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Contributed Session: One-Way Models in Engineering Applications
One-Way Analysis Strategies for Cylindrical Data
Christine M. Anderson-Cook
Cylindrical data are bivariate responses where one component is a circular measure (located on a unit circle) and the other is a linear or scalar quantity. Examples occurring in industry include direction and magnitude of rotating parts as well as location and severity of defects on round components. This talk will review one of the existing modelling strategies for the relationship between responses, which assumes a single sine curve can adequately describe the conditional distribution of the linear variable given the circular one. Several approaches to extending this model to the one-way case are presented. Two methods for obtaining an adequate model to described the observed behaviour between groups with an efficient number of parameters are illustrated with an automotive example. [Christine M. Anderson-Cook, Dept. of Statistics & Actuarial Sciences, Univ. of Western Ontario, London, Ontario, N6A 5B7 CANADA; cmanders@stats.uwo.ca ] Repeatability & Reproducibility for Pass/Fail Data
John Mandel A distribution-free method is presented for the estimation of repeatability and reproducibility standard deviations for pass/fail data. Because it is distribution-free, this method applies without restriction to binomial data, as well as to other distributions. It will be illustrated in terms of real sets of data. [John Mandel, Chemical Science & Technology Laboratory, NIST, Gaithersburg, MD, 20899-0001 USA; ] Analysis of a Series of Similar Experiments: Bayesian Approach, Variance Bounds & Asymptotic Study
Andrew L. Rukhin
Mark G. Vangel
In the analysis of data on a quantity measured by several laboratories, which includes non-negligible between-laboratory variability, as well as different within-laboratory variances, an estimator due to Mandel and Paule is commonly used. We obtain some bounds on the mean squared error of this estimator and of the maximum likelihood estimator. The Bayesian setting of the problem is investigated when within laboratories variances have a non-informative prior. Also we look at the situation with a large number of laboratories and study the asymptotic behavior of the class of statistics including the modified maximum likelihood procedure and the Paule-Mandel rule. In this situation the number of nuisance parameters increases, and we face a Neyman-Scott type of problem. It turns out that neither the maximum likelihood estimator nor the Mandel-Paule rule are asymptotically optimal. [Andrew L. Rukhin, Dept. of Mathematics & Statistics, UMBC, Baltimore, MD 21228 USA; rukhin@math.umbc.edu ] New Results for the Analysis of a Series of Similar Experiments
Mark G. Vangel
Andrew L. Rukhin This presentation introduces new results for the analysis of a series of experiments made on nominally the same quantity. The method introduced has broad applicability; an illustrative example of an analysis of interlaboratory study data is discussed. Following Cochran (1937, 1954, 1980) and others, this problem is formulated as a one-way unbalanced random-effects ANOVA with heteroscedastic within-group variances. A reparametrization of the likelihood leads to simplified computations, easy identification and interpretation of multimodality of the likelihood, and (via a non-informative prior Bayesian approach) approximate confidence intervals on the mean and between-group variances. The close relationship between maximum-likelihood and an estimator due to Mandel and Paule (Mandel and Paule 1970, Paule and Mandel 1982) is also demonstrated. [Mark G. Vangel, Statistical Engineering Div., NIST, Gaithersburg, MD, 20899-0001 USA; vangel@cam.nist.gov ]
Date created: 6/5/2001 |