Citation: Liu, S.; Du, S.; Xi, L.; Shao,
Y.; Huang, D. A Novel Analytical
Modeling Approach for Quality
Propagation of Transient Analysis of
Serial Production Systems. Sensors
2022, 22, 2409. https://doi.org/
10.3390/s22062409
Academic Editors: Wenjun
(Chris) Zhang, Dhanjoo N. Ghista,
Kelvin K.L. Wong and Andrew
W.H. Ip
Received: 1 March 2022
Accepted: 18 March 2022
Published: 21 March 2022
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Article
A Novel Analytical Modeling Approach for Quality
Propagation of Transient Analysis of Serial Production Systems
Shihong Liu
1
, Shichang Du
1,
*, Lifeng Xi
1
, Yiping Shao
2
and Delin Huang
3
1
Department of Industrial Engineering and Management, School of Mechanical Engineering,
Shanghai Jiao Tong University, Shanghai 200240, China; liukang1644@sjtu.edu.cn (S.L.);
lfxi@sjtu.edu.cn (L.X.)
2
College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310023, China;
syp123gh@zjut.edu.cn
3
College of Mechanical Engineering, Donghua University, Shanghai 201620, China; huangdelin@dhu.edu.cn
* Correspondence: lovbin@sjtu.edu.cn
Abstract:
Production system modeling (PSM) for quality propagation involves mapping the princi-
ples between components and systems. While most existing studies focus on the steady-state analysis,
the transient quality analysis remains largely unexplored. It is of significance to fully understand
quality propagation, especially during transients, to shorten product changeover time, decrease
quality loss, and improve quality. In this paper, a novel analytical PSM approach is established
based on the Markov model, to explore product quality propagation for transient analysis of serial
multi-stage production systems. The cascade property for quality propagation among correlated
sequential stages was investigated, taking into account both the status of the current stage and the
quality of the outputs from upstream stages. Closed-form formulae to evaluate transient quality
performances of multi-stage systems were formulated, including the dynamics of system quality,
settling time, and quality loss. An iterative procedure utilizing the aggregation technique is presented
to approximate transient quality performance with computational efficiency and high accuracy.
Moreover, system theoretic properties of quality measures were analyzed and the quality bottleneck
identification method was investigated. In the case study, the modeling error was 0.36% and the calcu-
lation could clearly track system dynamics; quality bottleneck was identified to decrease the quality
loss and facilitate continuous improvement. The experimental results illustrate the applicability of
the proposed PSM approach.
Keywords: production systems; transient analysis; quality; bottleneck; Markov models
1. Introduction
Production system modeling (PSM) is the process of mapping system principles
between fundamental component-level elements (e.g., machine reliability, quality fail-
ure, and repair probability) and their impacts on system-level performance measures
(e.g., quality and throughput). PSM is critical for analysis, disclosure, and understanding
of production procedure principles for quality improvement. For example, General Motors
implemented PSM at more than 30 plants, such as system performance estimation, bot-
tleneck identification, and resource allocation optimization. As a result, General Motors
improved revenue and saved more than USD 2.1 billion.
The literature on PSM, regarding quality propagation, mainly consists of two research
lines. Traditionally, the research line focuses on the fundamental physical law. For in-
stance, the state space models are established in a pioneering paper by Jin and Shi [
1
],
linking the engineering knowledge for sources of variations with final product quality
measures. More extensions of state space models are introduced to the three-dimensional
assembly system [
2
] and machining system [
3
–
5
]. Although state space models are still
popular, essential problems exist for this research. Namely, the state space models rely on
Sensors 2022, 22, 2409. https://doi.org/10.3390/s22062409 https://www.mdpi.com/journal/sensors
