ControlCharts are
TimeSeriesPlots whose vertical axes measure observed values of a variable (weight, diameter, ...) or counts (or percentages) of an attribute (not acceptable, defective, ...). Their purpose is to move
QualityControl from the end of a process, when corrections are expensive and information that might improve the process is lost, to individual work stations.
A statistician, engineer, or other knowledgeable person develops a
SamplingPlan that directs the worker's data collection. S/he chooses a small sample (often five items or fewer) according to a stated rule at a specified interval. The example involves a variable but the process is essentially the same for attributes. Each item is measured and the
SampleMean and
SampleRange are calculated. The calculated values are plotted on a pair of
ControlCharts, one for means (the X-Bar chart) and the other for Ranges (the R-Chart).
Regardless of the actual distribution, the distribution of errors is assumed to be Normal (bell-shaped) with mean and variance specified in the object's design. Values plotted on the vertical axis are therefore expected to follow the Normal distribution; about 68% within one
StandardDeviation of the mean, about 95% within two
StandardDeviations, and well over 99% within three
StandardDeviations.
Workers are instructed to correct or seek help in correcting process problems if either the
SampleMean or
SampleRange are more than three standard deviations from the mean. In some contemporary settings, workers are required to stop the process until it is fixed. At least some Japanese auto manufacturers, for example, use such a process. The worker pulls a cord that stops the line and sets of a siren and flashing red light. Engineers and others assigned to correct problems rush to the work station and the line is restarted only when the problem is resolved.
Perhaps more important than
ControlCharts themselves,
WalterShewhart developed tables and formulas that allow the substitution of
SampleRanges for
StandardDeviations.
ControlCharts were developed in the 1920's, well before pocket calculators, at a time that most factory workers had limited educations. Calculating a
SampleRange is both easy to do and more easy to understand than a
StandardDeviation.
--
GeorgeBrower