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Probability Plot Use in QC

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.

assign Test_variable 1000*100
let Test_variable = rannorm(Test_variable,20)

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.