Taguchi methods
Encyclopedia
Taguchi methods are statistical
methods developed by Genichi Taguchi
to improve the quality of manufactured goods, and more recently also applied to, engineering, biotechnology, marketing and advertising. Professional statistician
s have welcomed the goals and improvements brought about by Taguchi methods, particularly by Taguchi's development of designs for studying variation, but have criticized the inefficiency
of some of Taguchi's proposals.
Taguchi
's work includes three principal contributions to statistics:
s: Under the conditions of the Gauss-Markov theorem, least squares
estimators have minimum variance among all mean-unbiased estimators. The emphasis on comparisons of means also draws (limiting) comfort from the law of large numbers
, according to which the sample means converge to the true mean. Fisher's textbook on the design of experiments
emphasized comparisons of treatment means.
Gauss
proved that the sample-mean minimizes the expected squared-error loss-function
(while Laplace proved that a median
-unbiased estimator minimizes the absolute
-error loss function). In statistical theory
, the central role of the loss function was renewed by the statistical decision theory of Abraham Wald
.
However, loss functions were avoided by Ronald A. Fisher.
mainly from the followers of Ronald A. Fisher, who also avoided loss function
s.
Reacting to Fisher's methods in the design of experiments
, Taguchi interpreted Fisher's methods as being adapted for seeking to improve the mean
outcome of a process. Indeed, Fisher's work had been largely motivated by programmes to compare agricultural yields under different treatments and blocks, and such experiments were done as part of a long-term programme to improve harvests.
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 quality engineering
should start with an understanding of quality costs
in 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 externalities and are usually ignored by manufacturers, which are more interested in their private costs than social cost
s. Such externalities prevent markets from operating efficiently, according to analyses of public economics. 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 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:
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:
s, 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 widely.
and innovation
.
.
).
is idiosyncratic and often flawed, but contains much that is of enormous value. He made a number of innovations.
(following Fisher). Taguchi contended that conventional sampling
is inadequate here as there is no way of obtaining a random sample
of future conditions. In Fisher's design of experiments
and analysis of variance
, experiments aim to reduce the influence of nuisance factors to allow comparisons of the mean treatment-effects. Variation becomes even more central in Taguchi's thinking.
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.
s, allowing no scope for estimation of 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, it is claimed. Taguchi argues that such interactions have the greatest importance in achieving a design that is robust to noise factor variation. The Taguchi approach provides more complete interaction information than typical fractional factorial designs, its adherents claim.
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.
and minute analysis.
. 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. Although some of the statistical aspects of the Taguchi methods are disputable, there is no dispute that they are widely applied to various processes. A quick search in related journals, as well as the World Wide Web, reveals that the method is being successfully implemented in diverse areas,such as the design of VLSI; optimization of communication & information networks, development of electronic circuits, laser engraving
of photo masks, cash-flow optimization in banking,government policymaking, runway utilization improvement in airports, and even robust eco-design.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
methods developed by Genichi Taguchi
Genichi Taguchi
is an engineer and statistician. From the 1950s onwards, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods...
to improve the quality of manufactured goods, and more recently also applied to, engineering, biotechnology, marketing and advertising. Professional statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
s have welcomed the goals and improvements brought about by Taguchi methods, particularly by Taguchi's development of designs for studying variation, but have criticized the inefficiency
Efficiency (statistics)
In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. The notion of “best possible” relies upon the choice of a particular loss function — the function which quantifies the relative degree of undesirability of estimation errors...
of some of Taguchi's proposals.
Taguchi
Genichi Taguchi
is an engineer and statistician. From the 1950s onwards, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods...
's work includes three principal contributions to statistics:
- A specific loss functionLoss functionIn statistics and decision theory a loss function is a function that maps an event onto a real number intuitively representing some "cost" associated with the event. Typically it is used for parameter estimation, and the event in question is some function of the difference between estimated and...
— see Taguchi loss functionTaguchi loss functionThe Taguchi Loss Function is a graphical depiction of loss developed by the Japanese business statistician Genichi Taguchi to describe a phenomenon affecting the value of products produced by a company. Praised by Dr. W...
