A Max-Plus Algebra Approach to Study Time Disturbance Propagation within a Robustness Improvement Context

Abstract

Industry 4.0 aims to ensure the future competitiveness of the manufacturing industry, where one of the major challenges faced by its implementation is the manufacturing/production system robustness (that is, able to perform in the presence of noise), as they may not be able to absorb input disruptions without bending or breaking. In this paper we propose to use the Max-Plus algebra approach to study the propagation of manufacturing disturbances (i.e., processing time variations), presenting a case study and performing a sensitivity analysis, with the idea of understanding under which conditions disturbance propagation takes place. Findings show that the impact propagation depends on where the variation source is located within the manufacturing system. Two are the main original contributions of this paper: the use of Max-Plus algebra to study the impact propagation of processing time variations and a four-step methodology to derive the equations representing the deterministic manufacturing system.

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“…The ability to absorb manufacturing disruptions and to adapt is a crucial characteristic to achieve with the support of the I4.0 concept and elements implementations. According to [16,22] robustness and resilience do not necessarily co-exist, but both provide production systems with a sustainable competitive advantage. When trying to connect disturbances and deviations to I4.0, the terms are assessed in works that address resilience and robustness [16,23,24], with focus on a) analyzing the variation and its adjustability, b) analyzing variation in terms of disturbances propagation and their effects and that leads to c) concentrating on the characteristics necessary to build resilience.…”

“…The deviation is mentioned only as variation in the physical product specification related to quality and design. On their work [16] studies the propagation of disturbances, making a clear distinction between resilience and robust system and highlights the objective of systems for I4.0, which are intended to be robust i.e. have the ability to absorb disruptions without failing or breaking and resilient i.e.…”

“…One major challenge faced by the implementation of the I4.0 concept is the robustness and resilience of the manufacturing production system, that is, the ability to absorb manufacturing disruptions without failing or breaking and to adapt to major variations/disturbances and gradually return to its original level of performance [16,17]. New technologies enable an entirely new set of capabilities, which according to [18] can be grouped into four areas: monitoring, control, optimization, and autonomy.…”

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“…Empirical cases in research are frequently centered around presenting single applications, emphasizing the low-cost factor as a main advantage and strength of their application [3,[12][13][14][15][16][17]. The implementation of the I4.0 concept implies a major challenge which is resilience and robustness of the production system, which is the ability to absorb manufacturing disturbances without failing or breaking and be able to adapt to major variations and gradually return to its original state or "normal" state and level of performance [18,19]. When trying to connect production processes disturbances and deviations to I4.0, the terms are assessed in works that address resilience and robustness [18,20,21], they often focus on (a) analyzing the variation and its adjustability, (b) analyzing variation in terms of disturbances' propagation and their effects which leads to (c) concentrating on the characteristics necessary to build resilience.…”

“…Absorbing manufacturing disruptions and adapting is a crucial characteristic to reach with the support of the I4.0 concept and component implementations. In [18,28] highlight the fact that robustness and resilience may not necessarily concur, but together provide production systems with a sustainable competitive advantage. Previous research [29,30] has shown that for achieving sustainable production it is crucial to measure performance efficiently, which demands more automatic collection and management of data.…”