Page 337 - The Handbook for Quality Management a Complete Guide to Operational Excellence

324 C o n t i n u o u s I m p r o v e m e n t A n a l y z e S t a g e 325

Although it is possible to do advanced analysis without plotting the
scatter diagram, this is generally bad practice. This misses the enormous
learning opportunity provided by the graphical analysis of the data.

Determine Process Drivers
Process drivers refer to the factors that have the largest influence on the
process. For any business process, there are likely to be many factors that
contribute to process variation. Process improvement will require either a
reduction in process variation, or a movement of the process centerline to
a more favorable setting. In either case, focusing on the key process drivers
will facilitate this improvement.

Correlation and Regression Analysis
Correlation analysis (the study of the strength of the linear relationships
among several variables) and regression analysis (modeling the rela-
tionship between one or more independent variables and a dependent
variable) are closely related to the scatter diagram. A regression problem
considers the frequency distributions of one variable when another is
held fixed at each of several levels. A correlation problem considers the
joint variation of two variables, neither of which is restricted by the
experimenter. Correlation and regression analyses are designed to assist
the engineer in studying cause and effect. They may be employed in all
stages of the problem-solving and planning process. Of course, statistics
cannot by themselves establish cause and effect. Proving cause and
effect requires sound scientific understanding of the situation at hand.
The statistical methods described in this section assist in performing this
analysis.

Linear Models. A simple linear model is a mathematical expression of the
association between two variables, x and y. A linear relationship simply
means that a change of a given size in x produces a proportionate change
in y. Linear models have the form:
y = a + bx

where a and b are constants. The equation simply says that when x changes
by one unit, y will change by b units. This relationship can be shown
graphical ly.
In the scatter diagram shown in Fig. 15.4, a = 3.847 and b = 0.110. The
term a is called the intercept and b is called the slope. When x = 0, y is equal
to the intercept.
Many types of associations are non-linear. For example, over a
given range of x values y might increase, and for other x values y might
decrease. This curvilinear relationship is shown in Fig. 15.6.

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