Taguchi Methods and Optimization for Robust Software

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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.

A Response Surface Approach for Robust Parameter Design

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 costs.

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:. 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 widely. 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.

Taguchi methods

The process has three stages:. This is design at the conceptual level, involving creativity and innovation. 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.

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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.

Robust parameter designs consider controllable and uncontrollable noise variables; they seek to exploit relationships and optimize settings that minimize the effects of the noise variables. 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. Taguchi developed his experimental theories independently. Taguchi read works following R.

Fisher only in Taguchi's framework for design of experiments is idiosyncratic and often flawed, but contains much that is of enormous value. Taguchi's designs aimed to allow greater understanding of variation than did many of the traditional designs from the analysis of variance following Fisher.

Taguchi contended that conventional sampling is inadequate here as there is no way of obtaining a random sample of future conditions. Variation becomes even more central in Taguchi's thinking.


Taguchi methods - Wikipedia

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. Many of the orthogonal arrays that Taguchi has advocated are saturated arrays , allowing no scope for estimation of interactions. This is a continuing topic of controversy.

The Single Array Method for Robust Design

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. 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.

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    Robust Design Program Development of Taguchi Method Based on Matlab

    Ganesh Kumar; R. Shetty Prakasham; Phil J. Hobbs March Biotechnology Journal. Retrieved Sreenivas; R. Prakasham; K. The software industry stands on the brink of an era of dramatic change. We expect the industry to continue the restructuring process already begun, emerging as a much smaller number of horizontally structured firms mostly doing business with each other.

    As software becomes highly "componentized," the industry will begin to resemble the automotive industry, with many small firms making parts, but only a few large ones assembling them into finished products. Software automation in the form of application generation technology will become the norm as system analysts and other domain specialists become the new application programmers, writing in specification languages. Meanwhile, the more talented of today's application programmers will become system programmers, writing the meta-compilers that will transform specification language codes into Java and C application programs.

    It is still true that new technologies do not replace old technologies, at least not at first; in their infancy, they merely supplement them. Chapters 16, 17, 18 and 19 of the book Design for Trustworthy Software address the transition period during which robust, trustworthy software is still created by current technology and processes as the new technology and its streamlined processes emerge. This short cut is a reproduction of Chapter 17 of Design for Trustworthy Software. It illustrates how Taguchi's quality loss function provides a measure of the overall loss to society when a product fails to meet its target functionality and reliability.

    Article Abstract

    It describes howsignal-to-noise ratio measures the positive quality contribution from controllable or design factors versus the negative quality contribution from uncontrollable or noise factors. It presents Taguchi Methods involving seven steps, beginning with a clear statement of thedesign problem and ending with a confirming statisticalexperiment showing how parameter choices will enhance robustness.

    An example from electrical circuit design is presented, because it is much more similar to software design than mechanical design, where Taguchi Methods have found their largest applications. A more detailed example from software design or product improvement builds on the previous example.