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Question 15:



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To calculate a z-score or process sigma for a two-sided spec you calculate a z for the lower spec and a z for the upper spec, add them to get a Z total and then use that to find the area under the normal curve. To get DPMO, or Defects Per Million Opportunities you multiply the area times 1 million. In the example above Z lower is (-0.00306 - -0.008) / 0.003642 = 1.357. Z upper is (0.008-0.00306)/ 0.003642 = 3.036. Z total is 1.357 + 3.036 = 4.39. The area above and below this value is the normal curve is the defect area.

A Z of 4.39 corresponds to .999994 of the area, so the defect area is .00035 or .035%. The DPMO is .00035 * 1 million = 345 defects per million opportunities. For a visual representation of Z-Scores see the Interactive Graph of the Standard Normal Curve.

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