; - The philosophy of off-line quality control; and
- Innovations in the design of experimentsDesign of experimentsIn general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
.
Loss functions in statistical theory
Traditionally, statistical methods have relied on mean-unbiased estimators of treatment effectTreatment effect
Treatment effect may refer to:* Design of experiments* Average treatment effect...
s: Under the conditions of the Gauss-Markov theorem, least squares
Least squares
The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...
estimators have minimum variance among all mean-unbiased estimators. The emphasis on comparisons of means also draws (limiting) comfort from the law of large numbers
Law of large numbers
In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times...
, according to which the sample means converge to the true mean. Fisher's textbook on the design of experiments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
emphasized comparisons of treatment means.
Gauss
Gauss
Gauss may refer to:*Carl Friedrich Gauss, German mathematician and physicist*Gauss , a unit of magnetic flux density or magnetic induction*GAUSS , a software package*Gauss , a crater on the moon...
proved that the sample-mean minimizes the expected squared-error loss-function
Loss function
In statistics and decision theory a loss function is a function that maps an event onto a real number intuitively representing some "cost" associated with the event. Typically it is used for parameter estimation, and the event in question is some function of the difference between estimated and...
(while Laplace proved that a median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
-unbiased estimator minimizes the absolute
Absolute value
In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...
-error loss function). In statistical theory
Statistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
, the central role of the loss function was renewed by the statistical decision theory of Abraham Wald
Abraham Wald
- See also :* Sequential probability ratio test * Wald distribution* Wald–Wolfowitz runs test...
.
However, loss functions were avoided by Ronald A. Fisher.
Taguchi's use of loss functions
Taguchi knew statistical theoryStatistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
mainly from the followers of Ronald A. Fisher, who also avoided loss function
Loss function
In statistics and decision theory a loss function is a function that maps an event onto a real number intuitively representing some "cost" associated with the event. Typically it is used for parameter estimation, and the event in question is some function of the difference between estimated and...
s.
Reacting to Fisher's methods in the design of experiments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
, Taguchi interpreted Fisher's methods as being adapted for seeking to improve the mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
outcome of a process. Indeed, Fisher's work had been largely motivated by programmes to compare agricultural yields under different treatments and blocks, and such experiments were done as part of a long-term programme to improve harvests.
However, Taguchi realised that in much industrial production, there is a need to produce an outcome on target, for example, to machine
Machine
A machine manages power to accomplish a task, examples include, a mechanical system, a computing system, an electronic system, and a molecular machine. In common usage, the meaning is that of a device having parts that perform or assist in performing any type of work...
a hole to a specified diameter, or to manufacture a cell
Electrochemical cell
An electrochemical cell is a device capable of either deriving electrical energy from chemical reactions, or facilitating chemical reactions through the introduction of electrical energy. A common example of an electrochemical cell is a standard 1.5-volt "battery"...
to produce a given voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
. He also realised, as had Walter A. Shewhart
Walter A. Shewhart
Walter Andrew Shewhart March 18, 1891 - March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.W...
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 quality engineering
Quality Engineering
Quality Engineering is a quarterly academic journal focusing on quality control and quality assurance management through use of physical technology, standards information, and statistical tools. The journal is co-published between American Society for Quality and Marcel Dekker, Inc....
should start with an understanding of quality costs
Quality costs
The concept of quality costs is a means to quantify the total cost of quality-related efforts and deficiencies. It was first described by Armand V. Feigenbaum in a 1956 Harvard Business Review article....
in various situations. In much conventional industrial engineering
Industrial engineering
Industrial engineering is a branch of engineering dealing with the optimization of complex processes or systems. It is concerned with the development, improvement, implementation and evaluation of integrated systems of people, money, knowledge, information, equipment, energy, materials, analysis...
, 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 externalities and are usually ignored by manufacturers, which are more interested in their private costs than social cost
Social cost
Social cost, in economics, is generally defined in opposition to "private cost". In economics, theorists model individual decision-making as measurement of costs and benefits...
s. Such externalities prevent markets from operating efficiently, according to analyses of public economics. 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
Tragedy of the commons
The tragedy of the commons is a dilemma arising from the situation in which multiple individuals, acting independently and rationally consulting their own self-interest, will ultimately deplete a shared limited resource, even when it is clear that it is not in anyone's long-term interest for this...
