{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T06:34:05Z","timestamp":1772001245980,"version":"3.50.1"},"reference-count":51,"publisher":"ASME International","issue":"2","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2016,6,1]]},"abstract":"<jats:p>Tolerance analysis is increasingly becoming an important tool for mechanical design, process planning, manufacturing, and inspection. It provides a quantitative analysis tool for evaluating the effects of manufacturing variations on performance and overall cost of the final assembly. It boosts concurrent engineering by bringing engineering design requirements and manufacturing capabilities together in a common model. It can be either worst-case or statistical. It may involve linear or nonlinear behavior. Monte Carlo simulation is the simplest and the most popular method for nonlinear statistical tolerance analysis. Monte Carlo simulation offers a powerful analytical method for predicting the effects of manufacturing variations on design performance and production cost. However, the main drawbacks of this method are that it is necessary to generate very large samples to assure calculation accuracy, and that the results of analysis contain errors of probability. In this paper, a quasi-Monte Carlo method based on good point (GP) set is proposed. The difference between the method proposed and Monte Carlo simulation lies in that the quasi-random numbers generated by Monte Carlo simulation method are replaced by ones generated by the method proposed in this paper. Compared with Monte Carlo simulation method, the proposed method provides analysis results with less calculation amount and higher precision.<\/jats:p>","DOI":"10.1115\/1.4032909","type":"journal-article","created":{"date-parts":[[2016,3,7]],"date-time":"2016-03-07T17:30:58Z","timestamp":1457371858000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":11,"title":["Application of Quasi-Monte Carlo Method Based on Good Point Set in Tolerance Analysis"],"prefix":"10.1115","volume":"16","author":[{"given":"Yanlong","family":"Cao","sequence":"first","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, College of Mechanical Engineering, Zhejiang University, Zheda Road 38, Hangzhou 310027, China;"},{"name":"Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, College of Mechanical Engineering, Zhejiang University, Zheda Road 38, Hangzhou 310027, China e-mail:"}]},{"given":"Huiwen","family":"Yan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, College of Mechanical Engineering, Zhejiang University, Zheda Road 38, Hangzhou 310027, China e-mail:"}]},{"given":"Ting","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, College of Mechanical Engineering, Zhejiang University, Zheda Road 38, Hangzhou 310027, China e-mail:"}]},{"given":"Jiangxin","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, College of Mechanical Engineering, Zhejiang University, Zheda Road 38, Hangzhou 310027, China e-mail:"}]}],"member":"33","published-online":{"date-parts":[[2016,5,10]]},"reference":[{"key":"2019100602261623500_bib1","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/978-1-84996-311-4_2","article-title":"Geometric Tolerance Analysis","volume-title":"Geometric Tolerances","year":"2011"},{"issue":"1","key":"2019100602261623500_bib2","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/BF01580066","article-title":"A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies","volume":"3","year":"1991","journal-title":"Res. Eng. Des."},{"issue":"7","key":"2019100602261623500_bib3","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1016\/0010-4485(91)90045-X","article-title":"Review of Dimensioning and Tolerancing: Representation and Processing","volume":"23","year":"1991","journal-title":"Comput. Aided Des."},{"issue":"9","key":"2019100602261623500_bib4","doi-asserted-by":"publisher","first-page":"2111","DOI":"10.1080\/00207549208948140","article-title":"Tolerancing Techniques: The State-of-the-Art","volume":"30","year":"1992","journal-title":"Int. J. Prod. Res."},{"issue":"1","key":"2019100602261623500_bib5","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1016\/0010-4485(95)90748-5","article-title":"Review of Statistical Approaches to Tolerance Analysis","volume":"27","year":"1995","journal-title":"Comput. Aided Des."