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Dynamic demand satisfaction probability of consecutive sliding window systems with warm standby components

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  • Levitin, Gregory
  • Xing, Liudong
  • Ben-Haim, Hanoch
  • Huang, Hong-Zong

Abstract

Motivated by practical applications such as heating systems, radar, and sensor monitoring, this paper models and analyzes a linear consecutive multi-state sliding window system with warm standby components (CSWS-WS). The system contains n linearly ordered components, each being a warm standby configuration of multiple elements with heterogeneous time-to-failure distributions and nominal performances. Thus, depending on the currently operating (online) element, each component may exhibit multiple states, corresponding to different failure behaviors and performance rates. The system function depends on the accumulated performance (sum of performance rates) of r consecutive components, referred to as a r-sized window. The system is considered being failed if the accumulated performance in each of at least m consecutive overlapping r-sized windows is lower than a random demand. To evaluate the reliability (demand satisfaction probability) of a CSWS-WS, a probabilistic model is first presented to determine the dynamic performance distribution of each warm standby component; a universal generating function-based method is then suggested for obtaining the dynamic demand satisfaction probability (DSP). Based on the DSP evaluation, the optimal element distribution and sequencing problem is formulated and solved for the CSWS-WS system. As demonstrated through examples, solutions to the considered optimization problems can facilitate a proper choice of element distribution and activation sequencing, maxmizing the minimum instananeous DSP or expected DSP over a certain mission time.

Suggested Citation

  • Levitin, Gregory & Xing, Liudong & Ben-Haim, Hanoch & Huang, Hong-Zong, 2019. "Dynamic demand satisfaction probability of consecutive sliding window systems with warm standby components," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 397-405.
    • Handle: RePEc:eee:reensy:v:189:y:2019:i:c:p:397-405
    DOI: 10.1016/j.ress.2019.05.002
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    1. Sakurahara, Tatsuya & Schumock, Grant & Reihani, Seyed & Kee, Ernie & Mohaghegh, Zahra, 2019. "Simulation-Informed Probabilistic Methodology for Common Cause Failure Analysis," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 84-99.
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    3. Levitin, Gregory & Ben-Haim, Hanoch, 2011. "Consecutive sliding window systems," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1367-1374.
    4. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, February.
    5. Hui Xiao & Rui Peng & Wenbin Wang & Fei Zhao, 2016. "Optimal element loading for linear sliding window systems," Journal of Risk and Reliability, , vol. 230(1), pages 75-84, February.
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    Cited by:

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