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Analysis of a two‐component series system with a geometric process model

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  • Yeh Lam
  • Yuan Lin Zhang

Abstract

In this article, a geometric process model is introduced for the analysis of a two‐component series system with one repairman. For each component, the successive operating times form a decreasing geometric process with exponential distribution, whereas the consecutive repair times constitute an increasing geometric process with exponential distribution, but the replacement times form a renewal process with exponential distribution. By introducing two supplementary variables, a set of partial differential equations is derived. These equations can be solved analytically or numerically. Further, the availability and the rate of occurrence of failure of the system are also determined. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:4:p:491-502
    DOI: 10.1002/(SICI)1520-6750(199606)43:43.0.CO;2-2
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    Cited by:

    1. 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.
    2. Showkat Ahmad Lone & Intekhab Alam & Ahmadur Rahman, 2023. "Statistical Analysis Under Geometric Process in Accelerated Life Testing Plans for Generalized Exponential Distribution," Annals of Data Science, Springer, vol. 10(6), pages 1653-1665, December.
    3. Zhao, Bing & Yue, Dequan & Liao, Haitao & Liu, Yuanhui & Zhang, Xiaohong, 2021. "Performance analysis and optimization of a cold standby system subject to δ-shocks and imperfect repairs," Reliability Engineering and System Safety, Elsevier, vol. 208(C).

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