},{"issue":"11","key":"2019100602261623500_bib6","doi-asserted-by":"publisher","first-page":"2425","DOI":"10.1080\/00207540210128242","article-title":"A Comprehensive Review of Tolerancing Research","volume":"40","year":"2002","journal-title":"Int. J. Prod. Res."},{"issue":"11\u201312","key":"2019100602261623500_bib7","doi-asserted-by":"publisher","first-page":"1106","DOI":"10.1007\/s00170-008-1790-0","article-title":"A Review of Two Models for Tolerance Analysis of an Assembly: Vector Loop and Matrix","volume":"43","year":"2009","journal-title":"Int. J. Adv. Manuf. Technol."},{"issue":"1","key":"2019100602261623500_bib8","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1080\/0951192X.2010.531286","article-title":"A Review of Two Models for Tolerance Analysis of an Assembly: Jacobian and Torsor","volume":"24","year":"2011","journal-title":"Int. J. Comput. Integr. Manuf."},{"issue":"7","key":"2019100602261623500_bib9","doi-asserted-by":"publisher","first-page":"2014","DOI":"10.1080\/00207543.2011.576275","article-title":"Taxonomy of Models for Tolerance Analysis in Assembling","volume":"50","year":"2012","journal-title":"Int. J. Prod. Res."},{"issue":"2","key":"2019100602261623500_bib10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cad.2014.02.014","article-title":"A Comprehensive Study of Three Dimensional Tolerance Analysis Methods","volume":"53","year":"2014","journal-title":"Comput. Aided Des."},{"issue":"3","key":"2019100602261623500_bib11","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1109\/38.210493","article-title":"Variational Solid Modeling for Tolerance Analysis","volume":"13","year":"1993","journal-title":"IEEE Comput. Graphics Appl."},{"issue":"4","key":"2019100602261623500_bib12","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1023\/A:1007694506696","article-title":"Relative Positioning of Toleranced Polyhedral Parts in an Assembly","volume":"33","year":"2001","journal-title":"IIE Trans."},{"key":"2019100602261623500_bib13","first-page":"263","article-title":"General 2-D Tolerance Analysis of Mechanical Assemblies With Small Kinematic Adjustments","volume":"5","year":"1995","journal-title":"J. Des. Manuf."},{"issue":"4","key":"2019100602261623500_bib14","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF01608399","article-title":"Representation of Geometric Variations Using Matrix Transforms for Statistical Tolerance Analysis in Assemblies","volume":"6","year":"1994","journal-title":"Res. Eng. Des. Theory Appl. Concurrent Eng."},{"issue":"4","key":"2019100602261623500_bib15","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1115\/1.1497362","article-title":"A New Mathematical Model for Geometric Tolerances as Applied to Round Faces","volume":"124","year":"2002","journal-title":"ASME J. Mech. Des."},{"key":"2019100602261623500_bib16","doi-asserted-by":"publisher","DOI":"10.1115\/DETC2013-12394","article-title":"Tolerance Analysis of Parallel Assemblies Using Tolerance-Maps\u00ae and a Functional Map Derived From Induced Deformations","volume-title":"ASME","year":"2013"},{"issue":"1\u20134","key":"2019100602261623500_bib17","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/s00170-014-5792-9","article-title":"Using Tolerance Maps to Validate Machining Tolerances for Transfer of Cylindrical Datum in Manufacturing Process","volume":"73","year":"2014","journal-title":"Int. J. Adv. Manuf. Technol."},{"issue":"6","key":"2019100602261623500_bib18","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1007\/BF01748479","article-title":"A Dimensioning and Tolerancing Assistance Model for CAD\/CAM Systems","volume":"9","year":"1994","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"2019100602261623500_bib19","unstructured":"Cl\u00e9ment, A., Desrochers, A., and Riviere, A., 1991, \u201cTheory and Practice of 3-D Tolerancing for Assembly,\u201d CIRP International Working Seminar on Computer-Aided Tolerancing, Penn State University, State College, PA, May 16\u201317, pp. 25\u201355."},{"key":"2019100602261623500_bib20","unstructured":"Cl\u00e9ment, A., and Riviere, A., eds., 1993, \u201cTolerancing Versus Nominal Modeling in Next Generation CAD\/CAM System,\u201d 3rd CIRP Seminar on Computer Aided Tolerancing-Tol\u00e9rancement G\u00e9om\u00e9trique, Ecole Normale Sup\u00e9rieure de Cachan, Paris."