Evaluating failure time probabilities for a Markovian wear process

Evaluating failure time probabilities for a Markovian wear process

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Article ID: iaor2006773
Country: United Kingdom
Volume: 32
Issue: 5
Start Page Number: 1131
End Page Number: 1145
Publication Date: May 2005
Journal: Computers and Operations Research
Authors: ,
Keywords: statistics: distributions
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.

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