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Taguchi methods are
statistical methods developed largely by
Genichi Taguchi to improve the quality of manufactured goods.
Taguchi methods are controversial among many conventional Western
statisticians.
Taguchi's principle contributions to
statistics are:
- Taguchi loss-function;
- The philosophy of off-line quality control; and
- Innovations in the
design of experiments.
Loss functions
Taguchi's reaction to the classical
design of experiments methodology of
R. A. Fisher was that it was perfectly adapted in seeking to improve
the
mean outcome of a
process. As
Fisher's work had been largely motivated by programmes to increase
agricultural production, 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
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 counter-productive.
He, therefore, argued that quality engineering should start with an
understanding of the
cost of poor quality in various situations. In much conventional
industrial engineering the
cost of poor quality is 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 consided
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
externalities and are usually ignored by manufacturers. In the wider
economy the
Coase Theorem predicts that they prevent markets from operating
efficiently.
Taguchi argued that such losses would inevitably find their way back
to the originating corperation (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. 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 within
statistics. Taguchi specified three situations:
- 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 on the grounds:
- It is the first symmetric term in the
Taylor series expansion of any reasonable, real-life
loss function, and so is a "first-order" approximation;
- Total loss is measured by the
variance. As
variance is additive it is an attractive model of cost; and
- There was an established body of
statistical theory around the use of the
least squares principle.
The squared-error
loss function had been used by
John von Neumann and
Oskar Morgenstern in the
1930s. There is a theorem I think - help appreciated
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
mean of 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 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:
- System design;
- Parameter design; and
- 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
detailed design phase of conventional engineering. In
1802, philosopher
William Paley had observed that the
inverse-square law of
gravitation was the only law that resulted in stable orbits if the
planets were perturbed in their motion.
Paley's understanding that
engineering should aim at designs robust against variation led him to
use the phenomenon of
gravitation as an
argument for the existence of God.
William Sealey Gosset in his work at the
Guinness brewery suggested as early as the beginning of the
20th century that the company might breed strains of barley that not
only yielded and malted well but whose characteristics were robust against
variation in the different soils and climates in which they were grown.
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 approach is often known as
robust design.
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 (see
Pareto principle).
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 framwork for
design of experiments is idioyncratic and often flawed but contains
much that is of enormous value. He made a number of innovations.
Outer arrays
In his later work,
R. A. Fisher had started to consider the prospect of using
design of experiments to understand variation in a wider inductive
basis.
Taguchi sought to understand the influence that parameters had on
variation, not just on the mean. He contended, as had
W. Edwards Deming in 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 conventional
design of experiments, 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, itself an
orthogonal array that 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 sceptical. An alternative approach
proposed by
Ellis R. Ott is to use a
chunk variable.
Management of interactions
Many of the
orthogonal arrays that
Taguchi has advocated are
saturated allowing no scope for
estimation of
interactions. This is a continuing topic of controversy.
- Followers of
Taguchi argue that the designs offer rapid results and that
interactions can be eliminated by proper choice of quality
characteristic and by transforming the data. That notwithstanding, a
confirmation experiment offers protection against any residual
interactions.
- 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 Box, and 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 variance and
minute analysis. Little of this work has been validated by
Western
statisticians.
Assessment
Genichi Taguchi has made seminal and valuable methodological
innovations in
statistics and
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
statistics and, while this may have facilitated his creativity, much
of the technical detail of Taguchi methods is flawed.
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