},{"issue":"1","key":"2019100602261623500_bib21","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1115\/1.1573235","article-title":"Application of a Unified Jacobian\u2014Torsor Model for Tolerance Analysis","volume":"3","year":"2003","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"key":"2019100602261623500_bib22","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/1-4020-5438-6_11","article-title":"Re-Design of Mechanical Assemblies Using the Unified Jacobian\u2013Torsor Model for Tolerance Analysis","volume-title":"Models for Computer Aided Tolerancing in Design and Manufacturing","year":"2007"},{"issue":"15","key":"2019100602261623500_bib23","doi-asserted-by":"publisher","first-page":"4609","DOI":"10.1080\/00207540902824982","article-title":"Statistical Tolerance Analysis Using the Unified Jacobian\u2013Torsor Model","volume":"48","year":"2010","journal-title":"Int. J. Prod. Res."},{"issue":"13","key":"2019100602261623500_bib24","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1016\/S0010-4485(99)00055-X","article-title":"A Computer Aided Tolerancing Model: Proportioned Assembly Clearance Volume","volume":"31","year":"1999","journal-title":"Comput. Aided Des."},{"key":"2019100602261623500_bib25","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/1-4020-5438-6_10","article-title":"Tolerance Analysis and Synthesis by Means of Deviation Domains, Axi-Symmetric Cases","volume-title":"Models for Computer Aided Tolerancing in Design and Manufacturing","year":"2007"},{"issue":"3","key":"2019100602261623500_bib26","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1016\/S0278-6125(02)80163-7","article-title":"Assembly Specification by Gauge With Internal Mobilities (GIM)\u2014A Specification Semantics Deduced From Tolerance Synthesis","volume":"21","year":"2002","journal-title":"J. Manuf. Syst."},{"issue":"2","key":"2019100602261623500_bib27","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/j.cad.2004.06.008","article-title":"Tolerance Synthesis: Quantifier Notion and Virtual Boundary","volume":"37","year":"2005","journal-title":"Comput. Aided Des."},{"key":"2019100602261623500_bib28","volume-title":"An Application of Statistics to the Dimensioning of Machine Parts","year":"1959"},{"key":"2019100602261623500_bib29","doi-asserted-by":"publisher","DOI":"10.4271\/680490","article-title":"Statistical Tolerancing as it Relates to Quality Control and the Designer (6 Times 2.5\u2009=\u20099)","volume-title":"SAE","year":"1968"},{"issue":"1","key":"2019100602261623500_bib30","first-page":"50","article-title":"Design Issues in Mechanical Tolerance Analysis","volume":"1","year":"1988","journal-title":"Manuf. Rev."},{"key":"2019100602261623500_bib31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00224065.1975.11980657","article-title":"Statistical Tolerancing: The State of the Art\u2014II: Methods for Estimating Moments","volume":"7","year":"1975","journal-title":"J. Qual. Technol."},{"issue":"2","key":"2019100602261623500_bib32","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1080\/00401706.1971.10488786","article-title":"An Application of Numerical Integration Techniques to Statistical Tolerancing\u2014II: A Note on the Error","volume":"13","year":"1971","journal-title":"Technometrics"},{"issue":"1","key":"2019100602261623500_bib33","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1080\/00401706.1972.10488880","article-title":"An Application of Numerical Integration Techniques to Statistical Tolerancing\u2014III: General Distributions","volume":"14","year":"1972","journal-title":"Technometrics"},{"issue":"3","key":"2019100602261623500_bib34","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1115\/1.3256395","article-title":"The Application of Reliability Methods to Tolerancing","volume":"104","year":"1982","journal-title":"ASME J. Mech. Des."},{"issue":"2","key":"2019100602261623500_bib35","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1115\/1.2899553","article-title":"Tolerances: Their Analysis and Synthesis","volume":"112","year":"1990","journal-title":"J. Eng. Ind."},{"issue":"6","key":"2019100602261623500_bib36","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1080\/00207547808930043","article-title":"Performance Analysis Design","volume":"16","year":"1978","journal-title":"Int. J. Prod. Res."