Throughput, flow times, and service level in an unreliable assembly system

This paper considers an unreliable assembly network where different types of components are processed by two separate work centers before being merged at an assembly station. The operation complexity of the system is a result of finite inter-station buffers, uncertain service times, and random breakdowns that lead to blocking at the work centers and starvation at the assembly station. The objective of this study is to gain an understanding of the behavior of such systems so that we can find a way to maximize the system throughput while maintaining the required customer service level. By constructing appropriate Markov processes, we obtain the probability distribution of the production flow time and derive formulas for throughput, the loss probability of type-2 workpieces, and the mean flow time. We present expressions for average work-in-process and study their monotone properties. Using the distribution of the flow time, a customer service level can be defined and computed. We then formulate a system optimization model that can be used to maximize the throughput while maintaining an acceptable service level.