranty Policy – from the Customer’sto the Manufacturer’s Point of View. International Journal of Applied Physics and Mathematics, 2(5), 333–335. https://doi.org/10.7763/ijapm.2012.v2.126
[25]    Stamenković, D., Popović, V., Spasojević-Brkić, V., & Radivojević, J. (2011). Combination free replacement and pro-rata warranty policy optimization model. Journal of Applied Engineering Science, 9(4), 456–464. https://doi.org/10.5937/JAES9-1202
[26]    Murthy, D. N. P., & Blischke, W. R. (1992). Product warranty management - III: A review of mathematical models. European Journal of Operational Research, 62, 1–34.
[27]    جولای، ف. و اسودی، ت. (1383). مدل کنترل موجودی دوسطحی اقلام فاسد شدنی با در نظر گرفتن اثرات تورم. نشریه دانشکده فنی، 38(1)، 121–132.