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of typical performance. If typical performance were random variation about a fixed mean, the picture
can be a classical control chart with warning limits and action limits drawn at some statistically defined
distance above and below the mean (e.g., three standard deviations). Obviously, the symmetry of the
action limits is based on assuming that the random fluctuations are normally distributed about the mean.
A current observation outside control limits is presumptive evidence that the process has changed (is
out of control), and the operator is expected to determine what has changed and what adjustment is
needed to bring the process into acceptable performance.
This could be done without plotting the results on a chart. The operator could compare the current
observation with two numbers that are posted on a bulletin board. A computer could log the data, make
the comparison, and also ring an alarm or adjust the process. Eliminating the chart takes the human
element out of the control scheme, and this virtually eliminates the elements of quality improvement and
productivity improvement. The chart gives the human eye and brain a chance to recognize new patterns
and stimulate new ideas.
A simple chart can incorporate rules for detecting changes other than “the current observations falls
outside the control limits.” If deviations from the fixed mean level have a normal distribution, and if
each observation is independent and all measurements have the same precision (variance), the following
are unusual occurrences:

1. One point beyond a 3σ control limit (odds of 3 in 1000)
2. Nine points in a row falling on one side of the central line (odds of 2 in 1000)
3. Six points in a row either steadily increasing or decreasing
4. Fourteen points in a row alternating up and down
5. Two out of three consecutive points more than 2σ from the central line
6. Four out of five points more than 1σ from the central line
7. Fifteen points in a row within 1σ of the central line both above and below
8. Eight points in a row on either side of the central line, none falling within 1σ of the central line

Variation and Statistical Control

Understanding variation is central to the theory and use of control charts. Every process varies. Sources
of variation are numerous and each contributes an effect on the system. Variability will have two
components; each component may have subcomponents.

1. Inherent variability results from common causes. It is characteristic of the process and can
not be readily reduced without extensive change of the system. Sometimes this is called the
noise of the system.
2. Identifiable variability is directly related to a specific cause or set of causes. These sometimes
are called “assignable causes.”

The purpose of control charts is to help identify periods of operation when assignable causes exist in
the system so that they may be identified and eliminated. A process is in a state of statistical control
when the assignable causes of variation have been detected, identified, and eliminated.
Given a process operating in a state of statistical control, we are interested in determining (1) when
the process has changed in mean level, (2) when the process variation about that mean level has changed
and (3) when the process has changed in both mean level and variation.
To make these judgments about the process, we must assume future observations (1) are generated by
the process in the same manner as past observations, and (2) have the same statistical properties as past
observations. These assumptions allow us to set control limits based on past performance and use these
limits to assess future conditions.
© 2002 By CRC Press LLC