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STUDY OF INSTANT SYSTEM AVAILABILITY

Published online by Cambridge University Press:  15 September 2014

Kai Huang  and
Jie Mi
Kai Huang
Affiliation:
Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA E-mail: khuang@fiu.edu
Jie Mi
Affiliation:
Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA E-mail: mi@fiu.edu
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Abstract

In this paper, we study the instant availability A(t) of a repairable system by integral equation. We have proved initial monotonicity of availability, and derived lower bounds of A(t) and average availability. The availabilities of two systems are compared.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 1 , January 2015 , pp. 117 - 129
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Abate, J. & Whitt, W. (1992) The Fourier-series method for inverting transforms of probability distributions. Queueing Systems 10(1): 5–88.Google Scholar
2.Abate, J. & Whitt, W. (1995) Numerical inversion of Laplace transforms of probability distributions. INFORMS Journal on Computing 7: 36–43.Google Scholar
3.Aven, T. & Jensen, U. (1999) Stochastic models in reliability. NY: Springer.Google Scholar
4.Barlow, R.E & Hunter, L. (1960) System efficiency and reliability. Technometrics 2(1): 43–53.Google Scholar
5.Barlow, R.E. & Proschan. (1973) Availability theory for multicomponent systems. Multivariate analysis, III (Proc. Third Internat. Sympos., Wright State University, Dayton, OH, 1972), pp. 319–335. New York: Academic Press.Google Scholar
6.Baxter, L.A. (1981a) Availability measures for a two-state system. Journal of Applied Probability 18(1): 227–235.Google Scholar
7.Baxter, L.A. (1981b) A two-state system with partial availability in the failed state. Naval Research Logistic Quarterly 28(2): 231–236.Google Scholar
8.Baxter, L.A. (1983) Availability measures for coherent systems of separately maintained components. Journal of Applied Probability 20: 627–636.CrossRefGoogle Scholar
9.Bellman, R. & Cooke, K. (1963) Differential-difference equations. NY: Academic Press.Google Scholar
10.Biswas, A. & Sarkar, J. (2000) Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair. Statistics and Probability Letters 50: 105–114.CrossRefGoogle Scholar
11.Block, H.W., Borges, W.S. & Savits, T.H. (1985) Age-dependent minimal repair. Journal of Applied Probability 22(2): 370–385.Google Scholar
12.Cha, J.H. & Kim, J.J. (2001) On availability of Bayesian imperfect repair model. Statistics and Probability Letters 53(2): 181–187.Google Scholar
13.Cha, J.H. & Kim, J.J. (2002) On the existence of the steady state availability of imperfect repair model. Sankhya 64(1): 76–81.Google Scholar
14.Cha, J.H, Lee, S. & Mi, J. (2004) Comparison of steady system availability with imperfect repair. Applied Stochastic Models in Business and Industry 20(1): P27–P36.Google Scholar
15.Cohen, A. (2007) Numerical methods for Laplace transform inversion. NY: Springer.Google Scholar
16.Iyer, S. (1992) Availability results for imperfect repair. Management Science Serie B 54(2): 249–256.Google Scholar
17.Karlin, S. & Taylor, H. (1975) A first course in stochastic processes. 2 edn., San Diego: Academic Press.Google Scholar
18.Li, H & Shaked, M. (2003) Imperfect repair models with preventive maintenance. Journal of Applied Probability 40(4): 1043–1059.Google Scholar
19.Mi, J. (1995) Limiting behavior of some measures of system availability. Journal of Applied Probability 32(2): 482–493.Google Scholar
20.Mi, J. (1998) Some comparison results of system availability. Naval Research Logistics 45(2): P205–P218.Google Scholar
21.Mi, J. (2006) Limiting availability of system with non-identical lifetime distributions and non-identical repair time distributions. Statistics and Probability Letters 76(7): 729–736.Google Scholar
22.Rausand, M. & Houland, A. (2003) System reliability theory: models, statistical methods and applications. 2nd edn, New York: Wiley.Google Scholar
23.Sarkar, J. & Chaudhuri, G. (1999) Availability of a system with gamma life and exponential repair time under a perfect repair policy. Statistics and Probability Letters 43(2): P189–P196.Google Scholar