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It's Wrong to Average or Add Cp and Cpk

Folks,

Patty had been working with engineering on a new product that needed a very precise and controlled volume of the stencil printed “brick” of solder paste on the PWB pads.  The product had many 01005 passives and CSPs with 30 mil spacings and the application was “mission critical.” So solder joint integrity was critical. The critical factor in obtaining this solder joint integrity was a consistent volume in the stencil printed brick. Her favorite solder paste gave a Cp and Cpk of 1.5 in 500 prints. The upper and lower spec limits were 60% and 140% of the aperture volume.

Purchasing called to tell her that XLK company just announced a solder paste with a Cp and Cpk greater than 3, under the same printing conditions that this product required. Needless to say Patty was skeptical. When she looked at the report, she groaned. The data were collected by Mort Bittler. She had seen him give several presentations and he always seemed to misrepresent the data to make his company’s solder paste look better than it was. She was on her way to a team meeting and expected that this new “break through” would be discussed.

As the meeting came to order, the VP of Engineering, Todd Hamilton, spoke.

“I saw this new data from XLK with a printing Cpk = of 3.72, we will use this paste,” Todd commanded.

“What a minute,” Patty responded, “the decision on which solder paste to use is with my group.”

“But you group has dropped the ball, how could you not know about this superior paste?” Hamilton challenged.

“We have evaluated their pastes continuously, they have always been second rate,” Patty shot back.

“Well things have changed, get with it Coleman, this project is too important,” Todd shouted.

Patty was really angry, technically Todd was her superior, but she found his attitude and words insulting. Using her last name was a bit unfriendly too.

“I’ll travel to XLK tomorrow and review their data,” Patty responded, her voice shaking more from anger than anything else.

She called Mort Bittler and he was available, so he agreed to meet with her the next day.

As she hung up, Pete showed up at the door, “Hey kiddo, how’s it going?” Pete asked.

“You were at the meeting, so what do you think? Hamilton impugned all of us,” Patty said flatly.

“Anyway I can help?” Pete asked.

“Why don’t you go with me to XLK tomorrow, it might be good to have two people check the data.

Fortunately XLK was only 120 miles south of their southern New Hampshire office.  

Pete had become one of her best friend’s in the past year. They spoke in Spanish the whole way to XLK to get their skill level up. Patty had also taught Pete some Mandarin, but it was slow going. After 120 minutes of discussing the PGA Tour vis a vis Tiger Woods, in Spanish, they arrived at XLK. Mort was waiting.

Mort was 45 years old, with a thick Boston accent. He came across as being knowledgeable ….. to someone who wasn’t knowledgeable.   

After brief pleasantries, Patty asked to see the raw data.

“Patty, I already made the calculations, why do you need to see the raw data?” Mort asked.

“The Professor always told me to ‘look at the raw data,’” often one can glean things that the final calculations don’t show,” Patty answered evenly.

“Well maybe later, let me show you how we took the data first,” replied Mort evasively.

Patty and Mort went to the printing lab and Patty noticed that Pete was not with them.

After verifying that the printing process was reasonable, Patty asked if she could have a little time with Pete……if she could find him.

Patty and Mort found Pete in the break room. 

“Pete let’s pow-wow for a while,” Patty said.

Mort said he would go answer some emails and they would meet in 30 minutes.

“Pete, where have you been? You’re not going to embarrass me again are you?” Patty pleaded.

“Me embarrass anyone?” Pete sheepishly replied.

“I found the person who took the data, Beth Thompson,” Pete went on, “she told me they average Cpks.”

“Not again, Patty groaned, we just went through that with a vendor last week, when will they learn that it’s wrong to average Cpks.

In 30 minutes they went to Mort’s office. All agreed to go lunch.

After ordering, Patty asked, “Mort what are your thoughts on averaging Cpks?”

Mort seemed defensive, and he squirmed a little, finally he said, “seems OK to me, it’s just like averaging golf scores.”

“What about the non linearity of the standard deviation in the Cpk equation?” Patty asked.

Mort was clearly not grasping the issue.

Patty continued, “If you have two sets of data and calculate the Cpk of each and average them, you will not get the same result as if you calculated the Cpk of the data added together. One of the reasons is that the standard deviation is non-linear. For the same reason it is wrong to add Cpks together”

Patty came right out and asked, “Did you average the Cpks?”

“Yes,” Mort said glumly.

“Let’s look at the data when we get back from lunch,” Patty insisted.

When they looked at the data it showed Patty’s point, four runs, of 100 samples each, had Cpk’s of around 1.2 to 1.3 and one run had a Cpk of 15.56. The average Cpk was 3.73, but if one takes the data all together, the Cpk is 1.58. Patty had calculated the total Cpk on the spot with Minitab.

Cp Cpk

The Cp and Cpk Data.  The correct results, calculated by Patty, are in the last row.

“But the 1.58 still is quite good,” Mort pleaded.

“But the data suggest, that run 5 is a fluke, it is clearly not from the same population as runs 1-4. Let’s go out to the lab and run another 100 data points to see if we can reproduce run 5,” Patty asked, while essentially insisted.

 

They ran another 100 and the Cpk was 1.28. On the way over Pete whispered in Patty’s ear that he had more vital intel to share with her on the way home.

With the end of the data collection, Patty and Pete were done, so they headed home.

“OK, what is the vital intel you need to share with me?  she asked Pete in Spanish?

“While you were collecting data with Mort, I visited Beth again. She told me that Mort had her collect 150 data points on run 5 and he threw out the 50 points furthest from the mean. You were right, run 5 was from another population, a cheating one,” Pete chuckled.

“Well, I guess we will still use our favorite solder paste,” Patty summed up.

 

Cheers,

Dr. Ron