There’s a certain manufacturer makes carbon-based friction material in the form of a disk. A press and die are used in the final manufacturing operation to cure the carbon material into a functioning friction pad. Peak temperature uniformity is a critical characteristic during the cure cycle. Eight thermocouples are placed in the die to capture the temperatures during the cure cycle. Each cycle’s peak temperature at each thermocouple is recorded for SPC purposes.

As the company’s statistical process control expert, what’s the most appropriate and efficient charting method to determines patterns of uniformity of the peak temperatures among the eight thermocouple locations?

A) An Xbar and Range chart with a sample size of eight.
B) A Group individuals and moving-range chart with eight process streams.
C) An Xbar and sigma chart with a sample size of eight.
D) Eight individuals and moving-range charts—one for each thermocouple location.
E) A Target 3D Xbar and sigma chart with a sample size of eight.

B is the right answer. Each thermocouple location is a unique process stream with individual statistical personalities. The heat and pressure profile may be different at the top of the die than at the bottom. Therefore, each location needs to be treated as separate sets of data. One needs to be able to determine if the locations are behaving the same and if they aren’t, one will need to be able to determine which location(s) are different than the rest. To learn more, please visit www.infinityqs.com/content.asp?contentid=630.

Answers A and C are incorrect because converting the eight locations into a simple range or sigma chart confounds the effects of the eight locations. If the range or sigma chart were misbehaving, one wouldn’t be able to tell what area of the die was causing the problem. Confounding multiple process streams into a single subgroup is a common mistake seen in industry. Not only are the individual process streams “hidden,” but also the resulting control limits are confounding among all the process streams. Lastly, the centerline on the range of sigma chart would represent the variation of a single cycle (within cycle variation), whereas the Xbar chart represents the cycle-to-cycle variation. Because the Xbar control limits are a function of the range or sigma centerline, this approach would be incorrectly applying a within-cycle estimate of variation to a set of plot points that are tracking cycle-to-cycle variation. Two different components of variation are being incorrectly.

Answer D would be the second best answer. Monitoring each thermocouple location on its own individuals and moving-range chart is statistically correct. However, this approach is a bit inefficient and makes a difficult job of looking for comparative patterns among the locations. Those of you that have never heard of group charts should have picked answer D.