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Manufactured parts exhibit dimensional variation that is usually modeled statistically by the Gaussian bell curve or "normal" distribution. The average value of the distribution is the process mean (m). And m is designed to be as close as possible to the desired outcome of a manufacturing process. Fluctuations about the process mean usually are characterized by the standard deviation (sigma).
A normal distribution can be used to express the quality level of a manufacturing process. Mathematically, 68 percent of a normal distribution lies within the first standard deviation (m+/-sigma), and 95 percent lies within two standard deviations (m+/-2-sigma). A "one-sigma process" would produce 32 percent defects (100-68 percent)--a two-sigma process 5 percent defects (100-95). A six-sigma process, therefore, produces only 0.0000002 percent defects.
The process mean of a manufacturing process, though, usually shifts or drifts with time while the statistical variation about the mean remains unchanged. By convention, provisions are made in the statistical model for shifts as great as +/-1.5-sigma. Figure 1 shows a normal distribution with no shift, as well as normal distributions shifted +/-1.5-sigma. (Figure 1 omitted) The distribution of an unshifted process has only a small portion of the distribution outside the 3-sigma specification limit. But a process that has shifted 1.5-sigma produces a...