Assembly systems with non-exponential machines: Throughput and bottlenecks

Manufacturing equipment on the factory floor is typically unreliable and the buffers are finite. This makes production systems stochastic and nonlinear. Numerous studies addressed the performance analysis of production systems and, in particular, assembly systems, assuming that up- and downtimes of the machines are exponentially distributed. Empirical evidence indicates, however, that the coefficients of variation of up- and downtimes are often less than 1 and, hence, the statistics are not exponential. This paper provides methods for throughput analysis and bottleneck identification in assembly systems with non-exponential machines. Since the resulting systems are non-Markovian, analytical investigation is all but impossible. Therefore, a numerical approach is pursued, based on simulations of systems at hand and a subsequent analytical approximation of the results obtained. This leads to a closed formula for the throughput and a practical method for bottleneck identification.