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Stochastic Comparisons of Residual Lifetimes and Inactivity Times of Coherent Systems

Part of: Operations research and management science Distribution theory - Probability

Published online by Cambridge University Press:  30 January 2018

Nitin Gupta
Nitin Gupta*
Affiliation:
Jaypee University of Information Technology and Indian Institute of Technology Kharagpur
*
∗ Postal address: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India. Email address: [email protected]
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Abstract

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Under the assumption of independent and identically distributed (i.i.d.) components, the problem of the stochastic comparison of a coherent system having used components and a used coherent system has been considered. Necessary and sufficient conditions on structure functions have been provided for the stochastic comparison of a coherent system having used/inactive i.i.d. components and a used/inactive coherent system. As a consequence, for r-out-of-n systems, it has been shown that systems having used i.i.d. components stochastically dominate used systems in the likelihood ratio ordering.

Keywords

Likelihood ratio ordercoherent systemresidual lifeinactivity time

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 3 , September 2013 , pp. 848 - 860
Copyright
© Applied Probability Trust 

References

Barlow, R. E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. Silver Spring, MD.Google Scholar
Block, H. W., Savits, T. H. and Singh, H. (1998). The reversed hazard rate function. Prob. Eng. Inf. Sci. 12, 69–90.CrossRefGoogle Scholar
Chandra, N. K. and Roy, D. (2001). Some results on reversed hazard rate. Prob. Eng. Inf. Sci. 15, 95–102.CrossRefGoogle Scholar
Glaser, R. E. (2001). Bathtub and related failure rate characterizations. J. Amer. Statist. Assoc. 75, 667–672.CrossRefGoogle Scholar
Gupta, N., Gandotra, N. and Bajaj, R. (2012). Reliability properties of residual life time and inactvity time of series and parallel system. J. Appl. Math. Statist. Inf. 8, 5–16.Google Scholar
Li, X. and Lu, J. (2003). Stochastic comparisons on residual life and inactivity time of series and parallel systems. Prob. Eng. Inf. Sci. 17, 267–275.CrossRefGoogle Scholar
Li, X. and Zuo, M. J. (2004). Stochastic comparison of residual life and inactivity time at a random time. Stoch. Models 20, 229–235.CrossRefGoogle Scholar
Meyer, P. L. (1970). Introductory Probability and Statistical Applications, 2nd edn. Addison-Wesley, Reading, MA.Google Scholar
Misra, N., Dhariyal, I. D. and Gupta, N. (2009). Optimal allocation of active spares in series systems and comparision of component and system redundancies. J. Appl. Prob. 46, 19–34.CrossRefGoogle Scholar
Misra, N., Gupta, N. and Dhariyal, I. D. (2008). Stochastic properties of residual life and inactivity time at a random time. Stoch. Models 24, 89–102.CrossRefGoogle Scholar
Pellerey, F. and Petakos, K. I. (2002). Closure property of the NBUC class under formation of parallel systems. IEEE Trans. Reliab. 51, 452–454.CrossRefGoogle Scholar
Ross, S. M. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar
Zhang, S. H. and Li, X. H. (2003). Comparision between a system of used components and a used system. J. Lanzhou Univ. 39, 11–13.Google Scholar