- Taguchi methods
Taguchi methods are statistical methods developed by
Genichi Taguchito improve the quality of manufactured goods, and more recently also applied to biotechnology, [ Ravella Sreenivas Rao, C. Ganesh Kumar, R. Shetty Prakasham, Phil J. Hobbs (2008) The Taguchi methodology as a statistical tool for biotechnological applications: A critical appraisal "Biotechnology Journal" 3:510–523.
R. Sreenivas Rao, R.S. Prakasham, K. Krishna Prasad, S. Rajesham,P.N. Sarma, L. Venkateswar Rao (2004) Xylitol production by Candida sp.: parameter optimization using Taguchi approach, "Process Biochemistry" 39:951–956] marketing and advertising. Taguchi methods are considered controversial among some traditional Western
statisticians, but others accept many of his concepts as being useful additions to the body of knowledge.
Taguchi's principal contributions to
#The philosophy of "off-line quality control"; and
#Innovations in the
design of experiments.
Taguchi's reaction to the classical
design of experimentsmethodology of R. A. Fisher was that it was perfectly adapted for seeking to improve the meanoutcome of a process. As Fisher's work had been largely motivated by programmes to increase agriculturalproduction, this was hardly surprising. However, Taguchi realised that in much industrial production, there is a need to produce an outcome "on target", for example, to machinea hole to a specified diameter, or to manufacture a cell to produce a given voltage. He also realised, as had Walter A. Shewhartand 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 quality engineering should start with an understanding of
quality costsin various situations. In much conventional industrial engineering, the quality costs are simply represented by the number of items outside specification multiplied by the cost of rework or scrap. However, Taguchi insisted that manufacturers broaden their horizons to consider "cost to society". Though the short-term costs may simply be those of non-conformance, any item manufactured away from nominal would result in some loss to the customer or the wider community through early wear-out; difficulties in interfacing with other parts, themselves probably wide of nominal; or the need to build in safety margins. These losses are externalitiesand are usually ignored by manufacturers. In the wider economy the Coase Theorempredicts that they prevent markets from operating efficiently. Taguchi argued that such losses would inevitably find their way back to the originating corporation (in an effect similar to the tragedy of the commons), and that by working to minimise them, manufacturers would enhance brand reputation, win markets and generate profits.
Such losses are, of course, very small when an item is near to nominal.
Donald J. Wheelercharacterised 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 Demingwould describe them, "unknown and unknowable", but Taguchi wanted to find a useful way of representing them statistically. Taguchi specified three situations:
#Larger the better (for example, agricultural yield);
#Smaller the better (for example,
carbon dioxideemissions); 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 on the following grounds:
*It is the first symmetric term in the
Taylor seriesexpansion of any reasonable, real-life loss function, and so is a "first-order" approximation;
*Total loss is measured by the
variance. As varianceis additive, it is an attractive model of cost; and
*There was an established body of
statistical theoryaround the use of the least-squares principle.
The squared-error loss function had also been used by
John von Neumannand Oskar Morgensternin the 1930s.
Though much of this thinking is endorsed by
statisticians and economists in general, Taguchi extended the argument to insist that industrial experiments seek to maximise an appropriate "signal-to-noise ratio", representing the magnitude of the meanof a process compared to its variation. Most statisticians believe Taguchi's "signal-to-noise ratios" to be effective over too narrow a range of applications, and they are generally deprecated.
Off-line quality control
Taguchi realised that the best opportunity to eliminate variation is during the design of a product and its manufacturing process (
Taguchi's rule for manufacturing). Consequently, he developed a strategy for quality engineering that can be used in both contexts. The process has three stages:
#Parameter design; and
This is design at the conceptual level, involving
Once the concept is established, the nominal values of the various dimensions and design parameters need to be set, the
detail designphase 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 minimise the effects on performance arising from variation in manufacture, environment and cumulative damage. This is sometimes called robustification.
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 (see
Design of experiments
Taguchi developed much of his thinking in isolation from the school of R. A. Fisher, only coming into direct contact in
1954. His framework for design of experimentsis idiosyncraticand often flawed, but contains much that is of enormous value. He made a number of innovations.
design of experimentswork of R. A. Fisher, Taguchi sought to understand the influence that parameters had on variation, not just on the mean. He contended, as had W. Edwards Demingin his discussion of analytic studies, that conventional sampling is inadequate here as there is no way of obtaining a random sample of future conditions. In R. A. Fisher's work, variation between experimental replications is a nuisance that the experimenter would like to eliminate whereas, in Taguchi's thinking, it is a central object of investigation.
Taguchi's innovation was to replicate each experiment by means of an
outer array, possibly an orthogonal arraythat seeks deliberately to emulate the sources of variation that a product would encounter in reality. This is an example of judgement sampling. Though statisticians following in the Shewhart-Deming tradition have embraced outer arrays, many academics are still skeptical.See Montgomery (1991) "Design and analysis of experiments" John Wiley and Sons]
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. This still emulates the extremes of noise variation but with fewer test samples required.
Management of interactions
Many of the orthogonal arrays that Taguchi has advocated are saturated, allowing no scope for
estimationof interactions. This is a continuing topic of controversy. However, this is only true for "control factors" or factors in the "inner array". By combining an inner array of control factors with an outer array of "noise factors", Taguchi's approach provides full information on control-by-noise interactions. His concept is that those are the interactions of most interest in achieving a design that is robust to noise factor variation. In this sense, the Taguchi approach provides more complete interaction information than typical fractional factorial experiments.
*Followers of Taguchi argue that the designs offer rapid results and that interactions can be eliminated by proper choice of quality characteristics and by transforming the data. That notwithstanding, a
confirmation experimentoffers 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.
*Western statisticians argue that interactions are part of the real world and that Taguchi's arrays have complicated
alias structures that leave interactions difficult to disentangle. George Boxand others have argued that a more effective and efficient approach is to use sequential assembly.
Analysis of experiments
Taguchi introduced many methods for analysing experimental results including novel applications of the
analysis of varianceand " minute analysis". Little of this work has been validated by Western statisticians.
Genichi Taguchi has made seminal and valuable methodological innovations in
statisticsand engineering, within the Shewhart-Deming tradition. His emphasis on "loss to society", techniques for investigating variation in experiments, and his overall strategy of system, parameter and tolerance design have been massively influential in improving manufactured quality worldwide. Much of his work was carried out in isolation from the mainstream of Western statisticsand, while this may have facilitated his creativity, much of the technical detail of "Taguchi methods" and their benefits to experimentation and research is only now being studied in the West.
*León, R V; Shoemaker, A C & Kacker, R N (1987) Performance measures independent of adjustment: an explanation and extension of Taguchi's signal-to-noise ratios (with discussion), "Technometrics" vol 29, pp. 253–285
* Moen, R D; Nolan, T W & Provost, L P (1991) "Improving Quality Through Planned Experimentation" ISBN 0-07-042673-2
*Nair, V N ("ed.") (1992) Taguchi's parameter design: a panel discussion, "Technometrics" vol34, pp. 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
*Ravella Sreenivas Rao, C. Ganesh Kumar, R. Shetty Prakasham, Phil J. Hobbs (2008) The Taguchi methodology as a statistical tool for biotechnological applications: A critical appraisal "Biotechnology Journal" Vol 3: pp. 510–523.
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