Modeling of variation propagation in multistation assembly processes is crucial in predicting product dimensional quality and general performance of manufacturing systems. Based on the state space modeling, this paper develops a variation propagation model, which can be applied for analysis of various tolerances such as size tolerance, bonus tolerance, floating tolerance, etc. The nonstationary tolerance/variation (varying variance) caused by bonus tolerance and floating tolerance is properly handled by the proposed method. Thus, by using the developed variation propagation model, the variations on key product characteristics (KPCs) can be accurately predicted. This enables broad applications of the proposed method in actual manufacturing processes. The results of the case study also validated the proposed model.

1.
Ceglarek
,
D.
, and
Shi
,
J.
, 1995, “
Dimensional Variation Reduction for Automotive Body Assembly
,”
Manuf. Rev.
0896-1611,
8
(
2
), pp.
139
154
.
2.
Shi
,
J.
, 2006,
Stream of Variation Modeling and Analysis for Multistage Manufacturing Processes
,
CRC
,
Boca Raton, FL
, pp.
1
2
.
3.
Ding
,
Y.
,
Ceglarek
,
D.
, and
Shi
,
J.
, 2000, “
Modeling and Diagnosis of Multistage Manufacturing Processes: Part I: State Space Model
,”
Proceedings of the Japan/USA Symposium on Flexible Automation
, Ann Arbor, MI, July 23–26.
4.
Hu
,
S.
, and
Wu
,
S. M.
, 1992, “
Identifying Root Causes of Variation in Automobile Body Assembly Using Principal Component Analysis
,”
Trans. NAMRI/SME
1047-3025,
20
, pp.
311
316
.
5.
Ceglarek
,
D.
,
Shi
,
J.
, and
Wu
,
S. M.
, 1994, “
A Knowledge-Based Diagnostic Approach for the Launch of the Autobody Assembly Process
,”
ASME J. Eng. Ind.
0022-0817,
116
(
4
), pp.
491
499
.
6.
Ceglarek
,
D.
, and
Shi
,
J.
, 1996, “
Fixture Failure Diagnosis for the Autobody Assembly Using Pattern Recognition
,”
ASME J. Eng. Ind.
0022-0817,
118
(
1
), pp.
55
66
.
7.
Rong
,
Q.
,
Ceglarek
,
D.
, and
Shi
,
J.
, 2000, “
Dimensional Fault Diagnosis for Compliant Beam Structure Assemblies
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
122
(
4
), pp.
773
780
.
8.
Barton
,
R. R.
, and
Gonzalez-Barreto
,
D. R.
, 1996, “
Process-Oriented Basis Representations for Multivariate Process Diagnosis
,”
Qual. Eng.
0898-2112,
9
, pp.
107
118
.
9.
Apley
,
D. W.
, and
Shi
,
J.
, 1998, “
Diagnosis of Multiple Fixture Faults in Panel Assembly
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
120
(
4
), pp.
793
801
.
10.
Chang
,
M.
, and
Gossard
,
D. C.
, 1998, “
Computational Method for Diagnosis of Variation-Related Assembly Problems
,”
Int. J. Prod. Res.
0020-7543,
36
, pp.
2985
2995
.
11.
Carlson
,
J. S.
, and
Soderberg
,
R.
, 2003, “
Assembly Root Cause Analysis: A Way to Reduce Dimensional Variation in Assembled Products
,”
Int. J. Flex. Manuf. Syst.
,
15
(
2
), pp.
113
150
. 0920-6299
12.
Ding
,
Y.
,
Ceglarek
,
D.
, and
Shi
,
J.
, 2002, “
Fault Diagnosis of Multistage Manufacturing Processes by Using State Space Approach
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
124
(
2
), pp.
313
322
.
13.
Kong
,
Z.
,
Ceglarek
,
D.
, and
Huang
,
W.
, 2008, “
Multiple Fault Diagnosis Method in Multi-Station Assembly Processes Using State Space Model and Orthogonal Diagonalization Analysis
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
130
(
1
), p.
011014
.
14.
Huang
,
W.
,
Lin
,
J.
,
Kong
,
Z.
, and
Ceglarek
,
D.
, 2007, “
Stream-of-Variation Modeling II: A Generic 3D Variation Model for Rigid Body Assembly in Multi Station Assembly Processes
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
129
(
4
), pp.
832
842
.
15.
Huang
,
W.
,
Lin
,
J.
,
Bezdecny
,
M.
,
Kong
,
Z.
