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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Analytical Results for a Single-Unit System Subject to Markovian Wear and Shocks

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

Finkelstein, Daniel E.

Paperback

Technology & EngineeringGeneral EducationProbability & Statistics

ISBN10: 124958812X
ISBN13: 9781249588122
Publisher: Biblioscholar
Published: Oct 3 2012
Pages: 96
Weight: 0.32
Height: 0.20 Width: 6.14 Depth: 9.21
Language: English

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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