The Classic Shewhart Charts

The principles of SPC are more important than the actual statistics. For our discussion assume that a business is following those principles; meaning that there is an operational definition of quality based on actual measurements; that we have identified the process involved; and that we have taken measurements of the products. Using these measurement data, we can produce the classic Shewhart charts.

Control Charts—Xbar: Using measurements from samples taken at regular intervals, calculate the mean measurement from each sample.367a Plot these over time. Given past data on these measurements, we know what the mean and standard deviation should be. Control lines on the plot show the UCL (upper control line) and LCL (lower control line), indicating the expected variation in this measurement. In some instances, a specification line is also plotted, indicating the range beyond which the measurement is beyond specifications.368 An example, generated by the simple program below, is Figure 14-1, "Xbar chart."

366 Quesenberry, SPC Methods for Quality Improvement, Chapter 1; citing W.Edward Deming, Out of the Crisis (Cambridge MA: MIT Press, 1986).

367 Quesenberry, SPC Methods for Quality Improvement, Chapter 1.

367a Because the sample mean of a distribution is often symbolized as X,these are known as "X bar charts."

368 "Out of Spec" does not mean "out of control." Control is based on predictable variation. A process that is "in control" will occasionally produce, due to statistical variation, outliers. Furthermore, specifications may be set by those unfamiliar with the variation in manufacturing processes, or may be substantially looser or tighter than the predicted variation.

FIGURE 14-1 Xbar chart.

Control Charts—S Charts: An S chart plots the standard deviation of the samples taken at regular intevals. Such a chart visually indicates when a process starts to exhibit increasing variation and, thereby, threatens to go out of control. Using this chart in conjunction with the Xbar chart provides a well-balanced view of the quality of the manuf acturing output. See Figure 14-2, "S chart."

Capability Chart: A capability analysis uses information on variation in past measurements together with proposed specifications and statistical distributions. With this information, assuming the process remains in control, we can predict the share of parts that will be outside the specification. See Figure 14-3, "Capability chart."

These figures, produced on a workstation, provide a supervisor on the assembly line strong information about the quality of the parts being produced.

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