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A Bivariate Optimal Random Replacement Model for the Warranted Product with Job Cycles

Author

Listed:
  • Lijun Shang

    (School of Quality Management and Standardization, Foshan University, Foshan 528225, China)

  • Yongjun Du

    (School of Economics and Management, Lanzhou University of Technology, Lanzhou 730050, China)

  • Cang Wu

    (School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China)

  • Chengye Ma

    (School of Economics and Management, Lanzhou University of Technology, Lanzhou 730050, China)

Abstract

A monitoring system (MS) has been used to monitor products’ job cycles. It is indicated that by incorporating the job cycle into the product’s life cycle, warrantors can devise novel warranty models and consumers can define and model random maintenances sustaining the reliability of the product through warranty. In this study, by incorporating limited job cycles and a refund into the traditional free repair warranty, a two-dimensional free repair warranty with a refund (2DFRW-R) is devised for guaranteeing the product reliability to consumers. Under the condition that 2DFRW-R is planned to guarantee product reliability, a bivariate random periodic replacement (BRPR) (i.e., a random periodic replacement where the accomplishment of the N th job cycle and the replacement time T are designed as replacement limits) is modeled to sustain the post-warranty reliability from the point of view of the consumer. From the point of view of the warrantor, the warranty cost related to 2DFRW-R is derived, and the characteristics of 2DFRW-R are explored. From the point of view of consumers, the expected cost rate related to BRPR is constructed, and the existence and uniqueness of the optimal BRPR are summarized as well. By discussing parameters, several special cases are derived. The characteristics of the proposed models are analyzed in numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2225-:d:847624
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    References listed on IDEAS

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    Cited by:

    1. Lijun Shang & Xiguang Yu & Liying Wang & Yongjun Du, 2022. "Design of Random Warranty and Maintenance Policy: From a Perspective of the Life Cycle," Mathematics, MDPI, vol. 10(20), pages 1-22, October.
    2. Lijun Shang & Baoliang Liu & Kaiye Gao & Li Yang, 2023. "Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity," Mathematics, MDPI, vol. 11(15), pages 1-22, July.
    3. Lijun Shang & Xiguang Yu & Yongjun Du & Anquan Zou & Qingan Qiu, 2022. "An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge," Mathematics, MDPI, vol. 10(18), pages 1-19, September.

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