Abstract
In this work we are focused on multi-state systems modeled by means of a special type of semi-Markov processes. The sojourn times are seen to be independent not necessarily identically distributed random variables and assumed to belong to a general class of distributions closed under extrema that includes, in addition to some discrete distributions, several typical reliability distributions like the exponential, Weibull, and Pareto. A special parametrization is proposed for the parameters describing the system, taking thus into account various types of dependencies of the parameters on the the states of the system. We obtain maximum likelihood estimators of the parameters and plug-in type estimators are furnished for the basic quantities describing the semi-Markov system under study.
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Acknowledgements
The research work of Vlad Stefan Barbu was partially supported by the projects XTerM—Complex Systems, Territorial Intelligence and Mobility (2014–2018) and MOUSTIC—Random Models and Statistical, Informatics and Combinatorial Tools (2016–2019) within the Large Scale Research Networks from the Region of Normandy, France. The research work of Alex Karagrigoriou was completed as part of the research activities of the Laboratory of Statistics and Data Analysis of the Department of Mathematics of the University of the Aegean.
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Barbu, V.S., Karagrigoriou, A. (2018). Modeling and Inference for Multi-state Systems. In: Lisnianski, A., Frenkel, I., Karagrigoriou, A. (eds) Recent Advances in Multi-state Systems Reliability. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-63423-4_4
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DOI: https://doi.org/10.1007/978-3-319-63423-4_4
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