Taguchi methods
Taguchi methods (
Taguchi's work includes three principal contributions to statistics:
- A specific loss function
- The philosophy of off-line quality control; and
- Innovations in the design of experiments.
Loss functions
Loss functions in the statistical theory
Traditionally, statistical methods have relied on
However, loss functions were avoided by
Taguchi's use of loss functions
Taguchi knew
However, Taguchi realised that in much industrial production, there is a need to produce an outcome on target, for example, to machine a hole to a specified diameter, or to manufacture a cell to produce a given voltage. He also realised, as had Walter A. Shewhart and others before him, that excessive variation lay at the root of poor manufactured quality and that reacting to individual items inside and outside specification was counterproductive.
He therefore argued that
Such losses are, of course, very small when an item is near to negligible. Donald J. Wheeler characterised the region within specification limits as where we deny that losses exist. As we diverge from nominal, losses grow until the point where losses are too great to deny and the specification limit is drawn. All these losses are, as W. Edwards Deming would describe them, unknown and unknowable, but Taguchi wanted to find a useful way of representing them statistically. Taguchi specified three situations:[7]
- Larger the better (for example, agricultural yield);
- Smaller the better (for example, carbon dioxide emissions); and
- On-target, minimum-variation (for example, a mating part in an assembly).
The first two cases are represented by simple monotonic loss functions. In the third case, Taguchi adopted a squared-error loss function for several reasons:[7]
- It is the first "symmetric" term in the real analyticloss-functions.
- Total loss is measured by the random variables, as variance is additive the total loss is an additive measurement of cost.
- The squared-error loss function is widely used in statistics, following Gauss's use of the squared-error loss function in justifying the method of least squares.
Reception of Taguchi's ideas by statisticians
Though many of Taguchi's concerns and conclusions are welcomed by statisticians and economists, some ideas have been especially criticized. For example, Taguchi's recommendation that industrial experiments maximise some signal-to-noise ratio (representing the magnitude of the mean of a process compared to its variation) has been criticized.[8]
Off-line quality control
Taguchi's rule for manufacturing
Taguchi realized that the best opportunity to eliminate variation of the final product quality is during the design of a product and its manufacturing process. Consequently, he developed a strategy for quality engineering that can be used in both contexts. The process has three stages:
- System design
- Parameter (measure) design
- Tolerance design
System design
This is design at the conceptual level, involving creativity and innovation.
Parameter design
Once the concept is established, the nominal values of the various dimensions and design parameters need to be set, the detail design phase of conventional engineering. Taguchi's radical insight was that the exact choice of values required is under-specified by the performance requirements of the system. In many circumstances, this allows the parameters to be chosen so as to minimize the effects on performance arising from variation in manufacture, environment and cumulative damage. This is sometimes called robustification.
Tolerance design
With a successfully completed parameter design, and an understanding of the effect that the various parameters have on performance, resources can be focused on reducing and controlling variation in the critical few dimensions.
Design of experiments
Taguchi developed his experimental theories independently. Taguchi read works following
Outer arrays
Taguchi's designs aimed to allow greater understanding of variation than did many of the traditional designs from the
Taguchi proposed extending each experiment with an "outer array" (possibly an orthogonal array); the "outer array" should simulate the random environment in which the product would function. This is an example of judgmental sampling. Many quality specialists have been using "outer arrays".
Later innovations in outer arrays resulted in "compounded noise." This involves combining a few noise factors to create two levels in the outer array: First, noise factors that drive output lower, and second, noise factors that drive output higher. "Compounded noise" simulates the extremes of noise variation but uses fewer experimental runs than would previous Taguchi designs.
Management of interactions
Interactions, as treated by Taguchi
Many of the orthogonal arrays that Taguchi has advocated are
- Followers of Taguchi argue that the designs offer rapid results and that interactions can be eliminated by proper choice of quality characteristics. That notwithstanding, a "confirmation experiment" offers protection against any residual interactions. If the quality characteristic represents the energy transformation of the system, then the "likelihood" of control factor-by-control factor interactions is greatly reduced, since "energy" is "additive".
Inefficiencies of Taguchi's designs
- Interactions are part of the real world. In Taguchi's arrays, interactions are confounded and difficult to resolve.
Statisticians in response surface methodology (RSM) advocate the "sequential assembly" of designs: In the RSM approach, a screening design is followed by a "follow-up design" that resolves only the confounded interactions judged worth resolution. A second follow-up design may be added (time and resources allowing) to explore possible high-order univariate effects of the remaining variables, as high-order univariate effects are less likely in variables already eliminated for having no linear effect. With the economy of screening designs and the flexibility of follow-up designs, sequential designs have great statistical efficiency. The sequential designs of response surface methodology require far fewer experimental runs than would a sequence of Taguchi's designs.[10]
Assessment
Genichi Taguchi has made valuable contributions to statistics and engineering. His emphasis on loss to society, techniques for investigating variation in experiments, and his overall strategy of system, parameter and tolerance design have been influential in improving manufactured quality worldwide.
See also
- Design of experiments – Design of tasks
- Optimal design– Experimental design that is optimal with respect to some statistical criterion
- Orthogonal array – Type of mathematical array
- Quality management – Business process to aid consistent product fitness
- Response surface methodology – Statistical approach
- Sales process engineering – Systematic design of sales processes
- Six Sigma – Business process improvement technique
- Engineering tolerance – Permissible limit or limits of variation in engineering
- Probabilistic design – Discipline within engineering design
References
- .
- S2CID 26543702. Archived from the originalon 2013-01-05. Retrieved 2009-04-01.
- .
- ISBN 0-87389-418-9.
