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Properties of the geometric and related processes

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  • W. John Braun
  • Wei Li
  • Yiqiang Q. Zhao

Abstract

Some properties of the geometric process are studied along with those of a related process which we propose to call the α‐series process. It is shown that the expected number of counts at an arbitrary time does not exist for the decreasing geometric process. The decreasing version of the α‐series process does have a finite expected number of counts, under certain conditions. This process also has the same advantages of tractability as the geometric process; it exhibits some properties which may make it a useful complement to the increasing geometric process. In addition, it may be fit to observed data as easily as the geometric process. Applications in reliability and stochastic scheduling are considered in order to demonstrate the versatility of the alternative model. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005

Suggested Citation

  • W. John Braun & Wei Li & Yiqiang Q. Zhao, 2005. "Properties of the geometric and related processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 607-616, October.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:7:p:607-616
    DOI: 10.1002/nav.20099
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    References listed on IDEAS

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    1. Yeh Lam & Yuan Lin Zhang, 1996. "Analysis of a two‐component series system with a geometric process model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 491-502, June.
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    Cited by:

    1. Halil Aydoğdu & İhsan Karabulut, 2014. "Power series expansions for the distribution and mean value function of a geometric process with Weibull interarrival times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(8), pages 599-603, December.
    2. Yevkin, Alexander & Krivtsov, Vasiliy, 2020. "A generalized model for recurrent failures prediction," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    3. Junyuan Wang & Jimin Ye, 2022. "A new repair model and its optimization for cold standby system," Operational Research, Springer, vol. 22(1), pages 105-122, March.
    4. 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).
    5. Mingjuan Sun & Qinglai Dong & Zihan Gao, 2022. "An Imperfect Repair Model with Delayed Repair under Replacement and Repair Thresholds," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    6. Mustafa Hilmi Pekalp & Halil Aydoğdu, 2018. "An integral equation for the second moment function of a geometric process and its numerical solution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(2), pages 176-184, March.

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