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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
Phase-Type Approximations for Wear Processes in a Semi-Markov Environment

Phase-Type Approximations for Wear Processes in a Semi-Markov Environment

Solo, Christopher J.

Paperback

Technology & EngineeringGeneral EducationProbability & Statistics

ISBN10: 1249592976
ISBN13: 9781249592976
Publisher: Biblioscholar
Published: Oct 9 2012
Pages: 140
Weight: 0.45
Height: 0.30 Width: 6.14 Depth: 9.21
Language: English

The reliability of a single-unit system experiencing degradation (wear) due to the influence of a general, observable environment process is considered. In particular, the failure time distribution is evaluated using only observations of the unit's current operating environment which is characterized as a finite semi-Markov process (SMP). In order to impose the Markov property, generally distributed environment state sojourn times are approximated as phase-type (PH) random variables using observations of state holding times and transition rates. The use of PH distributions facilitates the use of existing analytical results for reliability evaluation of units subjectto an environment process that evolves as a continuous-time Markov chain. The procedure is illustrated through three numerical examples, and results are compared with those obtained via Monte Carlo simulation. The maximum absolute deviation in probability for failure time distributions was on the order of 0.004. The results of this thesis provide a novel approach to the reliability analysis of units operating in randomly evolving environments for which degradation or failure time observations are difficult or impossible to obtain.

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