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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: May 18, 2007., Revised: July 8, 2008., Accepted: September 29, 2008.
Rights and permissions
About this article
Cite this article
Mihova, M., Popeska, Z. Multi-state Systems with Graduate Failure and Equal Transition Intensities. MedJM 6, 61–72 (2009). https://doi.org/10.1007/s00009-009-0167-4
Issue Date:
DOI: https://doi.org/10.1007/s00009-009-0167-4