Design specifications require that a key dimension on a product measure 100 10 units. A process being considered for producing this product has a standard deviation of four units.

Questions

4.1

If the process mean is centered (i.e., equal to the spec mean), what can you say (quantitatively) regarding the process capability? Calculate the Cpk and interpret it.

4.2

Suppose the process average shifts to 92. Calculate the new process capability (Cpk).

4.3

What can you say about the process after the shift? (Interpret the new Cpk in item 4.2)

4.4

If the process mean is centered, to achieve four sigma quality (i.e., Cpk = 1.33), what should be the process standard deviation? (hint: the process standard deviation is part of the denominator in the Cpk formula)

Factor for Determining 3-Sigma Limits for R-bar and x-bar Charts Factor for R Chart Number of Observatio Factor Lower Upper ns in for x-bar Control Control Subgroup Chart Limit Limit A2 D3 n D4 N AW 5 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31 0.29 0.27 0.25 0.24 0.22 0.21 0.20 0.19 0.19 0.18 0.00 0.00 0.00 0.00 0.00 0.08 0.14 0.18 0.22 0.26 0.28 0.31 0.33 0.35 0.36 0.38 0.39 0.40 0.41 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 1.69 1.67 1.65 1.64 1.62 1.61 1.60 1.59