- ^
Professional statisticians have welcomed Taguchi's concerns and emphasis on understanding variation (and not just the mean):
- Logothetis, N.; Wynn, H. P. (1989). Quality Through Design: Experimental Design, Off-line Quality Control, and Taguchi's Contributions. Oxford University Press, Oxford Science Publications. pp. 464+xi. ISBN 0-19-851993-1.
- Wu, C. F. Jeff; Hamada, Michael (2002). Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley.
- Box, G. E. P. and Draper, Norman. 2007. Response Surfaces, Mixtures, and Ridge Analyses, Second Edition [of Empirical Model-Building and Response Surfaces, 1987], Wiley.
- Atkinson, A. C.; Donev, A. N.; Tobias, R. D. (2007). Optimum Experimental Designs, with SAS. Oxford University Press. pp. 511+xvi. ISBN 978-0-19-929660-6.
- Logothetis, N.; Wynn, H. P. (1989). Quality Through Design: Experimental Design, Off-line Quality Control, and Taguchi's Contributions. Oxford University Press, Oxford Science Publications. pp. 464+xi.
- loss functionsas being better suited for American businessmen and Soviet comisars than for empirical scientists (in Fisher's 1956 attack on Wald in the 1956 JRSS).
- ^ ISBN 978-3-319-50829-0.
- ^ Montgomery, D. C.
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(help) - ^ Similar truisms about the problem of induction had been voiced by Hume and (more recently) by W. Edwards Deming in his discussion of analytic studies.
- ^
Statisticians have developed designs that enable experiments to use fewer replications (or experimental runs), enabling savings over Taguchi's proposed designs:
- Atkinson, A. C.; Donev, A. N.; Tobias, R. D. (2007). Optimum Experimental Designs, with SAS. Oxford University Press. pp. 511+xvi. )
- Box, G. E. P. and Draper, Norman. 2007. Response Surfaces, Mixtures, and Ridge Analyses, Second Edition [of Empirical Model-Building and Response Surfaces, 1987], Wiley.
- Goos, Peter (2002). The Optimal Design of Blocked and Split-plot Experiments. Lecture Notes in Statistics. Vol. 164. Springer.
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- Logothetis, N. and Wynn, H. P. (1989). ISBN 0-19-851993-1.)
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- Pukelsheim, Friedrich (2006). Optimal Design of Experiments. ISBN 978-0-89871-604-7.
- Wu, C. F. Jeff & Hamada, Michael (2002). Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley. ISBN 0-471-25511-4.
- R. H. Hardin and N. J. A. Sloane, "A New Approach to the Construction of Optimal Designs", Journal of Statistical Planning and Inference, vol. 37, 1993, pp. 339-369
- R. H. Hardin and N. J. A. Sloane, "Computer-Generated Minimal (and Larger) Response Surface Designs: (I) The Sphere"
- R. H. Hardin and N. J. A. Sloane, "Computer-Generated Minimal (and Larger) Response Surface Designs: (II) The Cube"
- Ghosh, S.; ISBN 0-444-82061-2.
Box-Draper, Atkinson-Donev-Tobias, Goos, and Wu-Hamada discuss the sequential assembly of designs.
Bibliography
- Atkinson, A. C.; Donev, A. N.; Tobias, R. D. (2007). Optimum Experimental Designs, with SAS. Oxford University Press. pp. 511+xvi. )
- Box, G. E. P. and Draper, Norman. 2007. Response Surfaces, Mixtures, and Ridge Analyses, Second Edition [of Empirical Model-Building and Response Surfaces, 1987], Wiley.
- Goos, Peter (2002). The Optimal Design of Blocked and Split-plot Experiments. Lecture Notes in Statistics. Vol. 164. Springer.
{{cite book}}
: External link in
(help)|publisher=
and|series=
- Logothetis, N. and Wynn, H. P. (1989). ISBN 0-19-851993-1.)
{{cite book}}
: External link in
(help)CS1 maint: multiple names: authors list (link|author=
- Pukelsheim, Friedrich (2006). Optimal Design of Experiments. ISBN 978-0-89871-604-7.
- Wu, C. F. Jeff & Hamada, Michael (2002). Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley. ISBN 0-471-25511-4.
- R. H. Hardin and N. J. A. Sloane, "A New Approach to the Construction of Optimal Designs", Journal of Statistical Planning and Inference, vol. 37, 1993, pp. 339-369
- R. H. Hardin and N. J. A. Sloane, "Computer-Generated Minimal (and Larger) Response Surface Designs: (I) The Sphere"
- R. H. Hardin and N. J. A. Sloane, "Computer-Generated Minimal (and Larger) Response Surface Designs: (II) The Cube"
- Ghosh, S.; ISBN 0-444-82061-2.
- León, R V; Shoemaker, A C; Kacker, R N (1987). "Performance measures independent of adjustment: an explanation and extension of Brett's signal-to-noise ratios (with discussion)". Technometrics. 29 (3): 253–285. JSTOR 1269331.
- Moen, R D; Nolan, T W & Provost, L P (1991) Improving Quality Through Planned Experimentation ISBN 0-07-042673-2
- Nair, V N (1992). "Taguchi's parameter design: a panel discussion". Technometrics. 34 (2): 127–161. .
- Bagchi Tapan P and Madhuranjan Kumar (1992) Multiple Criteria Robust Design of Electronic Devices, Journal of Electronic Manufacturing, vol 3(1), pp. 31–38
- Sreenivas Rao, Ravella; Kumar, C. Ganesh; Prakasham, R. Shetty; Hobbs, Phil J. (2008). "The Taguchi methodology as a statistical tool for biotechnological applications: A critical appraisal". Biotechnology Journal. 3 (4): 510–523. S2CID 26543702.
- Montgomery, D. C. Ch. 9, 6th Edition [of Design and Analysis of Experiments, 2005], Wiley.