), 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 negligible. Donald J. Wheeler
Donald J. Wheeler
Donald J. Wheeler is an American author, statistician and expert in quality control.Wheeler graduated from the University of Texas in 1966 and holds M.S. and Ph.D. degrees in statistics from Southern Methodist University. From 1970 to 1982 he taught in the Statistics Department at the University of...
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
W. Edwards Deming
William Edwards Deming was an American statistician, professor, author, lecturer and consultant. He is perhaps best known for his work in Japan...
would 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 dioxideCarbon dioxideCarbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...
emissions); and - On-target, minimum-variation (for example, a mating part in an assembly).
The first two cases are represented by simple monotonic
Monotonic function
In mathematics, a monotonic function is a function that preserves the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory....
loss functions. In the third case, Taguchi adopted a squared-error loss function for several reasons:
- It is the first "symmetric" term in the Taylor seriesTaylor seriesIn mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....
expansion of real analytic loss-functions. - Total loss is measured by the varianceVarianceIn probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
. For uncorrelatedUncorrelatedIn probability theory and statistics, two real-valued random variables are said to be uncorrelated if their covariance is zero. Uncorrelatedness is by definition pairwise; i.e...
random variables, as variance is additive the total loss is an additive measurement of cost. - The squared-error loss function is widely used in statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, following Gauss's use of the squared-error loss function in justifying the method of least squaresLeast squaresThe method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...
.
Reception of Taguchi's ideas by statisticians
Though many of Taguchi's concerns and conclusions are welcomed by statisticians and economistEconomist
An economist is a professional in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy...
s, some ideas have been especially criticized. For example, Taguchi's recommendation that industrial experiments maximise some signal-to-noise ratio
Signal-to-noise ratio
Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
(representing the magnitude of the mean
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
of a process compared to its variation) has been criticized widely.
Taguchi's rule for manufacturing
Taguchi realized that the best opportunity to eliminate variation 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 creativityCreativity
Creativity refers to the phenomenon whereby a person creates something new that has some kind of value. What counts as "new" may be in reference to the individual creator, or to the society or domain within which the novelty occurs...
and innovation
Innovation
Innovation is the creation of better or more effective products, processes, technologies, or ideas that are accepted by markets, governments, and society...
.
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 robustificationRobustification
Robustification is a form of optimisation whereby a system is made less sensitive to the effects of random variability, or noise, that is present in that system’s input variables and parameters...
.
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 principlePareto principle
The Pareto principle states that, for many events, roughly 80% of the effects come from 20% of the causes.Business-management consultant Joseph M...
).
Design of experiments
Taguchi developed his experimental theories independently. Taguchi read works following R. A. Fisher only in 1954. Taguchi's framework for design of experimentsDesign of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
is idiosyncratic and often flawed, but contains much that is of enormous value. He made a number of innovations.
Outer arrays
Taguchi's designs aimed to allow greater understanding of variation than did many of the traditional designs from the analysis of varianceAnalysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
(following Fisher). Taguchi contended that conventional sampling
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
is inadequate here as there is no way of obtaining a random sample
Simple random sample
In statistics, a simple random sample is a subset of individuals chosen from a larger set . Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of k individuals has...
of future conditions. In Fisher's design of experiments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
and analysis of variance
Analysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
, experiments aim to reduce the influence of nuisance factors to allow comparisons of the mean treatment-effects. Variation becomes even more central in Taguchi's thinking.
Taguchi proposed extending each experiment with an "outer array" (possibly an orthogonal array
Orthogonal array
Orthogonal array testing is a black box testing technique which is a systematic, statistical way of software testing.It is used when the number of inputs to the system is relatively small, but too large to allow for exhaustive testing of every possible input to the systems...
); the "outer array" should simulate the random environment in which the product would function. This is an example of judgmental sampling
Nonprobability sampling
Sampling is the use of a subset of the population to represent the whole population. Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular sample may be calculated. Nonprobability sampling does not meet this criterion and should be...
. 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.
