Data Analysis with Microsoft Excel: Updated for Office 2007

492 Statistical Methods

Another common example of a process that is out of control, even though

all points lie between the control limits, appears in Figure 12-4. The fi rst

eight observations are below the center line, whereas the last seven obser-

vations all lie above the center line. Because of prolonged periods where

values are either small or large, this process is out of control. One could use

the Runs test, discussed in Chapter 8 in the context of examining residuals,

to test whether the data values are clustered in a nonrandom way.

Figure 12-4
A process out
of control
because of a
nonrandom
pattern

Here are two other situations that may show a process out of control, even

though all values lie within the control limits.

9 points in a row, all on the same side of the center line

14 points in a row, alternating above and below the center line

Other suspicious patterns could appear in control charts. Unfortunately,

we cannot discuss them all here. In general, though, any clear pattern in the

process values indicates that a process is subject to uncontrolled variation

and that it is not in control.

Statisticians usually highlight out-of-control points in control charts by

circling them. As you can see, the control chart makes it very easy for you to

identify visually points and processes that are out of control without using

complicated statistical tests. This makes the control chart an ideal tool for

the shop fl oor, where quick and easy methods are needed.

Control Charts and Hypothesis Testing

The idea underlying control charts should be familiar to you. It is closely

related to confi dence intervals and hypothesis testing. The associated null

hypothesis is that the process is in control; you reject this null hypothesis if

any point lies outside the control limits or if any clear pattern appears in the

distribution of the process values. Another insight from this analogy is that

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