Page 436 - Design for Six Sigma for Service (Six SIGMA Operational Methods)

394 Chapter Eleven

In Example 11.1, clearly the film thickness varies from wafer to wafer, so it
is a random variable. A random variable is either discrete or continuous. If
the set of all possible values is finite or countably infinite, then the random
variable is discrete; if the set of all possible values of the random variable is
an interval, then the random variable is continuous. Clearly, the film
thickness variable is continuous.
The theoretical basis for modern data analysis is statistics. There are
different methods in statistics that can be used to analyze data; some of
them are very simple, such as descriptive statistics. Descriptive statistics
can provide intuitive display and analysis of the data. Some methods are
more sophisticated, such as the probability distribution models and sta-
tistical inferences; these analyses are more powerful, can provide more
insights, and are able to provide credible inference and prediction about the
process based on data. All popular Six Sigma performance metrics are based
on the theory of statistics; therefore, familiarity with basic statistics is very
essential in understanding Six Sigma metrics.

In Sec. 11.2 we review several descriptive statistical methods. In Sec. 11.3
we review several commonly used probability distribution models. In
Sec. 11.4 we review some basic aspects of statistical estimation. Finally, in
Sec. 12.6, we discuss Six Sigma metrics.

11.2 Descriptive Statistics

11.2.1 Graphical Descriptive Statistics
Descriptive statistics are a set of simple graphical and numerical methods
that can quickly show some intuitive properties displayed in the data. The
commonly used graphical descriptive statistical methods include the dot
plot, histogram, and box plot.

Dot Plot
The dot plot, as illustrated by Fig. 11.1, is a simple yet effective diagram;
each dot represents a piece of data. The dot plot can display the distribution
pattern and the spread of data points.

Histogram
A histogram is a diagram displaying the frequency distribution. The hor-
izontal axis is partitioned into many small segments. The number of data
points (or the percentage of points) that fall in each segment is called the