Control Charts

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