Evaluating failure time probabilities for a Markovian wear process

Authors:
Jeffrey P. Kharoufeh;Jeffrey A. Sipe
Affiliations:
Department of Operational Sciences, Air Force Institute of Technology, AFIT/ENS, Bldg 640, 2950 Hobson Way, Wright Patterson AFB OH;Headquarters Air Mobility Command, HQ AMC TACC/XONCY, 402 Scott Drive, Unit 2K1, Scott AFB IL
Venue:
Computers and Operations Research
Year:
2005

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Abstract

We present simplified analytical results for the numerical evaluation of failure time probabilities for a single-unit system whose cumulative wear over time depends on its external environment. The failure time distribution is derived as a one-dimensional Laplace-Stieltjes transform with respect to the temporal variable using a direct solution approach and by inverting an existing two-dimensional result with respect to the spatial failure threshold variable. Two numerical examples demonstrate that accurate cumulative probability values can be obtained in a straightforward manner using standard computing environments.