This paper proposes a new method to estimate the process capability for a profile geometric tolerance as defined by the ASME Y14.5 standard. The novelty of the method is that it uses the known process capability of a given geometry to predict, using the order statistics theorem, new capabilities for different geometries of higher or lower complexity. By considering the geometrical complexity of mechanical parts, a manufacturing process may be capable (e.g., Cpk > 1.5) for parts with simple geometry and incapable (e.g., Cpk < 1) for parts with complex geometry. In the proposed model, the process capability becomes a mathematical function of both the statistical behavior of the process (e.g., expectation and variance) and the geometric complexity of manufactured surfaces. Three experimental case studies are presented to illustrate the usefulness and the validity of the developed model.
Issue Section:
Research Papers
References
1.
Pullan
, T. T.
, Bhasi
, M.
, and Madhu
, G.
, 2010
, “Application of Concurrent Engineering in Manufacturing Industry
,” Int. J. Comput. Integr. Manuf.
, 23
(5
), pp. 425
–440
.2.
Choi
, W.
, and Chung
, H.
, 2015
, “Variation Simulation of Compliant Metal Plate Assemblies Considering Welding Distortion
,” ASME J. Manuf. Sci. Eng.
, 137
(3
), p. 031008
.3.
American Society of Mechanical Engineers
, 2009
, Dimensioning and Tolerancing
, American Society of Mechanical Engineers
, New York, p. 207
.4.
Montgomery
, D. C.
, 2007
, Introduction to Statistical Quality Control
, 4th ed., Wiley India Pvt. Limited
, Delhi.5.
ISO
, 2007
, Statistical Methods in Process Management Capability and Performance. Part 4: Process Capability Estimates and Performance Measures, International Standard Organisation
, London, p. 58
.6.
Wu
, C.-W.
, Pearn
, W. L.
, and Kotz
, S.
, 2009
, “An Overview of Theory and Practice on Process Capability Indices for Quality Assurance
,” Int. J. Prod. Econ.
, 117
(2
), pp. 338
–359
.7.
Huang
, Q.
, Nouri
, H.
, Xu
, K.
, Chen
, Y.
, Sosina
, S.
, and Dasgupta
, T.
, 2014
, “Statistical Predictive Modeling and Compensation of Geometric Deviations of Three-Dimensional Printed Products
,” ASME J. Manuf. Sci. Eng.
, 136
(6
), p. 061008
.8.
Mannar
, K.
, and Ceglarek
, D.
, 2009
, “Functional Capability Space and Optimum Process Adjustments for Manufacturing Processes With In-Specs Failure
,” IIE Trans.
, 42
(2
), pp. 95
–106
.9.
American National Standards Institute and American Society of Mechanical Engineers
, 1955
, Preferred Limits and Fits for Cylindrical Parts: ANSI ASA B4.1-1955
, UDC 621.753.1/.3, American Society of Mechanical Engineers
, New York.10.
Swift
, K. G.
, and Booker
, J. D.
, 1996
, “Engineering for Conformance
,” TQM Mag.
, 8
(3
), pp. 54
–60
.11.
Korosec
, M.
, Balic
, J.
, and Kopac
, J.
, 2005
, “Neural Network Based Manufacturability Evaluation of Free Form Machining
,” Int. J. Mach. Tools Manuf.
, 45
(1
), pp. 13
–20
.12.
Delaney
, K. D.
, and Phelan
, P.
, 2009
, “Design Improvement Using Process Capability Data
,” J. Mater. Process. Technol.
, 209
(1
), pp. 619
–624
.13.
Whitney
, D. E.
, 2004
, Mechanical Assemblies: Their Design, Manufacture, and Role in Product Development
, Oxford University Press
, New York.14.
Barari
, A.
, ElMaraghy
, H. A.
, and ElMaraghy
, W. H.
, 2009
, “Design for Manufacturing of Sculptured Surfaces: A Computational Platform
,” ASME J. Comput. Inf. Sci. Eng.
, 9
(2
), p. 021006
.15.
