16-4 INTRODUCTION TO CONTROL CHARTS 6051LCL2 3 4 5 6 7 8 9 10111213141516171819202122232425
Sample numberUCLCenter
linexFigure 16-4 An
control chart.X1LCL23456789101112131415Center
lineUCL
xSample numberFigure 16-5 An
chart with a cyclic pat-
tern.Xis called a run down. This control chart has an unusually long run up (beginning with the fourth
point) and an unusually long run down (beginning with the eighteenth point).
In general, we define a run as a sequence of observations of the same type. In addition to
runs up and runs down, we could define the types of observations as those above and below the
center line, respectively, so two points in a row above the center line would be a run of length 2.
A run of length 8 or more points has a very low probability of occurrence in a random
sample of points. Consequently, any type of run of length 8 or more is often taken as a signal
of an out-of-control condition. For example, eight consecutive points on one side of the cen-
ter line will indicate that the process is out of control.
Although runs are an important measure of nonrandom behavior on a control chart, other
types of patterns may also indicate an out-of-control condition. For example, consider the
chart in Fig. 16-5. Note that the plotted sample averages exhibit a cyclic behavior, yet they all
fall within the control limits. Such a pattern may indicate a problem with the process, such as
operator fatigue, raw material deliveries, and heat or stress buildup. The yield may be im-
proved by eliminating or reducing the sources of variability causing this cyclic behavior
(see Fig. 16-6). In Fig. 16-6, LSLand USLdenote the lower and upper specification limits of
the process. These limits represent bounds within which acceptable product must fall and they
are often based on customer requirements.
The problem is one of pattern recognition,that is, recognizing systematic or nonrandom
patterns on the control chart and identifying the reason for this behavior. The ability to interpretXc16.qxd 5/22/02 2:43 PM Page 605 RK UL 6 RK UL 6:Desktop Folder:TOD Y {22/5/2002} CH 16: