Entropy and safety monitoring systems

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Abstract

We consider the optimal structure of safety monitoring systems composed of unnecessarily stochastically independentn sensors, which output signals in response to the state of the monitored system. In this paper the conditional entropy of safety monitoring systems with respect to the monitored system is used as the optimality criterion. This conditional entropy means the ambiguity level of signals which the safety monitoring systems output. We formulate safety monitoring systems as monotone systems which are well known concept in reliability theory, and then show that ak — out — of — n system is one of the systems which minimize the conditional entropy among monotone systems composed of at mostn sensors, when the transition probability is exchangeable. Furthermore, assuming that the monitored system has only two states, i.e., normal and abnormal, and the transition probability is dual, we show that one of the optimal structures of safety monitoring systems is series or parallel.

Key words

conditional entropy safety monitoring system k —out —of —n system dual probability exchangeable probability 
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References

  1. [1]
    J. Ansell and A. Bendell, On the optimality of k-out-of-n: G systems. IEEE Trans. Reliability,R-31 (1982), 206–210.CrossRefGoogle Scholar
  2. [2]
    R.E. Barlow and F. Proschan, Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Wihston, Inc., 1975.MATHGoogle Scholar
  3. [3]
    R.E. Barlow and A.S. Wu, Coherent system with multi-state components. Math. Oper. Resea.,3 (1978), 275–281.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    P. Billingsley, Ergodic Theory and Information. John Wiley & Sons, 1960.Google Scholar
  5. [5]
    Z.W. Birnbaum, J.D. Esary and S.C. Saunders, Multi-component systems and structures and their reliability, Technometrics,3 (1961), 55–77.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    K.L. Chung, A Course in Probability Theory (Second Edition). Academic Press, 1974.Google Scholar
  7. [7]
    H. Hagihara, F. Ohi and T. Nishida, An optimal structure of safety monitoring systems. Math. Japonica,31 (1986), 389–397.MATHMathSciNetGoogle Scholar
  8. [8]
    H. Hagihara, M. Sakurai, F. Ohi and T. Nishida, Application of Barlow-Wu systems to safety monitoring systems. Technology Reports of The Osaka University,36 (1986), 245–248.MathSciNetGoogle Scholar
  9. [9]
    K. Inoue, T. Kohda, H. Kumamoto and I. Takami, Optimal structure of sensor systems with two failure modes. IEEE Trans. Reliability,R-31 (1982), 119–120.CrossRefGoogle Scholar
  10. [10]
    T. Kohda, K. Inoue, H. Kumamoto and I. Takami, Optimal logical structure of safety monitoring systems with two failure modes. Transactions of the Society of Instrument and Control Engineers,17 (1981), 36–41.Google Scholar
  11. [11]
    M.J. Phillips, The reliability of two-terminal parallel-series networks subject top two kinds of failure. Microelectronics and Reliability,15 (1976), 535–549.CrossRefGoogle Scholar
  12. [12]
    M.J. Phillips, k-out-of-n: G systems are preferable. IEEE Trans. Reliability,R-29 (1980), 166–169.CrossRefGoogle Scholar
  13. [13]
    K. Tanaka, Mathematical models of safety monitoring system considering uncertainty. ÔYÔ SÛRI,5 (1995), 2–13.Google Scholar

Copyright information

© JJIAM Publishing Committee 2000

Authors and Affiliations

  1. 1.Department of Systems EngineeringNagoya Institute of TechnologyNagoyaJapan

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