Interactions, as treated by Taguchi
Many of the orthogonal arrays that Taguchi has advocated are saturated arraySaturated array
In experiments in which additional factors are not likely to interact with any of the other factors, a saturated array can be used. In a saturated array, a controllable factor is substituted for the interaction of two or more by-products. Using a saturated array, a two-factor test matrix could be...
s, allowing no scope for estimation of 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, it is claimed. Taguchi argues that such interactions have the greatest importance in achieving a design that is robust to noise factor variation. The Taguchi approach provides more complete interaction information than typical fractional factorial designs, its adherents claim.
- Followers of Taguchi argue that the designs offer rapid results and that interactionInteraction (statistics)In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive...
s 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".
Inefficencies of Taguchi's designs
- Interactions are part of the real worldReal WorldThe real world is another term for reality. It may also refer to:-Television:* The Real World, a television show* "The Real World" , a television episode-Music:* "Real World" , an album by Kokia...
. In Taguchi's arrays, interactions are confoundedConfoundingIn statistics, a confounding variable is an extraneous variable in a statistical model that correlates with both the dependent variable and the independent variable...
and difficult to resolve.
Statisticians in response surface methodology
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
(RSM) advocate the "sequential assembly" of designs
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
: In the RSM approach, a screening
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
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
Higher-order statistics
Higher-order statistics are descriptive measures of, among other things, qualities of probability distributions and sample distributions, and are, themselves, extensions of first- and second-order measures to higher orders. Skewness and kurtosis are examples of this...
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
Efficiency (statistics)
In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. The notion of “best possible” relies upon the choice of a particular loss function — the function which quantifies the relative degree of undesirability of estimation errors...
. The sequential designs of response surface methodology
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
require far fewer experimental runs than would a sequence of Taguchi's designs.
Analysis of experiments
Taguchi introduced many methods for analysing experimental results including novel applications of the analysis of varianceAnalysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
and minute analysis.
Assessment
Genichi Taguchi has made valuable contributions to statistics and engineeringEngineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
. 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. Although some of the statistical aspects of the Taguchi methods are disputable, there is no dispute that they are widely applied to various processes. A quick search in related journals, as well as the World Wide Web, reveals that the method is being successfully implemented in diverse areas,such as the design of VLSI; optimization of communication & information networks, development of electronic circuits, laser engraving
Laser engraving
Laser engraving, or laser marking, is the practice of using lasers to engrave or mark an object. The technique does not involve the use of inks, nor does it involve tool bits which contact the engraving surface and wear out...
of photo masks, cash-flow optimization in banking,government policymaking, runway utilization improvement in airports, and even robust eco-design.
See also
- Design of experimentsDesign of experimentsIn general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
- Optimal designOptimal designOptimal designs are a class of experimental designs that are optimal with respect to some statistical criterion.In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance...
- Orthogonal arrayOrthogonal arrayOrthogonal array testing is a black box testing technique which is a systematic, statistical way of software testing.It is used when the number of inputs to the system is relatively small, but too large to allow for exhaustive testing of every possible input to the systems...
- Quality managementQuality managementThe term Quality management has a specific meaning within many business sectors. This specific definition, which does not aim to assure 'good quality' by the more general definition , can be considered to have four main components: quality planning, quality control, quality assurance and quality...
- Response surface methodologyResponse surface methodologyIn statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
- Sales process engineeringSales process engineeringSales process engineering has been described as “the systematic application of scientific and mathematical principles to achieve the practical goals of a particular sales process". Selden pointed out that in this context, sales referred to the output of a process involving a variety of functions...
- Six sigmaSix SigmaSix Sigma is a business management strategy originally developed by Motorola, USA in 1986. , it is widely used in many sectors of industry.Six Sigma seeks to improve the quality of process outputs by identifying and removing the causes of defects and minimizing variability in manufacturing and...
- Tolerance (engineering)Tolerance (engineering)Engineering tolerance is the permissible limit or limits of variation in# a physical dimension,# a measured value or physical property of a material, manufactured object, system, or service,# other measured values ....
- Probabilistic designProbabilistic designProbabilistic design is a discipline within engineering design. It deals primarily with the consideration of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects are related to quality and reliability...