15.6.2 Noise Factors

The input parameters that affect the quality of the product or process may be

classifi ed as design parameters and disturbance factors. The former are parameters

that can be specifi ed freely by the designer. It is the designer’s responsibility to

select the optimum levels of the design parameters. Disturbance factors are the

parameters that are either inherently uncontrollable or impractical to control.

Taguchi uses the term noise factors to refer to those parameters that are either

too diffi cult or too expensive to control when a product is in service or during

manufacture of its components. The noise factors can be classifi ed into four

categories:

● Variational noise is the unit-to-unit variation that nominally identical products

will exhibit due to the differences in their components or their assembly. ● Inner noise is the long-term change in product characteristics over time due to

deterioration and wear.

748 engineering design

● Design noise is the variability introduced into the product due to the design

process. This consists mostly of the tolerance variability that practical design

limitations impose on the design. ● External noise , also called outer noise, represents the disturbance factors that

produce variations in the environment in which the product operates. Examples

of external noise factors are temperature, humidity, dust, vibration, and the skill

of the operator of the product.

The Taguchi method is unusual among methods of experimental investigation in

that it places heavy emphasis on including noise factors in every experimental

design. Taguchi was the fi rst to articulate the importance of considering external

noise directly in design decisions.

15.6.3 Signal-to-Noise Ratio

W henever a series of experiments is to be carried out, it is necessary to decide

what response o r output of the experiment will be measured. Often the nature of

the experiment provides a natural response. For example, in the control chart in

Fig. 15.5, which evaluated the effectiveness of a heat-treating process for

hardening steel bearings, a natural response was the Rockwell hardness

measurement. The Taguchi method uses a special response variable called the

signal-to-noise ratio , S/N . The use of this response is somewhat controversial,

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but its use is justifi ed on the basis that it encompasses both the mean (signal) and

the variation (noise) in one parameter, just as the quality loss function does. 1

Following are three forms of the S/N ratio corresponding to the three forms

of the loss function curves shown in Fig. 15.6.

For the nominal-is-best type of problem,

2

S / N =10 log (15.15)

where µ= nl ∑

l n yi and 2 = n1−1∑

i=n 1

(yi −

µ)2

=1

and n is the number of external noise observation combinations used for each

design parameter matrix (inner array) combination. For example, if four tests are

made to allow for noise for each combination of the control parameters, then n =

4. For the smaller-the-better type of problem,

S / N =−10 log

nl ∑yi

2 (15.16)

chapter 15: Quality, Robust Design, and Optimization 749

For the larger-the-better type of problem, the quality performance characteristic

is continuous and nonnegative. We would like y to be as large as possible. To fi nd

the S/N, we turn this into a smaller-the-better problem by using the reciprocal of

the performance characteristic.

1 . Dr. Taguchi was an electrical engineer with the national telephone system of Japan, so the concept of

signal-to-noise ratio, the ratio of signal strength to unwanted interference in a communications circuit, was

very familiar to him.

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