Content By Scott A. Hindle

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By: Scott A. Hindle

When considering how good a production process is, it’s important to ask, “Can we expect the output to be fully conforming?” An assessment of process capability can answer this. Data are needed, but how many? Is “30” the right number? This article examines these last two questions.

First, why 30?

There’s an old joke about statisticians not knowing the difference between 30 and infinity, and figure 1 should shed light on its origin. Degrees of freedom, shown on the x-axis and hereafter referred to as “d.f.,” help to determine how precise, or “solid,” an estimate of standard deviation is, given its estimated uncertainty (the y-axis).1 Figure 1 shows that by the time an estimate of standard deviation is based on 30 d.f., it’s about as precise an estimate as it’s likely to get. (If 30 d.f. aren’t sufficient, getting up to 120 d.f.—a fourfold increase—is necessary to reduce the uncertainty by half.) This is potentially important because an estimate of standard deviation is essential to make an assessment of process capability possible.