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Analytical Results for a Single-Unit System Subject to Markovian Wear and Shocks by Daniel E. Finkelstein

Analytical Results for a Single-Unit System Subject to Markovian Wear and Shocks

by Daniel E. Finkelstein
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Book cover type: Paperback
  • ISBN13: 9781249588122
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Biblioscholar
  • Publisher Imprint: Biblioscholar
  • Publication Date:
  • Pages: 96
  • Original Price: GBP 11.95
  • Language: English
  • Edition: N/A
  • Item Weight: 146 grams
  • BISAC Subject(s): General

This thesis develops and analyzes a mathematical model for the reliability measures of a single-unit system subject to continuous wear due to its operating environment and randomly occurring shocks that inflict a random amount of damage to the unit. Assuming a Markovian operating environment and shock arrival mechanism, Laplace-Stieltjes transform expressions are obtained for the failure time distribution and all of its moments. Moreover, an analytical expression is derived for the long-run availability of the single-unit system when it is subject to an inspect-and-replace maintenance policy. The analytical results are illustrated, and their results compared with those of Monte Carlo-simulated failure data. The numerical results indicate that the reliability measures may be accurately computed via numerical inversion of the transform expressions in a straightforward manner when the input parameters are known a priori. In stark contrast to the simulation model which requires several hours to obtain the reliability measures, the analytical procedure computes the same measures in only a few seconds.

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