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Analysis of field data under two-dimensional warranty

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  • Jung, M.
  • Bai, D.S.

Abstract

This paper proposes a method of estimating lifetime distribution for products under two-dimensional warranty in which age and usage are used simultaneously to determine the eligibility of a warranty claim. To analyze two-dimensional warranty data, univariate and bivariate approaches which use a reliability model including both age and usage can be considered. Most of previous works are centered on the univariate approach which assumes a functional relationship between age and usage. We consider a bivariate approach which assumes that the two variables are statistically correlated in a bivariate distribution. Methods of obtaining maximum likelihood estimators are outlined, and specific formulas are obtained for the cases where marginal distributions are Weibull. An illustrative example is given and numerical studies are performed to compare the two approaches.

Suggested Citation

  • Jung, M. & Bai, D.S., 2007. "Analysis of field data under two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 135-143.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:2:p:135-143
    DOI: 10.1016/j.ress.2005.11.011
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    References listed on IDEAS

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    1. Jye Lu & Gouri Bhattacharyya, 1990. "Some new constructions of bivariate Weibull models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 543-559, September.
    2. Jehoshua Eliashberg & Nozer D. Singpurwalla & Simon P. Wilson, 1997. "Calculating the Reserve for a Time and Usage Indexed Warranty," Management Science, INFORMS, vol. 43(7), pages 966-975, July.
    3. D. N. P. Murthy & B. P. Iskandar & R. J. Wilson, 1995. "Two-Dimensional Failure-Free Warranty Policies: Two-Dimensional Point Process Models," Operations Research, INFORMS, vol. 43(2), pages 356-366, April.
    4. J.F. Lawless, 1998. "Statistical Analysis of Product Warranty Data," International Statistical Review, International Statistical Institute, vol. 66(1), pages 41-60, April.
    5. Roy, Dilip & Mukherjee, S. P., 1998. "Multivariate Extensions of Univariate Life Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 72-79, October.
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    Citations

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    Cited by:

    1. Wu, Shaomin, 2013. "A review on coarse warranty data and analysis," Reliability Engineering and System Safety, Elsevier, vol. 114(C), pages 1-11.
    2. Wu, Shaomin, 2014. "Construction of asymmetric copulas and its application in two-dimensional reliability modelling," European Journal of Operational Research, Elsevier, vol. 238(2), pages 476-485.
    3. Jung, Ki Mun & Park, Minjae & Park, Dong Ho, 2010. "System maintenance cost dependent on life cycle under renewing warranty policy," Reliability Engineering and System Safety, Elsevier, vol. 95(7), pages 816-821.
    4. Gupta, Sanjib Kumar & Bhattacharya, Debasis, 2022. "Non-parametric estimation of bivariate reliability from incomplete two-dimensional warranty data," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    5. Lin, Kunsong & Chen, Yunxia, 2021. "Analysis of two-dimensional warranty data considering global and local dependence of heterogeneous marginals," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    6. Jack, N. & Iskandar, B.P. & Murthy, D.N.P., 2009. "A repair–replace strategy based on usage rate for items sold with a two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 611-617.
    7. Minjae Park & Ki Mun Jung & Dong Ho Park, 2016. "Optimal warranty policies considering repair service and replacement service under the manufacturer’s perspective," Annals of Operations Research, Springer, vol. 244(1), pages 117-132, September.
    8. Wu, Shaomin, 2011. "Warranty claim analysis considering human factors," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 131-138.
    9. Xiaolin Wang & Wei Xie, 2018. "Two-dimensional warranty: A literature review," Journal of Risk and Reliability, , vol. 232(3), pages 284-307, June.
    10. Wei Xie, 2017. "Optimal pricing and two-dimensional warranty policies for a new product," International Journal of Production Research, Taylor & Francis Journals, vol. 55(22), pages 6857-6870, November.
    11. Kumar Gupta, Sanjib & De, Soumen & Chatterjee, Aditya, 2017. "Some reliability issues for incomplete two-dimensional warranty claims data," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 64-77.
    12. Park, Minjae & Jung, Ki Mun & Park, Dong Ho, 2018. "Optimization of periodic preventive maintenance policy following the expiration of two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 1-9.
    13. Huang, Yeu-Shiang & Gau, Wei-Yo & Ho, Jyh-Wen, 2015. "Cost analysis of two-dimensional warranty for products with periodic preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 51-58.
    14. Gupta, Sanjib Kumar & De, Soumen & Chatterjee, Aditya, 2014. "Warranty forecasting from incomplete two-dimensional warranty data," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 1-13.
    15. Shah Limon & Om Prakash Yadav & Ming J Zuo & Jason Muscha & Russell Honeyman, 2016. "Reliability estimation considering usage rate profile and warranty claims," Journal of Risk and Reliability, , vol. 230(3), pages 297-308, June.

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