We have learned that 99.73% of the parts from a process in control will fall within 6 standard deviations of the mean or average (3 above the mean and 3 below the mean). This particular width, 6 standard deviations, is called the natural tolerance. Data from a screw machine indicates a process mean = .39483 and a standard deviation = .00011. What is the natural tolerance of this process?

So by the definition we have mean, m and standard deviation, s.

So the upper limit is m+ 3 s = 0.39483 + 3* 0.00011 = 0.39516

So the lower limit is m+ 3 s = 0.39483 – 3* 0.00011 = 0.39450

Hence the natural tolerance is 0.39450 to 0.39516

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