In this paper, a new algorithm, based on a nonlinear optimization method (NOM), has been developed. The accuracy as well as the reliability/robustness of the new algorithm have been verified by applying it to more than 200 CMM measured data sets on differently manufactured parts. The results have been compared with that of Least Squares Method (LSM) and Convex Hull (CVH) method applied to the same data sets. A data filter is proposed to be enclosed in the new algorithm to detect and delete outliers in the data sets. [S1087-1357(00)01102-3]

1.
ASME, 1994, “Mathematical Definition of Dimensioning and Tolerancing,” ASME Y14.5.1M-1994.
2.
Fukuda, M., and Shimokohbe, A., 1984, “Algorithms for Form Evaluation, Methods of Minimum Zone and Least Squares,” Proceedings of the International Symposium on Metrology for Quality Control in Production, Tokyo, 197–202.
3.
Lai, K. W., and Wang, J., 1988, “A Computational Geometry Approach to Geometric Tolerancing,” The 16th NAMRI, 376–379.
4.
Mark
,
T. T.
,
Sanjay
,
J.
,
Richard
,
A. W.
, and
Tom
,
M. C.
,
1989
, “
Evaluation of Straightness and Flatness Tolerances Using the Minimum Zone
,”
Manuf. Rev.
,
2
, No.
3
, pp.
189
195
.
5.
Huang
,
S. T.
,
Fan
,
K. C.
, and
John
,
H. W.
,
1993
, “
A New Minimum Zone Method for Evaluating Straightness Errors
,”
Precis. Eng.
,
15
, No.
3
, pp.
158
165
.
6.
Shunmugam
,
M. S.
,
1986
, “
On Assessment of Geometric Errors
,”
Int. J. Prod. Res.
,
24
, No.
2
, pp.
413
425
.
7.
Wang
,
Y.
,
1992
, “
Minimum Zone Evaluation of Form Tolerances
,”
Manuf. Rev.
,
5
, No.
3
, pp.
213
220
.
8.
Shunmugam
,
M. S.
,
1986
, “
Establishing Reference Figures for Form Evaluation of Engineering Surfaces
,”
J. Manuf. Syst.
,
10
, No.
4
, pp.
314
321
.
9.
Kanada
,
T.
, and
Suzukit
,
S.
,
1993
, “
Evaluation of Minimum Zone Flatness by Means of Nonlinear Optimization Techniques and its Verification
,”
Precis. Eng.
,
15
, No.
2
, pp.
93
99
.
10.
Elmaraghy
,
W. H.
,
Elmaraghy
,
H. A.
, and
Wu
,
Z.
,
1990
, “
Determination of Actual Geometric Deviations Using Coordinate Measuring Machine Data
,”
Manuf. Rev.
,
3
, No.
1
, pp.
32
39
.
11.
Carr
,
K.
, and
Ferreira
,
P.
,
1995
, “
Verification of Form Tolerances, Part I: Basic Issues, Flatness, and Straightness
,”
Precis. Eng.
,
17
, No.
2
, pp.
131
143
.
12.
Carr
,
K.
, and
Ferreira
,
P.
,
1995
, “
Verification of Form Tolerances, Part II: Cylindricity and Straightness of a Median Line
,”
Precis. Eng.
,
17
, No.
2
, pp.
144
156
.
13.
ASME, 1982, “Dimensioning and Tolerancing,” ASME Y14.5M-1982.
14.
Grubbs
,
Frank E.
,
1969
, “
Procedures for Detecting Outlying Observations in Samples
,”
Technometrics
,
11
, No.
1
, pp.
1
21
.
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