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Standby Redundancy Allocations in Series and Parallel Systems

Part of: Operations research and management science Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Neeraj Misra ,
Amit Kumar Misra  and
Ishwari Dutt Dhariyal
Neeraj Misra*
Affiliation:
Indian Institute of Technology Kanpur
Amit Kumar Misra*
Affiliation:
Indian Institute of Technology Kanpur
Ishwari Dutt Dhariyal*
Affiliation:
Indian Institute of Technology Kanpur
*
∗Postal address: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India.
∗Postal address: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India.
∗Postal address: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India.
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Abstract

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To enhance the performance of a system, a common practice employed by reliability engineers is to use redundant components in the system. In this paper we compare lifetimes of series (parallel) systems arising out of different allocations of one or two standby redundancies. These comparisons are made with respect to the increasing concave (convex) order, the hazard rate order, and the stochastic precedence order. The main results extend some related conclusions in the literature.

Keywords

Hazard rate orderIFRincreasing concave (convex) orderlikelihood ratio orderreversed hazard rate orderstochastic precedence orderusual stochastic order

MSC classification

Secondary: 62N05: Reliability and life testing 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 43 - 55
Copyright
Copyright © Applied Probability Trust 2011 

References

[1] Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
[2] Boland, P. J., El-Neweihi, E. and Proschan, F. (1992). Stochastic order for redundancy allocations in series and parallel systems. Adv. Appl. Prob. 24, 161–171.CrossRefGoogle Scholar
[3] Boland, P. J., Proschan, F. and Tong, Y. L. (1991). Standby redundancy policies for series systems. Tech. Rep. M-838, Florida State University.Google Scholar
[4] Lai, C. D. and Xie, M. (2006). Stochastic Ageing and Dependence for Reliability. Springer, New York.Google Scholar
[5] Li, X. and Hu, X. (2008). Some new stochastic comparisons for redundancy allocations in series and parallel systems. Statist. Prob. Lett. 78, 3388–3394.CrossRefGoogle Scholar
[6] Marshall, A. W. and Olkin, I. (2007). Life Distributions. Springer, New York.Google Scholar
[7] Mi, J. (1998). Bolstering components for maximizing system lifetime. Naval Res. Logistics 45, 497–509.3.0.CO;2-Z>CrossRefGoogle Scholar
[8] Müller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley, Chichester.Google Scholar
[9] Romera, R., Valdés, J. E. and Zequeira, R. I. (2004). Active-redundancy allocation in systems. IEEE Trans. Reliab. 53, 313–318.CrossRefGoogle Scholar
[10] Shaked, M. and Shanthikumar, J. G. (1992). Optimal allocation of resources to nodes of parallel and series systems. Adv. Appl. Prob. 24, 894–914.CrossRefGoogle Scholar
[11] Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar
[12] Singh, H. and Misra, N. (1994). On redundancy allocations in systems. J. Appl. Prob. 31, 1004–1014.CrossRefGoogle Scholar
[13] Valdés, J. E. and Zequeira, R. I. (2003). On the optimal allocation of an active redundancy in a two-component series system. Statist. Prob. Lett. 63, 325–332.CrossRefGoogle Scholar
[14] Valdés, J. E. and Zequeira, R. I. (2006). On the optimal allocation of two active redundancies in a two-component series system. Operat. Res. Lett. 34, 49–52.CrossRefGoogle Scholar