Ji
, S.
, Li
, X.
, Ma
, Y.
, and Cai
, H.
, 2000
, “Optimal Tolerance Allocation Based on Fuzzy Comprehensive Evaluation and Genetic Algorithm
,” Int. J. Adv. Manuf. Technol.
, 16
(7
), pp. 461
–468
.16.
Kerbrat
, O.
, Mognol
, P.
, and Hascoet
, J. Y.
, 2010
, “Manufacturing Complexity Evaluation at the Design Stage for Both Machining and Layered Manufacturing
,” CIRP J. Manuf. Sci. Technol.
, 2
(3
), pp. 208
–215
.17.
Tahan
, S. A.
, and Levesque
, S.
, 2009
, “Exploiting the Process Capability of Profile Tolerance According GDTASME-Y14.5M
,” International Conference on Computers and Industrial Engineering
(CIE
), Troyes, France
, July 6–9, IEEE Computer Society
, pp. 1285
–1290
.18.
Tahan
, A. S.
, and Cauvier
, J.
, 2012
, “Capability Estimation of Geometrical Tolerance With a Material Modifier by a Hasofer-Lind Index
,” ASME J. Manuf. Sci. Eng.
, 134
(2
), p. 021007
.19.
Papoulis
, A.
, and Pillai
, S. U.
, 2002
, Probability, Random Variables, and Stochastic Processes
, McGraw-Hill
, New York, p. 852
.20.
Bourdet
, P.
, and Mathieu
, L.
, 1998
, Tolérancement et métrologie dimensionnelle: Qualité des Produits dans les Entreprises
, Cetim
, Senlis (Oise).21.
Barari
, A.
, ElMaraghy
, H.
, and Knopf
, G.
, 2007
, “Evaluation of Geometric Deviations in Sculptured Surfaces Using Probability Density Estimation
,” Models for Computer Aided Tolerancing in Design and Manufacturing
, J. K.
Davidson
, ed., Springer
, Netherlands
, pp. 135
–146
.22.
Montgomery
, D. C.
, and Runger
, G. C.
, 2010
, Applied Statistics and Probability for Engineers
, Wiley
, New York.23.
Kotz
, S.
, and Lovelace
, C. R.
, 1998
, Process Capability Indices in Theory and Practice
, Arnold, London.24.
Guid
, N.
, Oblonsek
, C.
, and Zalik
, B.
, 1995
, “Surface Interrogation Methods
,” Comput. Graph.
, 19
(4
), pp. 557
–574
.25.
Joshi
, P.
, and Sequin
, C.
, 2007
, “Energy Minimizers for Curvature-Based Surface Functionals
,” Comput. Aided Des. Appl.
, 4
(1–6
), pp. 607
–617
.26.
Olsson
, C.
, and Boykov
, Y.
, 2012
, “Curvature-Based Regularization for Surface Approximation
,” IEEE Conference on Computer Vision and Pattern Recognition
(CVPR
), June 16–21, Los Alamitos, CA
, pp. 1576
–1583
.27.
Joshi
, P. P.
, 2008
, “Minimizing Curvature Variation for Aesthetic Surface Design,” Ph.D. dissertation
University of California
, Berkeley, CA
, p. 107
.28.
David
, H. A.
, and Nagaraja
, H. N.
, 2003
, Order Statistics
, 3rd ed., Wiley
, Hoboken, NJ
, p. 458
.29.
Durrans
, S. R.
, 1992
, “Distributions of Fractional Order Statistics in Hydrology
,” Water Resour. Res.
, 28
(6
), pp. 1649
–1655
.30.
Stigler
, S.
, 1977
, “Fractional Order Statistics, With Applications
,” J. Am. Stat. Assoc.
, 72
(359
), pp. 544
–550
.31.
Hutson
, A. D.
, 1999
, “Calculating Nonparametric Confidence Intervals for Quantiles Using Fractional Order Statistics
,” J. Appl. Stat.
, 26
(3
), pp. 343
–353
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