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Recursive Formulas for the Reliability of Multi-State Consecutive-k-out-of-n:F System

  • Author(s) / Creator(s)
  • In traditional reliability theory, both the system and its components are allowed to take only two possible states: working or failed. In a multi-state system, both the system and the components are allowed to be in M+1 states: 0, 1, 2,…, M, where M is a positive integer which represents a system or unit in perfect functioning state, while zero is complete failure state. A multi-state system reliability model provides more flexibility for the modeling of equipment conditions. Huang et al. (2003) proposed more general definitions of the multi-state consecutive-k-out-of-n:F and G systems and then provide an exact algorithm for evaluating the system state distribution of decreasing multi-state consecutive-k-out-of-n:F systems. Another algorithm is provided to bound the system state distribution of increasing multi-state consecutive-k-out-of-n:F and G systems. The multi-state consecutive-k-out-of-n:F system is applicable to, for example, quality control problems. In this paper, we provide two theorems and a recursive algorithm which evaluate the system state distribution of a multi-state consecutive-k-out-of-n:F system using the theorems. These recursive formulas are useful for any multi-state consecutive-k-out-of-n:F system, including the decreasing multi-state F system, the increasing multi-state F system and other non-monotonic F systems. We calculate the order of computing time and memory capacity of the proposed algorithm and show that, in cases when the number of components n is large, the proposed algorithm is more efficient than other algorithms. A numerical experiment shows that when n is large, the proposed method is efficient for evaluating the system state distribution of multi-state consecutive-k-out-of-n:F systems.

  • Date created
    2006
  • Subjects / Keywords
  • Type of Item
    Article (Published)
  • DOI
    https://doi.org/10.7939/R3Z31P25J
  • License
    Attribution 4.0 International
  • Language
  • Citation for previous publication
    • Akiba, T., Nagatsuka, H., Yamamoto, H., and Zuo, M. (2006). Recursive Formulas for the Reliability of Multi-State Consecutive-k-out-of-n:F System. The Journal of Japan Industrial Management Association, 56(6), 439-446.
  • Link to related item
    http://ci.nii.ac.jp/naid/110007539940/