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Uncertainty Bounds for a Monotone Multistate System

Published online by Cambridge University Press:  27 July 2009

Helge Langseth  and
Bo Henry Lindqvist
Helge Langseth
Affiliation:
SINTEF Industrial Management, Department of Safety and Reliability N-7034 Trondheim, Norway
Bo Henry Lindqvist
Affiliation:
Norwegian University of Science and Technology, Department of Mathematical Sciences N-7034 Trondheim, Norway
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Abstract

We consider a monotone multistate system with conditionally independent components given the component reliabilities, and random component reliabilities. Upper and lower bounds are derived for the moments of the random reliability function, extending results for binary systems. The second moment is given special attention, as this quantity is used to calculate the standard deviation of the system reliability estimate. The motivation for the paper is to establish a basis for uncertainty analysis and Bayesian estimation in connection with multistate systems.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 12 , Issue 2 , April 1998 , pp. 239 - 260
Copyright
Copyright © Cambridge University Press 1998

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References

1.Agrawal, A. & Barlow, R.E. (1984). A survey of network reliability and domination theory. Operations Research 32: 478–492.CrossRefGoogle Scholar
2.Aitchison, J. (1986). The statistical analysis of compositional data. London: Chapman and Hall.CrossRefGoogle Scholar
3.Aven, T. (1985). Reliability evaluation of multistate systems with multistate components. IEEE Transactions on Reliability R-34: 473–479.CrossRefGoogle Scholar
4.Aven, T. (1987). Availability evaluation of oil/gas production and transportation systems. Reliability Engineering 14: 35–44.CrossRefGoogle Scholar
5.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing: Probability models. Silver Spring, MD: To Begin With.Google Scholar
6.DeGroot, M.H. (1970). Optimal statistical decisions. New York: McGraw-Hill Inc.Google Scholar
7.Doulliez, P. & Jamoulle, J. (1972). Transportation networks with random arc capacities. Recherche Operationelle 3: 45–60.Google Scholar
8.Funnemark, E. & Natvig, B. (1985). Bounds for the availabilities in a fixed time interval for multistate monotone systems. Advances in Applied Probability. 17: 638–665.CrossRefGoogle Scholar
9.Griffith, W.S. (1980). Multistate reliability models. Journal of Applied Probability 17: 735–744.CrossRefGoogle Scholar
10.Lindqvist, B.H. (1988). Association of probability measures on partially ordered spaces. Journal of Multivariate Analysis 26: 111–132.CrossRefGoogle Scholar
11.Lindqvist, B.H. (1992). Moment inequalities for the reliability function. Statistics & Probability Letters 13: 85–88.CrossRefGoogle Scholar
12.Lindqvist, B.H. (1994). The minimal path upper bound for the moments of a reliability function. Scandinavian Journal of Statistics 21: 83–90.Google Scholar
13.Lindqvist, B.H. (1994). On the uncertainty of a system reliability estimate. Reliability Engineering and System Safety 46: 263–269.CrossRefGoogle Scholar
14.Natvig, B. (1980). Two suggestions on how to define a multistate coherent system. Advances in Applied Probability 14: 434–455.CrossRefGoogle Scholar
15.Natvig, B. & Eide, H. (1987). Bayesian estimation of system reliability. Scandinavian Journal of Statistics 14: 319–327.Google Scholar
16.Natvig, B., Sørmo, S., Holen, A.T., & Høgåsen, G. (1986). Multistate reliability theory—A case study. Advances in Applied Probability 18: 577–579.CrossRefGoogle Scholar
17.Scarsini, M. & Snaked, M. (1990). Stochastic ordering for permutation symmetric distributions. Statistics & Probability Letters 9: 217–222.CrossRefGoogle Scholar
18.Stoyan, D. (1983). Comparison methods far queues and other stochastic models. New York: Wiley.Google Scholar