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Warranty cost analysis with an alternating geometric process

Author

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  • Richard Arnold
  • Stefanka Chukova
  • Yu Hayakawa
  • Sarah Marshall

Abstract

In this study, we model the warranty claims process and evaluate the warranty servicing costs under non-renewing, renewing and restricted renewing free repair warranties. We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time. To accommodate the ageing of the product and repair equipment, we use a decreasing geometric process to model the consecutive operational times and an increasing geometric process to model the consecutive repair times. We identify and study the alternating geometric process, which is an alternating process with cycles consisting of the item’s operational time followed by the corresponding repair time. We derive new results for the alternating geometric process in a finite horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under a non-renewing free repair warranty, a renewing free repair warranty and a restricted renewing free repair warranty. Properties of the model are demonstrated using a simulation study and by fitting the models to real data from an automotive manufacturer.

Suggested Citation

  • Richard Arnold & Stefanka Chukova & Yu Hayakawa & Sarah Marshall, 2019. "Warranty cost analysis with an alternating geometric process," Journal of Risk and Reliability, , vol. 233(4), pages 698-715, August.
    • Handle: RePEc:sae:risrel:v:233:y:2019:i:4:p:698-715
    DOI: 10.1177/1748006X18820379
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    References listed on IDEAS

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    1. Shaomin Wu, 2018. "Doubly geometric processes and applications," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(1), pages 66-77, January.
    2. Stefanka Chukova & Yu Hayakawa, 2004. "Warranty cost analysis: non‐zero repair time," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 20(1), pages 59-71, January.
    3. Kao, Edward P. C. & Smith, Marion Spokony, 1996. "Computational approximations of renewal process relating to a warranty problem: The case of phase-type lifetimes," European Journal of Operational Research, Elsevier, vol. 90(1), pages 156-170, April.
    4. Xiaodong Yao & Xiaolan Xie & Michael C. Fu & Steven I. Marcus, 2005. "Optimal joint preventive maintenance and production policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 668-681, October.
    5. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
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    Cited by:

    1. Lijun Shang & Yongjun Du & Cang Wu & Chengye Ma, 2022. "A Bivariate Optimal Random Replacement Model for the Warranted Product with Job Cycles," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    2. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    3. Liu, Peng & Wang, Guanjun, 2022. "Minimal repair models with non-negligible repair time," Reliability Engineering and System Safety, Elsevier, vol. 217(C).

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