 |
 |
 |
 |
 |
 |
 |
|
|
 |
 |
 |
 |
 |
 |
 |
 |
|
|
|
Applications , page 6 |
|
|
|
Exercise 5: Determine the Cpk ratio of the current production. Refer to the statistics review pages for information about capability ratios. Since the process on the previous pages is in statistical control, it is possible to calculate the Cpk ratio. If special causes are present (indicated by a lack of statistical control) the process is subject to arbitrary changes, making a capability calculation unreliable. The capabilty ratio will also be inaccurate if the individual observations are not normally distributed, given the small sample size often used. To decide whether capability can be determined, make a histogram of the observations to be sure they are at least free of extreme skewness or outliers. |
|
|
|
Discussion. Figure 21 shows that the Cpk ratio is too low. The process center is close to the center of the specification limits, but process variability as measured by the Cpk calculation, is wider than the specifications. The solution is to decrease the variability of the hardness measures or to relax the specifications. Specifications can be set unrealistically tight. If the engineers can be persuaded to widen the specifications, the specs will be more in line with manufacturing.
A spreadsheet permits quick recalculation of the Cpk ratio to see the effect of widening the hardness tolerances.
|
|
|
|
 |
|
|
|
Fig. 21. Cpk calculation using a spreadsheet.
|
|
|
|
 |
|
Changing the LSL to 55 and the USL to 60 gives a new Cpk of 1.1 (figure 22). Since the distance to the nearest specification is now greater than 3 times the estimated process standard deviation, the Cpk is greater than one. The process is now "capable". |
|
|
Fig. 22. This Cpk indicates a capable process.
|
|
|
 |
|
Figure 23 shows how a change in the process center (from 57.6 to 57.9) changes the Cpk even though the process variability has not changed. This is the advantage of the Cpk as a measure of capability, compared to the Cp and PCI ratios. |
|
|
|
Fig. 23. A decreased distance to the upper specification limit.
|
|
|
|
Statistics and SPC: 1 2 3 4 5 6 7
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|