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A non-homogeneous Poisson process predictive model for automobile warranty claims

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  • Majeske, Karl D.

Abstract

Automobile warranties and thus lifetimes are characterized in the two-dimensional space of time and mileage. This paper presents a non-homogenous Poisson process (NHPP) predictive model for automobile warranty claims consisting of two components: a population size function and a failure or warranty claim rate. The population size function tracks the population in the time domain and accounts for mileage by removing vehicles from the population when they exceed the warranty mileage limitation. The model uses the intensity function of a NHPP—the instantaneous probability of failure—to model the occurrence of warranty claims. The approach was developed to support automobile manufacturers’ process of using claims observed during the early portion (first 7 months) of vehicle life to predict claims for the remainder of coverage, typically between 3 and 5 years. This paper uses manufacturer provided warranty data from a luxury car to demonstrate the NHPP model by predicting claims for three vehicle subsystems. Warranty predictions are then compared with the actual observed values and predictions made with a standard forecasting technique.

Suggested Citation

  • Majeske, Karl D., 2007. "A non-homogeneous Poisson process predictive model for automobile warranty claims," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 243-251.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:2:p:243-251
    DOI: 10.1016/j.ress.2005.12.004
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    References listed on IDEAS

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    1. Majeske, Karl D. & Lynch-Caris, Terri & Herrin, Gary, 1997. "Evaluating product and process design changes with warranty data," International Journal of Production Economics, Elsevier, vol. 50(2-3), pages 79-89, June.
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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. Adithya Thaduri, 0. "Nowcast models for train delays based on the railway network status," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 0, pages 1-12.
    3. Van Dyck, Jozef & Verdonck, Tim, 2014. "Precision of power-law NHPP estimates for multiple systems with known failure rate scaling," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 143-152.
    4. Zhou, Chongwen & Chinnam, Ratna Babu & Dalkiran, Evrim & Korostelev, Alexander, 2017. "Bayesian approach to hazard rate models for early detection of warranty and reliability problems using upstream supply chain information," International Journal of Production Economics, Elsevier, vol. 193(C), pages 316-331.
    5. Peng, Yizhen & Wang, Yu & Zi, YanYang & Tsui, Kwok-Leung & Zhang, Chuhua, 2017. "Dynamic reliability assessment and prediction for repairable systems with interval-censored data," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 301-309.
    6. Huang, Yeu-Shiang & Huang, Chao-Da & Ho, Jyh-Wen, 2017. "A customized two-dimensional extended warranty with preventive maintenance," European Journal of Operational Research, Elsevier, vol. 257(3), pages 971-978.
    7. Chehade, Abdallah & Savargaonkar, Mayuresh & Krivtsov, Vasiliy, 2022. "Conditional Gaussian mixture model for warranty claims forecasting," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    8. Tzougas, George, 2020. "EM estimation for the Poisson-Inverse Gamma regression model with varying dispersion: an application to insurance ratemaking," LSE Research Online Documents on Economics 106539, London School of Economics and Political Science, LSE Library.
    9. Wu, Shaomin & Akbarov, Artur, 2011. "Support vector regression for warranty claim forecasting," European Journal of Operational Research, Elsevier, vol. 213(1), pages 196-204, August.
    10. Wu, Shaomin, 2011. "Warranty claim analysis considering human factors," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 131-138.
    11. Xiaolin Wang & Wei Xie, 2018. "Two-dimensional warranty: A literature review," Journal of Risk and Reliability, , vol. 232(3), pages 284-307, June.
    12. Jiang, Jiahao & Li, Kaiyuan & Guo, Wei & Du, Luchun, 2021. "Energetic and entropic vibrational resonance," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    13. Chehade, Abdallah & Hassanieh, Wael & Krivtsov, Vasiliy, 2024. "SeqOAE: Deep sequence-to-sequence orthogonal auto-encoder for time-series forecasting under variable population sizes," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    14. George Tzougas, 2020. "EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking," Risks, MDPI, vol. 8(3), pages 1-23, September.
    15. Zhang, Zhikun & Dai, Min & Wang, Xiangjun, 2023. "Statistical inference for mixed jump processes by Markov switching model with application to identify seismicity levels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    16. 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.
    17. Wang, Shixuan & Syntetos, Aris A. & Liu, Ying & Di Cairano-Gilfedder, Carla & Naim, Mohamed M., 2023. "Improving automotive garage operations by categorical forecasts using a large number of variables," European Journal of Operational Research, Elsevier, vol. 306(2), pages 893-908.
    18. Giorgio, M. & Guida, M. & Pulcini, G., 2014. "Repairable system analysis in presence of covariates and random effects," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 271-281.
    19. Wu, Shaomin & Akbarov, Artur, 2012. "Forecasting warranty claims for recently launched products," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 160-164.
    20. Adithya Thaduri, 2020. "Nowcast models for train delays based on the railway network status," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(2), pages 184-195, July.
    21. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "On information-based warranty policy for repairable products from heterogeneous populationAuthor-Name: Lee, Hyunju," European Journal of Operational Research, Elsevier, vol. 253(1), pages 204-215.
    22. Anastasiadis, Simon & Anderson, Boyd & Chukova, Stefanka, 2013. "Auto warranty and driving patterns," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 126-134.

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