Performance evaluation models are used by companies to design, adapt, manage and control their production systems. Most of the effort has been spent in literature toward the development of efficient methodologies to estimate the first moment performance measures of the system, such as the expected production rate, the buffer levels and the lead time. However, 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 an efficient method to estimate the variance of the number of parts produced, in a given time period, by production lines composed of unreliable machines. The method is based on the exact solution for two-machine lines with one buffer, which is used to approximately calculate the output variance of a multi-stage line. The accuracy of the proposed method is assessed by comparing results with those provided by simulation and by other existing methods. Moreover, the developed approach is used to characterize the behavior of the variance in relation to the system parameters.

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