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CMA Intermediate · Operations Management and Strategic Management · Productivity Management and Quality Management

In a control chart for sample means, the centre line is 50 mm, and the standard error of the sample mean is 0.4 mm. Using 3-sigma limits, what are the upper and lower control limits?

The limits are 51.2 mm and 48.8 mm. Three-sigma control limits equal the centre line plus or minus three times the standard error of the mean: 3 × 0.4 = 1.2, so 50 + 1.2 = 51.2 and 50 − 1.2 = 48.8.

  1. A50.8 and 49.2
  2. B51.2 and 48.8Correct
  3. C51.2 and 49.2
  4. D52.0 and 48.0

Explanation

3-sigma limits are centre line ± 3 × standard error = 50 ± 3 × 0.4 = 50 ± 1.2, giving UCL 51.2 and LCL 48.8. Using 2 × 0.4 gives 50.8 and 49.2, which is wrong. Using 5 × 0.4 gives 52.0 and 48.0.

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