Signal-to-Noise Ratios, Performance Criteria, and Transformations

George E. P. Box

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Optimal Experimental Design Methods Statistical Methods and Applications Advanced Statistical Process Monitoring

Abstract

For the analysis of designed experiments, Taguchi uses performance criteria that he calls signal-to-noise (SN) ratios. Three such criteria are here denoted by SN T , SN L , and SN S . The criterion SN T was to be used in preference to the standard deviation for the problem of achieving, for some quality characteristic y, the smallest mean squared error about an operating target value. León, Shoemaker, and Kacker (1987) showed how SN T was appropriate to solve this problem only when σ y was proportional to μ y . On that assumption, the same result could be obtained more simply by conducting the analysis in terms of log y rather than y. A more general transformation approach is here introduced for other, commonly met kinds of dependence between σ y and μ y (including no dependence), and a lambda plot is presented that uses the data to suggest an appropriate transformation. The criteria SN L and SN S were for problems in which the objective was to make the response as large or as small as possible. It is argued here that these predecided “portmanteau” criteria can provide an inadequate summary of data and that, regarded as measures of location, they can be extremely inefficient. In preference to such performance criteria, the merits of simple methods of data analysis that can uncover information both expected and unexpected are urged. A reanalysis of an interesting experiment due to Quinlan (1985) illustrates the value of this approach and its contribution to the art of discovery. It is argued that improvement of quality will best be catalyzed by engineers using elementary data analysis with computer graphics rather than by those trained only to employ more rigid predecided criteria.

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References

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1996A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors 1998Efficient estimation of conditional variance functions in stochastic regression 1993STRATEGIES FOR ROBUST MULTIRESPONSE QUALITY ENGINEERING 1992AN OVERVIEW OF TAGUCHI METHOD AND NEWLY DEVELOPED STATISTICAL METHODS FOR ROBUST DESIGN 1992Response Surface Alternatives to the Taguchi Robust Parameter Design Approach 1988An explanation and critique of taguchi's contributions to quality engineering

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