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A Note on Closure Properties of Failure Rate Distributions

Author

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  • Anand Paul

    (Department of Decision and Information Sciences, Warrington College of Business, University of Florida, 351 Stuzin Hall, P.O. Box 117169, Gainesville, Florida 32611)

Abstract

Increasing generalized failure rate (IGFR) distributions were introduced as a tool in the study of contracting mechanisms in supply chains. In this note, we compare and contrast the closure—and the lack thereof—of IGFR and increasing failure rate (IFR) distributions with respect to standard operations on random variables. Some implications of these results for the use of IGFR distributions in supply chain models are noted.

Suggested Citation

  • Anand Paul, 2005. "A Note on Closure Properties of Failure Rate Distributions," Operations Research, INFORMS, vol. 53(4), pages 733-734, August.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:4:p:733-734
    DOI: 10.1287/opre.1040.0206
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    Cited by:

    1. Brusset, Xavier & Cattan-Jallet, Roxane, 2009. "Estimating the buyer's willingness to pay using Bayesian belief distribution with IFR," MPRA Paper 22638, University Library of Munich, Germany, revised 10 May 2010.
    2. Wang, Haijun & Tan, Jie & Guo, Shuojia & Wang, Shenhao, 2018. "High-value transportation disruption risk management: Shipment insurance with declared value," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 293-310.
    3. Li, Xiaohu & Fang, Rui & Mi, Jie, 2015. "On the timing to switch on the standby in k-out-of-n:G redundant systems," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 10-20.
    4. Paulo Oliveira & Nuria Torrado, 2015. "On proportional reversed failure rate class," Statistical Papers, Springer, vol. 56(4), pages 999-1013, November.
    5. Yun Fong Lim & Yunzeng Wang & Yue Wu, 2015. "Consignment Contracts with Revenue Sharing for a Capacitated Retailer and Multiple Manufacturers," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 527-537, October.
    6. Colombo, Luca & Labrecciosa, Paola, 2012. "A note on pricing with risk aversion," European Journal of Operational Research, Elsevier, vol. 216(1), pages 252-254.
    7. Georgia Perakis & Guillaume Roels, 2007. "The Price of Anarchy in Supply Chains: Quantifying the Efficiency of Price-Only Contracts," Management Science, INFORMS, vol. 53(8), pages 1249-1268, August.
    8. Bo Yan & Yanping Liu & Zijie Jin, 2023. "Joint coordination contract for capital‐constrained supply chains under asymmetric information," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(1), pages 251-270, January.
    9. Mihai Banciu & Prakash Mirchandani, 2013. "Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 61(4), pages 925-931, August.
    10. Anh Ninh & Zuo‐Jun Max Shen & Martin A. Lariviere, 2020. "Concavity and Unimodality of Expected Revenue Under Discrete Willingness to Pay Distributions," Production and Operations Management, Production and Operations Management Society, vol. 29(3), pages 788-796, March.
    11. Martin A. Lariviere, 2006. "A Note on Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 54(3), pages 602-604, June.
    12. Stefanos Leonardos & Costis Melolidakis & Constandina Koki, 2022. "Monopoly pricing in vertical markets with demand uncertainty," Annals of Operations Research, Springer, vol. 315(2), pages 1291-1318, August.
    13. Ye, Yu-Sen & Ma, Zu-Jun & Dai, Ying, 2016. "The price of anarchy in competitive reverse supply chains with quality-dependent price-only contracts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 86-107.

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