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

 

作者: George Box,  

 

期刊: Technometrics  (Taylor Available online 1988)
卷期: Volume 30, issue 1  

页码: 1-17

 

ISSN:0040-1706

 

年代: 1988

 

DOI:10.1080/00401706.1988.10488313

 

出版商: Taylor & Francis Group

 

关键词: Optimization;Experimental design;Taguchi;Parameter design;Data analysis;Art of discovery

 

数据来源: Taylor

 

摘要:

For the analysis of designed experiments, Taguchi uses performance criteria that he callssignal-to-noise (SN) ratios. Three such criteria are here denoted by SNT, SNL, and SNS. The criterion SNTwas to be used in preference to the standard deviation for the problem of achieving, for some quality characteristicy, the smallest mean squared error about an operating target value. León, Shoemaker, and Kacker (1987) showed how SNTwas appropriate to solve this problem only when σywas proportional to μy. On that assumption, the same result could be obtained more simply by conducting the analysis in terms of logyrather thany. A more general transformation approach is here introduced for other, commonly met kinds of dependence between σyand μy(including no dependence), and alambda plotis presented that uses the data to suggest an appropriate transformation. The criteria SNLand SNSwere 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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