, and
Ceglarek
,
D.
, 2007, “
Stream-of-Variation Modeling I: A Generic 3D Variation Model for Rigid Body Assembly in Single Station Assembly Processes
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
129
(
4
), pp.
821
831
.
16.
Bjorke
,
O.
, 1989,
Computer Aided Tolerancing
, 2nd ed.,
ASME
,
New York
, pp.
27
28
.
17.
Chase
,
K. W.
, and
Parkinson
,
A. R.
, 1991, “
A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies
,”
Res. Eng. Des.
0934-9839,
3
, pp.
23
37
.
18.
Roy
,
U.
,
Liu
,
C. R.
, and
Woo
,
T. C.
, 1991, “
Review of Dimensioning and Tolerancing: Representation and Processing
,”
Comput.-Aided Des.
0010-4485,
23
, pp.
466
483
.
19.
Jeang
,
A.
, 1994, “
Tolerancing Design: Choosing Optimal Tolerance Specifications in the Design of Machined Parts
,”
Qual. Reliab. Eng. Int
0748-8017,
10
, pp.
27
35
.
20.
1997,
Advanced Tolerancing Techniques
,
G.
Zhang
, ed.,
Wiley
,
New York
.
21.
Ngoi
,
B. K. A.
, and
Ong
,
C. T.
, 1998, “
Product and Process Dimensioning and Tolerancing Techniques: A State-of-the-Art Review
,”
Int. J. Adv. Manuf. Technol.
0268-3768,
14
, pp.
910
917
.
22.
Voelcker
,
H. B.
, 1998, “
The Current State of Affairs in Dimensional Tolerancing
,”
Integr. Manuf. Syst.
0957-6061,
9
, pp.
205
217
.
23.
Jin
,
J.
, and
Shi
,
J.
, 1999, “
State Space Modeling of Sheet Metal Assembly for Dimensional Control
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
121
(
4
), pp.
756
762
.
24.
DCS
, 2002,
3DCS-Analyst 6.2.2 User Manual
,
Dimensional Control Systems, Inc.
,
MI
.
25.
Djurdjanovic
,
D.
, and
Ni
,
J.
, 2002, “
Linear State Space Modeling of Dimensional Machining Errors
,”
Trans. NAMRI/SME
1047-3025,
24
, pp.
541
548
.
26.
Zhou
,
S.
,
Huang
,
Q.
, and
Shi
,
J.
, 2003, “
State Space Modeling of Dimensional Variation Propagation in Multistage Machining Process Using Differential Motion Vector
,”
IEEE Trans. Rob. Autom.
1042-296X,
19
(
2
), pp.
296
309
.
27.
Huang
,
Q.
, and
Shi
,
J.
, 2004, “
Variation Transmission Analysis and Diagnosis of Multi-Operational Machining Processes
,”
IIE Trans., Qual. Reliab. Eng.
1545-8830,
36
, pp.
807
815
.
28.
Kong
,
Z.
, and
Ceglarek
,
D.
, 2006, “
Stream of Variation Analysis for Multiple Station Assembly With Various Tolerance Modes
,”
Trans. NAMRI/SME
1047-3025,
34
, pp.
469
476
.
29.
Jin
,
J.
, and
Chen
,
Y.
, 2001, “
Quality and Reliability Information Integration for Design Evaluation of Fixture System Reliability
,”
Qual. Reliab. Eng. Int
0748-8017,
17
, pp.
355
372
.
30.
Ding
,
Y.
,
Jin
,
J.
,
Ceglarek
,
D.
, and
Shi
,
J.
, 2005, “
Process-Oriented Tolerancing for Multi-Station Assembly Systems
,”
IIE Trans., Qual. Reliab. Eng.
1545-8830,
37
(
6
), pp.
493
508
.
31.
ASME Y14.5M–1994b
,
Dimensioning and Tolerancing
,
ASME
,
New York
, pp.
81
82
.
32.
Drake
,
P. J.
, 1999,
Dimensioning and Tolerancing Handbook
,
McGraw-Hill
,
New York
.
34.
Evans
,
M.
,
Hastings
,
N.
, and
Peacock
,
B.
, 1993,
Statistical Distributions
,
Wiley
,
New York
, pp.
141
142
.
35.
DeGroot
,
M. H.
, and
Schervish
,
M. J.
, 2002,
Probability and Statistics
, 3rd ed.,
Addison-Wesley
,
New York
, pp.
223
224
.
You do not currently have access to this content.