Journal of Intelligent Manufacturing

, Volume 27, Issue 3, pp 535–548 | Cite as

A weighted-coupled network-based quality control method for improving key features in product manufacturing process

  • Guangzhou Diao
  • Liping Zhao
  • Yiyong Yao


There are some complicated coupling relations among quality features (QFs) in manufacturing process. Generally, the machining errors of one key feature may cause some errors of other features which are coupled with the key one. Considering the roles of key QFs, the weighted-coupled network-based quality control method for improving key features is proposed in this paper. Firstly, the W-CN model is established by defining the mapping rules of network elements (i.e. node, edge, weight). Secondly, some performance indices are introduced to evaluate the properties of W-CN. The influence index of node is calculated to identify the key nodes representing key features. Thirdly, three coupling modes of nodes are discussed and coupling degrees of key nodes are calculated to describe the coupling strengthen. Then, the decoupling method based on small world optimization algorithm is discussed to analyze the status changes of key nodes accurately. Finally, a case of engine cylinder body is presented to illustrate and verify the proposed method. The results show that the method is able to provide guidance for improving product quality in manufacturing process


Weighted-coupled network Quality control Influence indices Coupling modes Key nodes Decoupling 



\(\mathbf {Meaning}\)


\(i\)th quality feature of product

\(q- f_{i}\)

output quality of \(i\)th feature


set of quality feature \(f_{i}\)


total number of features

\(s_{i }\)

\(i\)th machining stage

\(S \)

set of machining stage \(s_{i}\)

\(m \)

total number of machining stages

\(l_{ij }\)

coupling relation between \(f_{i}\) and \(f_{j}\)

\(L \)

set of coupling relation


importance degree of \(f_{i}\)


set of importance degree


\(i\)th network node


node set


network edge between \(N_{i}\) and \(N_{j}\)

\(E \)

edge set


\(i\)th node weight

\(W \)

weight set


degree of \(i\)th node

\(C_{i }\)

clustering coefficient of \(i\)th node


sensitivity degree of \(i\)th node


influence index of \(i\)th node

\(\varphi \)

node strength coefficient

\(\rho \)

Weibull coefficient


coupling degree of \(N_{i}\) and\( N_{j}\)

\(\alpha \)

number of produced new nodes

\(\beta \)

possible maximum edges


time dimension of node state

\(x_{t}\), \(y_{t}\)

element of node state at time \(t\)

\(\gamma \)

the resolution ratio


key node


coupling degree of key nodes

\(\lambda \)

number of nodes coupled with key nodes


state set of key nodes


coupling data set of key nodes

\(c_{ckey, j}\)

coupling degree between key node and \(j\)th node


coefficient of status equation

\(B \)

initial solution

\(T \)

target solution

\(Q \)

number of total targets

\(u \)

start region

\(v \)

end region

\(\delta \)

objects in one search region

\(\sigma \)

region size


number of search regions

\(\sigma \)

search parameters


global random search steps

\(\psi \)

global search index

\(C_{\sigma }\)

global search constant


local walk search steps


neighbor points of \(B\)

\(\mu \)

local search coefficient


minimum accumulated error



This work is supported by grant no. 51275399 from the National Natural Science Foundation.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.State Key Laboratory for Manufacturing Systems EngineeringXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  2. 2.School of Mechanical EngineeringXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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