System Performance and Reliability Modeling of a Stochastic-Flow Production Network: A Confidence-Based Approach

Production network performance and reliability are essential to satisfy customer orders in a timely manner. This paper proposes a statistical method for a production system to satisfy customer demand with a desired level of confidence, referred to as yield confidence, while simultaneously considering system reliability, defined as the probability that the amount of input can be processed based on the capacities of the individual workstations. The approach models a production system as a stochastic-flow production network, characterized by a discrete time Markov chain (DTMC), where one or more rework actions are possible. This model quantifies the probability that raw input is transformed into a finished product, which is subsequently used to calculate the amount of raw input needed to satisfy demand with a user-specified level of yield confidence. A pair of case studies, taken from the tile and circuit board industries, illustrates the assessment techniques as well as methods to identify workstation level enhancements that can improve network performance and reliability most significantly. Our results indicate that improving the reliability of workstations can enhance yield confidence because a lower volume of raw input can produce the desired volume of output, thereby minimizing the load placed on the production network.