Multi-state Systems with Graduate Failure and Equal Transition Intensities
Journal
Mediterranean Journal of Mathematics
Date Issued
2009-03
Author(s)
Popeska, Zaneta
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.
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.
Subjects
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