Rasch Fit Criteria Mirror Industrial Tolerances

"The designer's considerations in establishing any specification limits [for industrial tolerances or quality-control fit statistics] may be classified into three groups, namely, (1) those related to the service needs of the article or part for which specifications are being written, (2) those related to the capabilities of the production process to produce to any given specification limits, and (3) those related to the means to be used for determining whether the specifications are actually met by the product.

"The fundamental basis of all specification limits is, of course, the service need of the part or article. This is not primarily a statistical matter. However, it often happens that the service need can be judged more accurately with the aid of statistical methods. The viewpoint that every quality characteristic is a frequency distribution is always helpful. This is particularly true in matters involving the interrelationships of specification limits.

"There is no use specifying desired tolerances [fit levels] on any quality characteristic without some prospect that these tolerances can be met. Whenever production methods will not meet the proposed tolerances, this fact needs to be known and considered before such tolerances are adopted. The inability of any process to meet its quality specifications is sure to be responsible for extra costs. These may be costs of spoilage and rework, or of changing to another more expensive production process, or - in the case of dimensional tolerances - costs incident to giving up the idea of interchangeable manufacture [or generalizability of measures] and adopting selective fitting of parts [measures only useable in a specific context]. If such costs are to be undertaken, this should be done deliberately after weighing the facts rather than unconsciously because the capabilities of a production process are unknown. One of the major contributions of statistical quality control to design can be in the information the control chart [fit plot] gives about the capacity of a production process to meet any given tolerances.

"The third matter which was stated as relevant in setting specification limits is the means to be used for determining whether the specification limits are actually met. Both Shewhart and Simon have emphasized in their writings the distinction between a design specification, i.e., what is desired, and an acceptance specification, the means of judging whether

Figure. Typical industrial quality-control chart, showing drift towards Upper Control Line.

what is desired is actually obtained. The relevance of the acceptance specification in determining the design specification is not always understood. Both design engineers and inspection executives sometimes say, `It is the designer's [test constructors] job to specify what is needed; it is the inspector's [analyst's] job to devise [statistical] tests and acceptance procedures to find out whether the designer's specifications have been met; let each stick to his own job.' This fails to take into account the fact that, although the designer [test constructor] may not devise [statistical] tests and acceptance procedures, he should not be indifferent to the tests and acceptance procedures that are to be applied. These constitute useful information for the designer for the same reason that he should know something about the capabilities of the production process; both influence the likelihood of obtaining what is specified."

Excerpted from Eugene L. Grant (1952) Statistical Quality Control. 2nd. Edn. New York: McGraw-Hill.

Shewhart W.A. (1931) Economic Control of Quality of Manufactured Product. New York: D. Van Nostrand Co.

Shewhart W.A. (1939) Statistical Method from the Viewpoint of Quality Control. W.E. Deming, Editor. Washington DC: Department of Agriculture.

Simon L.E. (1941) An Engineers' Manual of Statistical Methods. New York: John Wiley & Sons, Inc.

Rasch Fit and Industrial Tolerances Linacre J … Rasch Measurement Transactions, 1999, 12:4 p.

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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