Skip to main content Accessibility help
×
Home
Hostname: page-component-55b6f6c457-kv5sj Total loading time: 0.272 Render date: 2021-09-24T18:48:02.351Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Availability of periodically inspected systems with Markovian wear and shocks

Published online by Cambridge University Press:  14 July 2016

Jeffrey P. Kharoufeh*
Affiliation:
Air Force Institute of Technology
Daniel E. Finkelstein*
Affiliation:
Air Force Institute of Technology
Dustin G. Mixon*
Affiliation:
Air Force Institute of Technology
*
Postal address: Department of Operational Sciences, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433-7765, USA. Email address: jeffrey.kharoufeh@afit.edu
∗∗ Postal address: Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433-7765, USA.
∗∗ Postal address: Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433-7765, USA.
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We analyze a periodically inspected system with hidden failures in which the rate of wear is modulated by a continuous-time Markov chain and additional damage is induced by a Poisson shock process. We explicitly derive the system's lifetime distribution and mean time to failure, as well as the limiting average availability. The main results are illustrated in two numerical examples.

Type
Research Papers
Copyright
© Applied Probability Trust 2006 

References

Abate, J. and Whitt, W. (1995). Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. 7, 3643.CrossRefGoogle Scholar
Çinlar, E. (1977). Shock and wear models and Markov additive processes. In Theory and Application of Reliability: with Emphasis on Bayesian and Nonparametric Methods, eds Shimi, I. N. and Tsokos, C. P., Academic Press, New York, pp. 193214.CrossRefGoogle Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973). Shock models and wear processes. Ann. Prob. 1, 627649.CrossRefGoogle Scholar
Igaki, N., Sumita, U. and Kowada, M. (1995). Analysis of Markov renewal shock models. J. Appl. Prob. 32, 821831.CrossRefGoogle Scholar
Kharoufeh, J. P. (2003). Explicit results for wear processes in a Markovian environment. Operat. Res. Lett. 31, 237244.CrossRefGoogle Scholar
Kiessler, P. C., Klutke, G.-A. and Yang, Y. (2002). Availability of periodically inspected systems subject to Markovian degradation. J. Appl. Prob. 39, 700711.CrossRefGoogle Scholar
Klutke, G.-A. and Yang, Y. (2002). The availability of inspected systems subject to shocks and graceful degradation. IEEE Trans. Reliab. 51, 371374.CrossRefGoogle Scholar
Klutke, G.-A., Wortman, M. and Ayhan, H. (1996). The availability of inspected systems subject to random deterioration. Prob. Eng. Inf. Sci. 10, 109118.CrossRefGoogle Scholar
Nakagawa, T. (1979). Replacement problem of a parallel system in random environment. J. Appl. Prob. 16, 203205.CrossRefGoogle Scholar
Råde, J. (1976). Reliability systems in random environment. J. Appl. Prob. 13, 407410.CrossRefGoogle Scholar
Shanthikumar, J. G. and Sumita, U. (1983). General shock models associated with correlated renewal sequences. J. Appl. Prob. 20, 600614.CrossRefGoogle Scholar
Skoulakis, G. (2000). A general shock model for a reliability system. J. Appl. Prob. 37, 925935.CrossRefGoogle Scholar
You have Access
13
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Availability of periodically inspected systems with Markovian wear and shocks
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Availability of periodically inspected systems with Markovian wear and shocks
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Availability of periodically inspected systems with Markovian wear and shocks
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *