Abstract: The
probability plot can actually be an important
tool for SPC. This article provides some guidance
on that use.
Products:
Statit
e-QC, Statit
e-Server, Statit
Custom QC
The Probability Plot is often used to determine
the normality of a distribution. However it
can also be used to in Quality Control. While
it is no substitute for the time ordered display
in a Shewhart chart, it can be used to look
at the process. To illustrate, you can create
a variable that is normally distributed.
These commands will create a variable with
1000 cases having a mean of 100 and a standard
deviation of 20.
Probability Plot is under the Graphics
-> Distribution Plots.
We supply the variable name (Test_Variable).
Statit will by default display the Theoretical
Quantiles line but this could be turned off.
Statit will also perform a Shapiro-Wilk test
for normality unless we click "Do not perform
the test for normality".
Without going in to a great deal of detail,
note that you can also do a Local Selection
or supply the mean and standard deviation of
the distribution in "Distribution parameters".
What is of particular interest to the Quality
field is the "Display values for these
probabilities" and "Show lines at
values". The probability values of .00135
and .99865 correspond to 3 sigma below and above
the mean. In other words, approximately Lower
and Upper Control Limits on an Item Chart.
If we execute this command we get the result:
Here we can see an indication that there is
at least one point below the Lower Control Limit
and perhaps three points above the Upper Control
Limit.
If we look at the same data with a Individual
Chart:
In this particular example, all points indicated
as out of control on Probability Plot show out
of control on the Item Chart. This will not
happen each time you run this example. (Remember,
we are creating 1000 random values). Then you
might see more or less points out of control
on the Item Chart. Why the differences in the
charts? Remember that the item chart uses a
constant based on a subgroup size and a moving
range to calculate an estimate of sigma, while
the probability plot looks at the probability
based on the data. You see this difference if
you compare the values of the Upper Control
Limit and the .99865 Probability or the Lower
Control Limit and the .00135 Probability. The
Item Chart is usually a rougher estimate of
the process stability.
The Probability Plot is useful for a number
of reasons:
A probability plot is useful for larger sample
sizes where the Item Chart can become cluttered.
Thus the probability plot helps to look at a
longer time period and gives a good estimate
of the statistical control of the process, some
say sometimes even better then the Item Chart.
Some authors believe that the distribution
does not need to approximate normality for the
probability plot to be used in this manner.
What the Probability Plot does not do:
It does not show any trending rule violations
as the Item chart .
It does not time order the observations, so
it is not an immediate decision making tool.
The power of Shewhart charts comes from viewing
the data in time order so that you know when
the process is out of control.
Statit Express QC Note:
Statit Express QC has a somewhat limited probability
plot. While it allows the use of probability
endpoints, it does not draw the probability
lines.
