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3-Sigma Control Limits

Jim Outfitters makes custom fancy shirts for cowboys. The shirts could be flawed in various ways, including flaws in the weave or color of the fabric, loose buttons or decorations, wrong dimensions, and uneven stitches. Jim randomly examined 10 shirts, with the following results:

Shirt Defects
1 8
2 0
3 7
4 12
5 5
6 10
7 2
8 4
9 6
10 6

a) Assuming that 10 observations are adequate for these purposes, determine the 3-sigma control limits for defects per shirt?

b) Suppose that the next shirt has 13 flaws. What can you say about the process now?

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The standard deviation of the number of defects is 3.559, and the mean is 6. So, lets look at how many shirts fall within 1, 2, and 3 standard deviations of the mean.

One standard deviation; 6 ± 3.559 = (2.441, 9.559): 6 shirts
Two standard deviations; 6 ± 7.118 = (-1.118, 13.118): 6 + 4 = 10 shirts
Three ...

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