Multi-state Systems with Graduate Failure and Equal Transition Intensities |
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Authors: | Marija Mihova Zaneta Popeska |
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Institution: | (1) Faculty of Natural Sciences and Mathematics, Gazibaba bb, P.O. Box 162, 1000 Skopje, Macedonia |
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Abstract: | We consider unrecoverable homogeneous multi-state systems with graduate failures, where each component can work at M + 1 linearly ordered levels of performance. The underlying process of failure for each component is a homogeneous Markov
process such that the level of performance of one component can change only for one level lower than the observed one, and
the failures are independent for different components. We derive the probability distribution of the random vector X, representing the state of the system at the moment of failure and use it for testing the hypothesis of equal transition
intensities. Under the assumption that these intensities are equal, we derive the method of moments estimators for probabilities
of failure in a given state vector and the intensity of failure. At the end we calculate the reliability function for such
systems.
Received: May 18, 2007., Revised: July 8, 2008., Accepted: September 29, 2008. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 62N05 Secondary 62N02 |
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