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ON INTERVAL AND INSTANT AVAILABILITY OF THE SYSTEM

Published online by Cambridge University Press:  02 March 2020

Jie Mi Open the ORCID record for Jie Mi [Opens in a new window]
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

This article considers the interval availability and instant availability of the k-system. A certain relationship between the two types of availability is established. Some lower and upper bounds to interval availability are derived. It also provides a couple of conditions under which the availability of two systems can be compared. Several examples are given to show the complexity of comparisons of availability.

Keywords

applied probabilityreliability theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 581 - 594
Copyright
© Cambridge University Press 2020

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References

1.Barlow, R.E., & Proschan, F. (1981). Statistical theory of reliability and life testing: Probability models. Silver Springs, MD: To Begin With.Google Scholar
2.Biswas, A., & Sarkar, J. (2000). Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair. Statistics & Probability Letters 50: 105–114.CrossRefGoogle Scholar
3.Dorado, C., Hollander, M., & Sethuraman, J (1997). Nonparametric estimation for a general repair model. The Annals of Statistics 25: 1140–1160.CrossRefGoogle Scholar
4.Du, S., Zio, E., & Kang, R. (2018). New interval availability indexes for Markov repairable systems. IEEE Transactions on Reliability 67: 118–128.CrossRefGoogle Scholar
5.Huang, K., & Mi, J. (2013). Properties and computation of interval availability of system. Statistics and Probability Letters 83: 1388–1396.CrossRefGoogle Scholar
6.Huang, K., & Mi, J. (2015). Study of instant system availability. Probability in the Engineering and Information Sciences 29: 117–129.CrossRefGoogle Scholar
7.Karlin, S., & Taylor, H. (1975). A first course in stochastic processes, 2nd ed. New York, San Francisco, London: Academic Press.Google Scholar
8.Levitin, G., Xing, L.D., & Dai, Y.S. (2015). Optimal backup frequency in system with random repair time. Reliability Engineering & System Safety 144: 12–22.CrossRefGoogle Scholar
9.Liu, Y., Zuo, M.J., Li, Y.F., & Huang, H.Z. (2015). Dynamic reliability assessment for multi-state systems utilizing system-level inspection data. IEEE Transactions on Reliability 64: 1287–1299.CrossRefGoogle Scholar
10.Mathew, A., & Balakrishna, N. (2014). Nonparametric estimation of the interval reliability. Journal of Statistical Theory and Applications 13: 356–366.CrossRefGoogle Scholar
11.Naseri, M., Baraldi, P., Compare, M., & Zio, E. (2016). Availability assessment of oil and gas processing plants operating under dynamic Arctic weather conditions. Reliability Engineering & System Safety 152: 66–82.CrossRefGoogle Scholar
12.Ross, S.M. (1983). Stochastic processes. New York: John Williams & Sons.Google Scholar
13.Sabri-Laghaie, K., & Noorossana, R. (2016). Reliability and maintenance models for a competing-risk system subjected to random usage. IEEE Transactions on Reliability 65: 1271–1283.CrossRefGoogle Scholar
14.Shaked, M., & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
15.Zio, E. (2017). An introduction to the basics of reliability and risk analysis. Singapore: World Scientific.Google Scholar