Parameter Identification for Bernoulli Serial Production Line Model

Abstract

Model-based analysis of production systems is one of the main areas in manufacturing research. The foundation of the successful application of these theoretical studies is the availability of valid and high-fidelity mathematical models that are capable of capturing the behavior of job flow in production systems. The modeling process of a production system, however, may require a significant amount of nonstandardized work that can only be done properly by someone with solid training in the area and extensive experience through real case studies. This poses a critical challenge in the effective implementation of these valuable theoretical results in the Industry 4.0 era. To overcome this, we propose a new production systems modeling paradigm inspired by system identification: calculate production system model parameters that best match the standard system performance metrics measured on the factory floor. Specifically, in this article, we consider production lines characterized by the Bernoulli serial line model and develop algorithms that identify model parameters to fit the system throughput and work-in-process. Analytical algorithms are derived to solve this problem in a two-machine line case and then extended to multi-machine lines. The accuracy and computational efficiency of the algorithms are demonstrated through extensive numerical experiments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —A high-fidelity mathematical model is of critical importance to the implementation of any model-based production system analysis method. Currently, the construction of such models is carried out in an ad hoc manner. The quality of the resulting models may heavily depend on the training, experience, intuition, and personal preference of the modeler. The proposed model parameter identification method focuses on standard key performance indices commonly measured on the factory floor. The advantage is twofold. First, these standard performance metrics are consistently defined regardless of industry, thus avoiding any data-ambiguity issue that may occur when using complex machine/equipment status data. Second, measuring these performance metrics in real time is typically convenient and cost effective, even for manufacturing plants without high-end IT infrastructure, thus making the technology accessible to not only large but also small- and mid-sized manufacturers. Using the algorithms developed in this article, a practitioner can quickly construct a serial production line model and then utilize it to access the rich library of production analysis, design, and control methods available in the literature.