Surfstat.australia: an online text in introductory Statistics
STATISTICAL INFERENCE
STATISTICAL CONTROL CHARTS
Introduction
Control chart techniques are sometimes referred to as Statistical
Process Control (SPC) although the term now often is used to describe a
broader range of statistical methods for quality improvement.
A control chart is essentially a time plot (or run chart) of
observations with control limits added. The purpose of the control
limits is to indicate when the variability of the process is so great
that some special cause is likely to be operating. When a
process observation exceeds the control limits a search for a special
cause should be initiated.
Continuous quality improvement is more concerned with analytical
studies than enumerative ones. It is important to know WHY a process is
not performing to its capabilities; and when it is performing well, one
should be able to confidently predict its future performance.
Fundamental Principles
There are a few fundamental principles, to do with statistical thinking,
which underlie the construction and use of control charts:
- Variability is all around us. No two things in this world are
exactly identical. Even two measurements of the same thing will differ
if the measuring instrument is sufficiently precise.
- All processes have outputs, upon which measurements can be taken.
Processes, then, must exhibit variability.
- Any process has an inherent level of natural variability. This may
be small or large, acceptable or unacceptable, depending on the
process. With sufficient data we may be able to set the natural limits
of variability probabilistically; any observation falling outside these
limits is a signal that something unusual is happening - we should
investigate.
- A well behaved process may be expected to fluctuate randomly within
its natural limits of variability. Any non-random pattern, such as a
steady upward trend, is again an indication that something unusual is
occurring - again, we should investigate.