On a Markov-modulated shock and wear process
We present transient and asymptotic reliability indices for a single‐unit system that is subject to Markov‐modulated shocks and wear. The transient results are derived from the (transform) solution of an integro‐differential equation describing the joint distribution of the cumulative degradation pr...
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| Published in | Naval research logistics Vol. 56; no. 6; pp. 563 - 576 |
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| Format | Journal Article |
| Language | English |
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01.09.2009
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| Abstract | We present transient and asymptotic reliability indices for a single‐unit system that is subject to Markov‐modulated shocks and wear. The transient results are derived from the (transform) solution of an integro‐differential equation describing the joint distribution of the cumulative degradation process and the state of the modulating process. Additionally, we prove the asymptotic normality of a properly centered and time‐scaled version of the cumulative degradation at time t. This asymptotic result leads to a simple normal approximation for a properly centered and space‐scaled version of the systes lifetime distribution. Two numerical examples illustrate the quality of the normal approximation. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009 |
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| AbstractList | We present transient and asymptotic reliability indices for a single-unit system that is subject to Markov-modulated shocks and wear. The transient results are derived from the (transform) solution of an integro-differential equation describing the joint distribution of the cumulative degradation process and the state of the modulating process. Additionally, we prove the asymptotic normality of a properly centered and time-scaled version of the cumulative degradation at time t. This asymptotic result leads to a simple normal approximation for a properly centered and space-scaled version of the systes lifetime distribution. Two numerical examples illustrate the quality of the normal approximation. We present transient and asymptotic reliability indices for a single‐unit system that is subject to Markov‐modulated shocks and wear. The transient results are derived from the (transform) solution of an integro‐differential equation describing the joint distribution of the cumulative degradation process and the state of the modulating process. Additionally, we prove the asymptotic normality of a properly centered and time‐scaled version of the cumulative degradation at time t. This asymptotic result leads to a simple normal approximation for a properly centered and space‐scaled version of the systes lifetime distribution. Two numerical examples illustrate the quality of the normal approximation. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009 We present transient and asymptotic reliability indices for a single‐unit system that is subject to Markov‐modulated shocks and wear. The transient results are derived from the (transform) solution of an integro‐differential equation describing the joint distribution of the cumulative degradation process and the state of the modulating process. Additionally, we prove the asymptotic normality of a properly centered and time‐scaled version of the cumulative degradation at time t . This asymptotic result leads to a simple normal approximation for a properly centered and space‐scaled version of the systes lifetime distribution. Two numerical examples illustrate the quality of the normal approximation. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009 |
| Author | Kharoufeh, Jeffrey P. Mixon, Dustin G. |
| Author_xml | – sequence: 1 givenname: Jeffrey P. surname: Kharoufeh fullname: Kharoufeh, Jeffrey P. email: jkharouf@pitt.edu organization: Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261 USA – sequence: 2 givenname: Dustin G. surname: Mixon fullname: Mixon, Dustin G. organization: Air Force Research Laboratory, HE Directorate, Directed Energy Bioeffects Division, RF Radiation Branch, Brooks City-Base, Texas 78235 |
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| References_xml | – volume: 18 start-page: 149 year: 1993 end-page: 171 article-title: The Markov‐modulated Poisson process (MMPP) cookbook publication-title: Performance Evaluat – volume: 47 start-page: 299 year: 1993 end-page: 314 article-title: Limit theorems for cumulative processes publication-title: Stochastic Processes Appl – volume: 31 start-page: 237 year: 2003 end-page: 244 article-title: Explicit results for wear processes in a Markovian environment publication-title: Oper Res Lett – start-page: 193 year: 1977 end-page: 214 – volume: 16 start-page: 203 year: 1979 end-page: 205 article-title: Replacement problem of a parallel system in a random environment publication-title: J Appl Probab – volume: 37 start-page: 543 year: 2005 end-page: 557 article-title: Residual‐life distributions from component degradation signals: A Bayesian approach publication-title: IIE Trans – volume: 43 start-page: 303 year: 2006 end-page: 317 article-title: Availability of periodically inspected 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