Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-18T15:11:19.867Z Has data issue: false hasContentIssue false
  • English
  • Français

On the behavior of the failure rate and reversed failure rate in engineering systems

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

Published online by Cambridge University Press:  04 September 2020

Mahdi Tavangar Open the ORCID record for Mahdi Tavangar [Opens in a new window]
Mahdi Tavangar*
Affiliation:
University of Isfahan
*
*Postal address: Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan81746-73441, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran. Email: m.tavangar@sci.ui.ac.ir
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper the behaviour of the failure rate and reversed failure rate of an n-component coherent system is studied, where it is assumed that the lifetimes of the components are independent and have a common cumulative distribution function F. Sufficient conditions are provided under which the system failure rate is increasing and the corresponding reversed failure rate is decreasing. We also study the stochastic and ageing properties of doubly truncated random variables for coherent systems.

Keywords

Doubly truncated mean functionageing conceptsreliabilitystochastic orderingorder statistics

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 3 , September 2020 , pp. 899 - 910
Check for updates
Copyright
© Applied Probability Trust 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R. E. andProschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Block, H. W., Savits, T. H. andSingh, H. (1998). The reversed hazard rate function. Prob. Eng. Inf. Sci. 12 (1), 69–90.10.1017/S0269964800005064CrossRefGoogle Scholar
Boland, P. J. andSamaniego, F. (2004). The signature of a coherent system and its applications in reliability. In Mathematical Reliability: An Expository Perspective (International Series in Operational Research and Management Science), eds R. Soyer, T. Mazzuchi, and N. Singpurwalla, pp. 1–29. Kluwer, Boston.Google Scholar
Chandra, N. K. andRoy, D. (2001). Some results on reversed hazard rate. Prob. Eng. Inf. Sci. 15, 95–102.10.1017/S0269964801151077CrossRefGoogle Scholar
Finkelstein, M. andCha, J. H. (2013). Stochastic Modeling for Reliability: Shocks, Burn-in and Heterogeneous Populations. Springer, London.10.1007/978-1-4471-5028-2CrossRefGoogle Scholar
Karlin, S. (1968). Total Positivity, Vol. I. Stanford University Press, CA.Google Scholar
Klutke, G., Kiessler, P. C., andWortman, M. A. (2003). A critical look at the bathtub curve. IEEE Trans. Reliab. 52 (1), 125–129.10.1109/TR.2002.804492CrossRefGoogle Scholar
Kotlarski, I. I. (1972). On a characterization of some probability distributions by conditional expectations. Sankhyā A 34, 461–466.Google Scholar
Lai, C. D. andXie, M. (2006). Stochastic Ageing and Dependence for Reliability. Springer, New York.Google Scholar
Mahmoudi, M. andAsadi, M. (2011). The dynamic signature of coherent systems. IEEE Trans. Reliab. 60 (4), 817–822.10.1109/TR.2011.2161702CrossRefGoogle Scholar
Mi, J. (1996). Minimizing some cost functions related to both burn-in and field use. Operat. Res. 44 (3), 497–500.10.1287/opre.44.3.497CrossRefGoogle Scholar
Mi, J. (2003). Optimal burn-in time and eventually IFR. J. Chinese Inst. Indust. Engineers 20 (5), 533–543.10.1080/10170660309509258CrossRefGoogle Scholar
Navarro, J. andRubio, R. (2011). A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components. Naval Res. Logistics 58 (5), 478–489.10.1002/nav.20463CrossRefGoogle Scholar
Navarro, J., Balakrishnan, N. andSamaniego, F. J. (2008). Mixture representations of residual lifetimes of used systems. J. Appl. Prob. 45 (4), 1097–1112.CrossRefGoogle Scholar
Navarro, J., del Águila, Y., Sordo, M. A. andSuárez-Llorens, A. (2014). Preservation of reliability classes under the formation of coherent systems. Appl. Stoch. Models Business Industry 30, 444–454.10.1002/asmb.1985CrossRefGoogle Scholar
Navarro, J., Guillamón, A. andRuiz, M. C. (2009). Generalized mixtures in reliability modelling: applications to the construction of bathtub shaped hazard models and the study of systems. Appl. Stoch. Models Business Industry 25 (3), 323–337.10.1002/asmb.750CrossRefGoogle Scholar
Navarro, J., Ruiz, J. M. andSandoval, C. J. (2005). A note on comparisons among coherent systems with dependent components using signature. Statist. Prob. Lett. 72, 179–185.10.1016/j.spl.2004.12.017CrossRefGoogle Scholar
Samaniego, F. J. (2007). System Signatures and Their Applications in Engineering Reliability. Springer, New York.CrossRefGoogle Scholar
Samaniego, F. J., Balakrishnan, N. andNavarro, J. (2009). Dynamic signatures and their use in comparing the reliability of new and used systems. Naval Res. Logistics 56 (6), 577–591.Google Scholar
Shaked, M. andShanthikumar, J.G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar
Shanbhag, D.N. andRao, B.M. (1975). A note on characterization of probability distributions based on conditional expected values. Sankhyā A 37, 297–300.Google Scholar
Tavangar, M. (2016). Conditional inactivity time of components in a coherent operating system. IEEE Trans. Reliab. 65 (1), 359–369.10.1109/TR.2015.2422773CrossRefGoogle Scholar
Zhang, Z. (2010). Ordering conditional general coherent systems with exchangeable components. J. Statist. Planning Infer. 140, 454–460.10.1016/j.jspi.2009.07.029CrossRefGoogle Scholar