Browse > Article
http://dx.doi.org/10.7469/JKSQM.2014.42.1.001

Cost Analysis on Warranty Policies Using Freund's Bivariate Exponential Distribution  

Park, Minjae (College of Business Administration, Hongik University)
Kim, Jae-Young (Department of Business Administration, Korea University)
Publication Information
Journal of Korean Society for Quality Management / v.42, no.1, 2014 , pp. 1-14 More about this Journal
Abstract
Purpose: In this paper, the minimal repair-replacement warranty policy is used to carry out a warranty cost analysis with warranty servicing times and failure times that are statistically correlated to bivariate distributions. Methods: Based on the developed approach by Park and Pham (2012a), we investigate the property of the Freund's bivariate exponential distribution and obtain the number of warranty services using the field data to conduct the warranty cost analysis. Results: Maximum likelihood estimates are presented to estimate the parameters and the warranty model is investigated using a Freund's bivariate exponential distribution. A numerical example is discussed to deal with the applicability of the developed approach in the paper. Conclusion: A novel approach of analyzing the warranty cost is proposed for a product in which failure times and warranty servicing times are used simultaneously to investigate the eligibility of a warranty claim.
Keywords
Bivariate Distributions; Field Data; Maximum Likelihood Estimation; Replacement Service; Warranty Service;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Blischke, Wallace R. 1994. Warranty Cost Analysis: CRC Press.
2 Cha, Ji Hwan, Jung, Jong Tae, and Kim, Jae Joo. 2001. "Optimal Preventive Maintenance Policy for a Repairable System." Journal of the Korean Society for Quality Management 29:46-53.   과학기술학회마을
3 Hunter, Jeffrey J. 1974. "Renewal Theory in Two Dimensions: Basic Results." Advances in Applied Probability 6:376-391.   DOI   ScienceOn
4 Downton, F. 1970. "Bivariate exponential distributions in reliability theory." Journal of the Royal Statistical Society, Series B (Methodological):408-417.
5 Freund, John E. 1961. "A bivariate extension of the exponential distribution." Journal of the American Statistical Association:971-977.
6 Hawkes, Alan G. 1972. "A bivariate exponential distribution with applications to reliability." Journal of the Royal Statistical Society, Series B (Methodological):129-131.
7 McLeod, A. Ian. 2005. "Kendall rank correlation and Mann-Kendall trend test." R Package (Kendall). http://cran.r-project.org/web/packages/Kendall.
8 Nachlas, Joel A. 2005. Reliability engineering: probabilistic models and maintenance methods. CRC Press.
9 Nadarajah, Saralees., and Kotz, Samuel. 2006. "Reliability models based on bivariate exponential distributions." Probabilistic Engineering Mechanics 21:338-51.   DOI   ScienceOn
10 Nam, Kyung H., and Kim, Do Hoon. 2011. "A Study on Optimal Software Maintenance Policies with Warranty Period." Journal of the Korean Society for Quality Management 39:170-178.   과학기술학회마을
11 Park, Byung-gu. 1985. "Statistical inference for bivariate exponential distribution in reliability and life testing problems." Journal of the Korean Society for Quality Management 13:31-40.
12 Park, Minjae. 2010. "Cost Analyses on Warranty Policies for Systems Subject to Two Types of Warranty Periods." PhD diss., Rutgers, the State University of New Jersey.
13 Park, Minjae, Jung, Ki Mun, and Park, Dong Ho. 2013. "Optimal post-warranty policy with repair time threshold for minimal repair." Reliability Engineering and System Safety 111:147-153.   DOI   ScienceOn
14 Park, Minjae, and Pham, Hoang. 2012. "A new warranty policy with failure times and warranty servicing times." IEEE Transactions on Reliability 61:822-831.   DOI   ScienceOn
15 Park, Minjae, and Pham, Hoang. 2012. "Warranty Cost Analysis for k-out-of-n Systems With 2-D Warranty." IEEE Transactions on Systems Man and Cybernetics-Part A-Systems and Humans 42:947-957.
16 Blischke, Wallace R., and Murthy, D. N. Prabhakar. 1996. Product Warranty Handbook. CRC Press.
17 Park, Minjae, and Pham, Hoang. 2010. "Altered quasi-renewal concepts for modeling renewable warranty costs with imperfect repairs." Mathematical and Computer Modelling 52:1435-1450.   DOI   ScienceOn
18 Ross, Sheldon M. 2000. Introduction to Probability Models. San Diego: Academic Press.