Moments of Cumulated Output and Completion Time of Unreliable General Markovian Machines

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.