Contributed Session: Robust Design

Session Chair: Walter Liggett, NIST

SN Ratios & Other Measures: A Comparison

Julie Berube
Dept. of Statistics, Univ. of Michigan

Taguchi's parameter design, a quality improvement technique aimed at making products and processes insensitive to uncontrollable variations has received much attention in industry. The performance measure advocated by Taguchi, the SN ratio, while used in some industrial sectors, has been controversial. We look at the performance of SN ratios and other measures and methods for analysing parameter designs under a number of different models for the response. Systems with static and dynamic characteristics are considered. We show that for a few models, the SN ratio analysis can lead to factor levels that minimize the variation. For a large selection of models, though, use of the SN ratio can not only result in sub-optimal levels being selected, but can lead to a misclassification of the factors which makes it difficult to solve the parameter design. Is there a generally best alternative?

[Julie Berube, Dept. of Statistics, Univ. of Michigan, 1440 Mason Hall, Ann Arbor, MI 48109 USA; jber@umich.edu ]

Selection & Screening Procedures for Robust Product Design

Guohua Pan
Dept. of Mathematical Sciences, Oakland Univ.

Thomas J. Santner
Dept. of Statistics, Ohio State Univ.

This study considers statistical selection and screening procedures to identify product designs or processes that are robust with respect to variability in external noise factors. The objective of the selection procedures is to select the optimal design product with a prespecified confidence level by choosing the appropriate number of replications at the design stage. The objective of the screening procedures is to construct a random subset of all the product designs such that it contains the optimal product design and screens out inferior ones. In this study we focus on split-plot experiments and situations where a larger (smaller) response is considered to be better. Two measures of performances are considered: weighted average and minimum of the response of a product design over the levels of the noise factor. Examples are provided to illustrate the proposed procedures.

[Guohua Pan, Dept. of Mathematical Sciences, Oakland Univ., Rochester, MI 48309 USA; pan@vela.acs.oakland.edu ]

Mixture Experiments in the Presence of Noise Factors & Measurement Error

Stefan H. Steiner
Dept. of Statistics, Univ. of Waterloo

Mixture experiments involve the mixing or blending of two or more ingredients to form an end product. Typically, the quality of the end product is a function of the relative proportions of the ingredients and other extraneous process or noise factors such as heat or time. Noise variables are process variables that are either uncontrollable or difficult to control. In the presence of noise factors and/or measurement error the objective of our experiment becomes finding the mixture amounts and process settings that lead to a product of high quality that is also robust to the measurement error and noise. Due to the nature of mixture experiments this leads to a constrained optimization problem. This talk will discuss setting up an appropriate objective function and provides techniques for determining the robust mixture proportions in the presence of noise variables and mixture variable measurement error.

[Stefan Steiner, Dept. of Statistics, Univ. of Waterloo, Waterloo, Ontario, CANADA; shsteine@setosa.uwaterloo.ca ]

Multivariate Robust Designs: A Response Surface Approach

Suat Tanaydin
Dept. of Statistics, Purdue Univ.

In robust design problems the purpose is to estimate optimum (or best) control settings. This is usually accomplished by minimizing univariate performance measure, expected loss function. Analyzing multivariate problems in a univariate manner has been done for a very long time because of lack of computing power, data collecting techniques, and lack of available techniques. In recent years growing comfort in computing made the usage of multivariate modeling a necessity of statistical analysis. Technical people started recognizing quality as a multivariate property. In this paper, when the noise is from a multivariate normal distribution, these optimum settings are obtained explicitly for models which contain linear and quadratic control factors in each dimension of multivariate response surface. In addition to adjustable variables ( bias), variance adjustable variables are introduced and a method for identifying these variables are given as well. Finally a case study is given at the end with comparisons to univariate case.