Moments of Cumulated Output and Completion Time of
Unreliable General Markovian Machines
A. Angius, A. Horváth, M. Colledani
Abstract:
Performance evaluation models are used by companies to design, adapt,
manage and control their production systems. In the literature, most of the
effort has been dedicated to the development of efficient methodologies to
estimate the first moment performance measures of production systems, such
as the expected production rate, the buffer levels and the mean completion
time. However, there is industrial evidence that the variability of the
production output may drastically impact on the capability of managing the
system operations, causing the observed system performance to be highly
different from what expected. This paper presents a general theory and a
methodology to analyze the cumulated output and the lot completion time
variability of unreliable machines and systems characterized by general Markovian
models. Both discrete models and continuous reward models are
considered. We then discuss two simple examples that show how the theory
developed in this paper can be applied to analyse the dependency of the
output variability on the system parameters.
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horvath
2011-09-12