IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v92y2007i2p135-143.html
   My bibliography  Save this article

Analysis of field data under two-dimensional warranty

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S095183200500219X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2005.11.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Mitra, Amitava, 2021. "Warranty parameters for extended two-dimensional warranties incorporating consumer preferences," European Journal of Operational Research, Elsevier, vol. 291(2), pages 525-535.
    3. Wang, Yukun & Liu, Yiliu & Liu, Zixian & Li, Xiaopeng, 2017. "On reliability improvement program for second-hand products sold with a two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 452-463.
    4. Peng, Shizhe & Jiang, Wei & Wei, Lai & Wang, Xiao-Lin, 2022. "A new cost-sharing preventive maintenance program under two-dimensional warranty," International Journal of Production Economics, Elsevier, vol. 254(C).
    5. Murthy, D. N. P. & Djamaludin, I., 2002. "New product warranty: A literature review," International Journal of Production Economics, Elsevier, vol. 79(3), pages 231-260, October.
    6. Lu, Zhen & Shang, Jennifer, 2019. "Warranty mechanism for pre-owned tech products: Collaboration between E-tailers and online warranty provider," International Journal of Production Economics, Elsevier, vol. 211(C), pages 119-131.
    7. Peng, Shizhe & Jiang, Wei & Huang, Wenpo & Luo, Qinglin, 2024. "The impact of gamma usage processes on preventive maintenance policies under two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    8. Wu, Shaomin, 2013. "A review on coarse warranty data and analysis," Reliability Engineering and System Safety, Elsevier, vol. 114(C), pages 1-11.
    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. Chun Su & Xiaolin Wang, 2016. "Modeling flexible two-dimensional warranty contracts for used products considering reliability improvement actions," Journal of Risk and Reliability, , vol. 230(2), pages 237-247, April.
    11. Andrén, Daniela, 2001. "Short-Term Absenteeism Due To Sickness: The Swedish Experience, 1986 - 1991," Working Papers in Economics 46, University of Gothenburg, Department of Economics.
    12. Wang, Xiaolin & Li, Lishuai & Xie, Min, 2020. "An unpunctual preventive maintenance policy under two-dimensional warranty," European Journal of Operational Research, Elsevier, vol. 282(1), pages 304-318.
    13. 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.
    14. Daniel Villanueva & Andrés Feijóo & José L. Pazos, 2013. "Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment," Resources, MDPI, vol. 2(3), pages 1-15, September.
    15. Andrés Christen, J. & Ruggeri, Fabrizio & Villa, Enrique, 2011. "Utility based maintenance analysis using a Random Sign censoring model," Reliability Engineering and System Safety, Elsevier, vol. 96(3), pages 425-431.
    16. J. Baik & D.N.P. Murthy & N. Jack, 2004. "Two‐dimensional failure modeling with minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 345-362, April.
    17. Félix Belzunce & Julio Mulero & José María Ruíz & Alfonso Suárez-Llorens, 2015. "On relative skewness for multivariate distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 813-834, December.
    18. Ferencek Aljaž & Kofjač Davorin & Škraba Andrej & Sašek Blaž & Borštnar Mirjana Kljajić, 2020. "Deep Learning Predictive Models for Terminal Call Rate Prediction during the Warranty Period," Business Systems Research, Sciendo, vol. 11(2), pages 36-50, October.
    19. Cao, Zixia, 2022. "Brand equity, warranty costs, and firm value," International Journal of Research in Marketing, Elsevier, vol. 39(4), pages 1166-1185.
    20. Insua, David Rios & Ruggeri, Fabrizio & Soyer, Refik & Wilson, Simon, 2020. "Advances in Bayesian decision making in reliability," European Journal of Operational Research, Elsevier, vol. 282(1), pages 1-18.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:92:y:2007:i:2:p:135-143. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.