},{"issue":"4","key":"2019100602261623500_bib37","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1080\/00401706.1988.10488434","article-title":"Statistical Tolerancing Using a Modification of Taguchi's Method","volume":"30","year":"1988","journal-title":"Technometrics"},{"key":"2019100602261623500_bib38","doi-asserted-by":"publisher","DOI":"10.4271\/870263","article-title":"Assembly Tolerance Analysis With Simulation and Optimization Techniques","volume-title":"SAE","year":"1987"},{"issue":"1","key":"2019100602261623500_bib39","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/S0924-0136(97)00034-4","article-title":"Study of an Assembly Tolerance Allocation Model Based on Monte Carlo Simulation","volume":"70","year":"1997","journal-title":"J. Mater. Process. Technol."},{"issue":"10","key":"2019100602261623500_bib40","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1016\/j.mechmachtheory.2006.11.003","article-title":"Statistical Tolerance Analysis of Bevel Gear by Tooth Contact Analysis and Monte Carlo Simulation","volume":"42","year":"2007","journal-title":"Mech. Mach. Theory"},{"issue":"1","key":"2019100602261623500_bib41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cad.2008.11.003","article-title":"Worst-Case and Statistical Tolerance Analysis Based on Quantified Constraint Satisfaction Problems and Monte Carlo Simulation","volume":"41","year":"2009","journal-title":"Comput. Aided Des."},{"issue":"4","key":"2019100602261623500_bib42","doi-asserted-by":"publisher","first-page":"1402","DOI":"10.1016\/j.cie.2008.09.005","article-title":"Improved Algorithm for Tolerance Allocation Based on Monte Carlo Simulation and Discrete Optimization","volume":"56","year":"2009","journal-title":"Comput. Ind. Eng."},{"issue":"2","key":"2019100602261623500_bib43","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.cad.2011.10.004","article-title":"A Statistical Tolerance Analysis Approach for Over-Constrained Mechanism Based on Optimization and Monte Carlo Simulation","volume":"44","year":"2012","journal-title":"Comput. Aided Des."},{"issue":"10","key":"2019100602261623500_bib44","first-page":"795","article-title":"Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies","volume":"28","year":"1996","journal-title":"IIE Trans."},{"issue":"4","key":"2019100602261623500_bib45","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1023\/A:1007451225222","article-title":"Generalized 3-D Tolerance Analysis of Mechanical Assemblies With Small Kinematic Adjustments","volume":"30","year":"1998","journal-title":"IIE Trans."},{"key":"2019100602261623500_bib46","article-title":"Tolerance Analysis of 2-D and 3-D Assemblies With Small Kinematic Adjustments","year":"1999"},{"key":"2019100602261623500_bib47","article-title":"Monte Carlo Simulation of Tolerancing in Discrete Parts Manufacturing and Assembly","volume-title":"Report No. STAN-CS-76-555","year":"1976"},{"key":"2019100602261623500_bib48","volume-title":"Application of Number Theory to Numerical Analysis","year":"1981"},{"key":"2019100602261623500_bib49","first-page":"36","article-title":"An Estimate Concerning the Kolmogroff Limit Distribution","volume":"67","year":"1949","journal-title":"Trans. Am. Math. Soc."},{"issue":"1","key":"2019100602261623500_bib50","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/BF01386213","article-title":"On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals","volume":"2","year":"1960","journal-title":"Numerische Math."},{"issue":"2","key":"2019100602261623500_bib51","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1108\/AA-05-2013-050","article-title":"A Static Analogy for 2D Tolerance Analysis","volume":"34","year":"2014","journal-title":"Assem. Autom."}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4032909\/6100818\/jcise_016_02_021008.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4032909\/6100818\/jcise_016_02_021008.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,6]],"date-time":"2019-10-06T06:26:26Z","timestamp":1570343186000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/doi\/10.1115\/1.4032909\/474267\/Application-of-QuasiMonte-Carlo-Method-Based-on"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,10]]},"references-count":51,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,6,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4032909","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,10]]},"article-number":"021008"}}