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12

Fundamentals of Process Control Charts

KEY WORDS action limits, autocorrelation, control chart, control limits, cumulative sum, Cusum
chart, drift, EWMA, identifiable variability, inherent variability, mean, moving average, noise, quality
target, serial correlation, Shewhart chart, Six Sigma, specification limit, standard deviation, statistical
control, warning limits, weighted average.

Chapter 11 showed how to construct control charts to assure high precision and low bias in laboratory
measurements. The measurements were assumed to be on independent specimens and to have normally
distributed errors; the quality control specimens were managed to satisfy these conditions. The labo-
ratory system can be imagined to be in a state of statistical control with random variations occurring
about a fixed mean level, except when special problems intervene. A water or wastewater treatment
process, or a river monitoring station will not have these ideal statistical properties. Neither do most
industrial manufacturing systems. Except as a temporary approximation, random and normally distributed
variation about a fixed mean level is a false representation. For these systems to remain in a fixed state
that is affected only by small and purely random variations would be a contradiction of the second law
of thermodynamics. A statistical scheme that goes against the second law of thermodynamics has no
chance of success. One must expect a certain amount of drift in the treatment plant or the river, and
there also may be more or less cyclic seasonal changes (diurnal, weekly, or annual). The statistical name
for drift and seasonality is serial correlation or autocorrelation. Control charts can be devised for these
more realistic conditions, but that is postponed until Chapter 13.
1
The industrial practitioners of Six Sigma programs make an allowance of 1.5 standard deviations for
process drift on either side of the target value. This drift, or long-term process instability, remains even after
standard techniques of quality control have been applied. Six Sigma refers to the action limits on the control
charts. One sigma (σ) is one standard deviation of the random, independent process variation. Six Sigma
action limits are set at 6σ above and 6σ below the average or target level. Of the 6σ, 4.5σ are allocated to
random variation and 1.5σ are allocated to process drift. This allocation is arbitrary, because the drift in a real
process may be more than 1.5σ (or less), but making an allocation for drift is a large step in the right direction.
This does not imply that standard quality control charts are useless, but it does mean that standard charts
can fail to detect real changes at the stated probability level because they will see the drift as cause for alarm.
What follows is about standard control charts for stable processes. The assumptions are that variation
is random about a fixed mean level and that changes in level are caused by some identifiable and
removable factor. Process drift is not considered. This is instructive, if somewhat unrealistic.

Standard Control Chart Concepts
The greatest strength of a control chart is that it is a chart. It is a graphical guide to making process
control decisions. The chart gives the process operator information about (1) how the process has been
operating, (2) how the process is operating currently, and (3) provides an opportunity to infer from this
information how the process may behave in the future. New observations are compared against a picture

1
Six Sigma is the name for the statistical quality and productivity improvement programs used by such companies as Motorola,
General Electric, Texas Instruments, Polaroid, and Allied Signal.

© 2002 By CRC Press LLC