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There is a difference between “out of control” and “unacceptable process performance.” A particular
process may operate in a state of statistical control but fail to perform as desired by the operator. In this
case, the system must be changed to improve the system performance. Using a control chart to bring it
into statistical control solves the wrong problem. Alternatively, a process may operate in a way that is
acceptable to the process operator, and yet from time to time be statistically out of control. A process
is not necessarily in statistical control simply because it gives acceptable performance as defined by the
process operator. Statistical control is defined by control limits. Acceptable performance is defined by
specification limits or quality targets—the level of quality the process is supposed to deliver. Specification
limits and control chart limits may be different.

Decision Errors
Control charts do not make perfect decisions. Two types of errors are possible:

1. Declare the process “out of control” when it is not.
2. Declare the process “in control” when it is not.

Charts can be designed to consider the relative importance of committing the two types of errors, but
we cannot eliminate these two kinds of errors. We cannot simultaneously guard entirely against both
kinds of errors. Guarding against one kind increases susceptibility to the other. Balancing these two
errors is as much a matter of policy as of statistics.
Most control chart methods are designed to minimize falsely judging that an in-control process is out
of control. This is because we do not want to spend time searching for nonexistent assignable causes or
to make unneeded adjustments in the process.

Constructing a Control Chart

The first step is to describe the underlying statistical process of the system when it is in a state of
statistical control. This description will be an equation. In the simplest possible case, like the ones studied
so far, the process model is a straight horizontal line and the equation is:
Observation = Fixed mean + Independent random error

or
y t = η + e t

If the process exhibits some drift, the model needs to be expanded:
Observation = Function of prior observations + Independent random error

y t = fy t−1 , y t−2 ,…) + e t
(
or
Observation = Function of prior observations + Dependent error

(
(
y t = fy t−1 , y t−2 ,…) + ge t , e t−1 ,…)
These are problems in time series analysis. Models of this kind are explained in Tiao et al. (2000) and
Box and Luceno (1997). An exponentially weighted moving average will describe certain patterns of
drift. Chapters 51 and 53 deal briefly with some relevant topics.
© 2002 By CRC Press LLC