Page 450 - Design for Six Sigma for Service (Six SIGMA Operational Methods)

408 Chapter Eleven

process means will drift from time to time. When that happens, the prob-
ability calculation about nonconformance will be totally wrong when we
still use C . Therefore, one must consider where the process mean is
p
located relative to the specification limits. The index C is created to do
pk
exactly this.
⎧ USL − m m − LSL ⎫
C = Min ⎨ , ⎬ = Min{ C , C }
pk PU PL
⎩ 3 s 3 s ⎭
We have the following situation. The process standard deviation is s = 0.8
with a USL = 24, LSL = 18, and the process mean m = 22.

LSL = 18 Process USL = 24
center
Center = 22

−
⎧ 24 − 22 22 18 ⎫
C pk = Min ⎨ , ⎬ = Min 083 1 67( . , . ) = 083
.
×
×
⎩ 38 38 ⎭
It is also clear that
= 0.83 and C = 1.67
C PU PL
If the process mean is exactly centered between the specification limits,
= C = 1.25
C p pk
Example 11.8
For the film thickness data given in Example 11.1, LSL = 460 and USL = 660.
_
We do not know the exact value of m and s; however, we can calculate that y =
572.02 and s = 24.53. Because the sample size of this data set is fairly large
_
(n = 47), we can substitute m and s by using y and s. Then we have
−
⎧ 660 − 572 02 572 02 460 ⎫
.
.
C = Min ⎨ , ⎬ = Min 119 1 51) = 119
.
(. , .
×
×
pk
⎩ 324 53 324 53 ⎭
.
.
MINITAB can be used to conduct a comprehensive process capability analysis.
The following MINITAB output is the process capability analysis for the film
thickness data.