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

By Daniel E. Finkelstein

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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• Format: Paperback
• Language: English
• ISBN: 124958812X
• ISBN13: 9781249588122
• Release Date: October 2012
• Publisher: Biblioscholar
• Length: 98 Pages
• Weight: 0.42 lbs.
• Dimensions: 0.2" x 7.4" x 9.7"