Analytical Results for a Single-Unit System Subject to Markovian Wear and Shocks
Abstract
This thesis develops and analyzers 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 23, 2004
- Accession Number
- ADA422939
Entities
People
- Daniel E. Finkelstein
Organizations
- Air Force Institute of Technology