On a Markov-modulated shock and wear process

Authors

  • Jeffrey P. Kharoufeh,

    Corresponding author
    1. Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261 USA
    • Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261 USA
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  • Dustin G. Mixon

    1. Air Force Research Laboratory, HE Directorate, Directed Energy Bioeffects Division, RF Radiation Branch, Brooks City-Base, Texas 78235
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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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