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

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## Abstract

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

## Keywords

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

**Symbols/****parameters**\(\mathbf {Meaning}\)

- \(f_{i}\)
\(i\)th quality feature of product

- \(q- f_{i}\)
output quality of \(i\)th feature

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

- \(n\)
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

- \(p_{i}\)
importance degree of \(f_{i}\)

- \(P\)
set of importance degree

- \(N_{i}\)
\(i\)th network node

- \(N\)
node set

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

- \(E \)
edge set

- \(w_{i}\)
\(i\)th node weight

- \(W \)
weight set

- \(D_{i}\)
degree of \(i\)th node

- \(C_{i }\)
clustering coefficient of \(i\)th node

- \(E_{i}\)
sensitivity degree of \(i\)th node

- \(Q_{i}\)
influence index of \(i\)th node

- \(\varphi \)
node strength coefficient

- \(\rho \)
Weibull coefficient

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

- \(\alpha \)
number of produced new nodes

- \(\beta \)
possible maximum edges

- \(U\)
time dimension of node state

- \(x_{t}\), \(y_{t}\)
element of node state at time \(t\)

- \(\gamma \)
the resolution ratio

- \(N_{key}\)
key node

- \(c_{key}\)
coupling degree of key nodes

- \(\lambda \)
number of nodes coupled with key nodes

- \(X_{key}\)
state set of key nodes

- \(X_{ckey}\)
coupling data set of key nodes

- \(c_{ckey, j}\)
coupling degree between key node and \(j\)th node

- \(b_{0}\),\(b_{1}\),\(b_{2}\),\(b_{3}\)
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

- \(q\)
number of search regions

- \(\sigma \)
search parameters

- \(T_{l}\)
global random search steps

- \(\psi \)
global search index

- \(C_{\sigma }\)
global search constant

- \(T_{s}\)
local walk search steps

- \(r\)
neighbor points of \(B\)

- \(\mu \)
local search coefficient

- \(E\)
minimum accumulated error

## Notes

### Acknowledgments

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

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