Exploiting Virtual Elasticity of Production Systems to Respect OTD—Part 3: Basic Considerations for Modelling CPPS Characterized by Non-Ergodic Order Entry and Non-Deterministic Product-Mix for Fully Flexible Addressable Workstations

Abstract

The recently experienced hype concerning the so-called “4th Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production Systems (CPPS). However, important aspects such as the modelling of CPPS to understand the theory regarding the performance of highly non-ergodic and non-deterministic flexible manufacturing systems in terms of Exit Rate (ER), Manufacturing Lead Time (MLT), and On-Time Delivery (OTD) have not yet been examined systematically and even less modeled analytically. To develop the topic, in this paper, the prerequisites for modelling such systems are defined in order to be able to derive an explicit and dedicated production mathematics-based understanding of CPPS and its dynamics: switching from explorative simulation to rational modelling of the manufacturing “physics” led to an own and specific manufacturing theory. The findings have led to enouncing, among others, the Theorem of Non-Ergodicity as well as the Batch Cycle Time Deviation Function giving important insights to model digital twin-based CPPS for complying with the mandatory OTD.