Chaughule, Thorat - Statistical Analysis/Design of Experimentsthen this value of yield should be obtained regardless of the variation in factors such as
the quality of raw materials or fluctuations in humidity or other weather conditions.
These factors, that are called noise factors, are beyond the control of the operator.
Therefore, the product or process should be such that it is not affected by minor fluctua-
tions in these factors. The process of making a system insensitive to noise factors is re-
ferred to as Robust Design. Robust design was pioneered by the Japanese industrialist
Dr. Taguchi in the 1980s.
Taguchi's approach to achieve a high quality system consists of three stages, namely,
system design, parameter design and tolerance design.
I. System design: The stage when ideas for a new system are used to decide upon
the combinations of factors to obtain a functional and economical design.
II. Parameter design: The stage when factor settings are selected that make the sys-
tem less sensitive to variations in the uncontrollable factors affecting the system. There-
fore, if this stage is carried out successfully, the resulting system will have little variation
and the resulting tolerances will be tight.
III. Tolerance design: The final stage when tolerances are tightened around the best
value. This stage increases cost and is only needed if the required quality is not achieved
during parameter design. Thus, using parameter design, it is possible to achieve the de-
sired quality without much increase in the cost.
Taguchi divided the factors affecting any system into two categories control factors
and noise factors.
a) Control factors: The factors affecting a system that are easily set or controlled by
the experimenter. For example, if in a drying process the drying time is found to be a
factor affecting the product quality, then this factor is a control factor since it can be eas-
ily manipulated and set by the experimenter. The experimenter will choose the drying
time that improves the product quality.
b) Noise factors: The factors affecting a system that are difficult or impossible to
control. For example, ambient temperature and humidity may also have an effect on the
drying time of a fruit pulp, but ambient temperature and humidity could be a noise fac-
tor if it is beyond the control of the experimental settings. Thus, change in ambient tem-
perature and humidity will lead to variations in the drying time but such variations are
undesirable.
Taguchi studied the interaction between the control and noise factors using two ex-
periment designs viz; Inner array and outer array. The inner array is essentially any ex-
perimental design that is used to study the effect of the control factors on the response.
Taguchi then used an outer array for the noise factors so that each run of the inner array
was repeated for every treatment of the outer array. The resulting experiment design,
that uses both inner and outer arrays, is referred to as a cross array.
8.6.5. Box-Behnken designs
Box-Behnken designs (BBD) are response surface methodology rotatable second-
order designs based on three-level incomplete factorial designs. It is used to study the
quadratic effect of factors after identifying the significant factors using factorial experi-
ments. The special arrangement of the BBD levels allows the number of design points to