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Cpk can Only be Calculated from Data that are Normally Distributed

  • Indium Corporation
  • Folks,

    Let's look in on Patty....

    Patty was really nervous.  As a matter of fact, there was no time she remembered being this nervous.  The cause of her nervousness?  She was going to teach a series of classes at Ivy University.  This opportunity came about because one of the professors at IU was in a serious accident.  A full recovery was expected, but there was no way the prof could finish the last three weeks of the statistics course she was teaching.  Things are hopping in the Engineering Department at IU, and the Dean could not find another prof to take over.  The Professor himself was too busy, however, when the Dean asked his advice he immediately recommended Patty.  Patty was honored by the request and would be more so if she knew the behind the scenes story.  IU has an unwritten rule that all teaching profs had to have a PhD, which Patty did not.  However, if Bill Gates wanted to teach, an exception would be made, as he is a world class technical executive.  Patty was hired under that exception.  She was stunned to see she was on the front page of “The Ivy U Review,” under the headline, “Famed Executive to Teach at IU.”

    Well, her first class was tomorrow and she took comfort in the fact that her husband, Rob, told her she shouldn’t be nervous.  Pete wasn’t much help. He told her he would be so nervous that he wouldn’t be able to eat.  It was just unnerving teaching the best and the brightest.  She was proud of her academic accomplishments at Tech, but this was IU, arguably one of the top 10 universities in the country.

    “Rob, I have to tell you, even though I’m still nervous, it comforts me to know that you wouldn’t be nervous,” she said to her husband.

    “I never said I wouldn’t be nervous, I said you shouldn’t be nervous. After all, you're Patty Coleman,” Rob replied.

    At this Patty burst into tears and Rob came over and gave her a big hug.

    “But, you’re smarter than me,” Patty insisted.

    “No way,” Rob replied.

    They then spent the next ten minutes arguing that the other was smarter.  Patty always felt she had a good business sense, but for understanding deep technical things, she believed Rob was her superior.  After a while they looked at each other and laughed.

    “Not too many couples would get in to an argument, saying that the other person was smarter,” Rob teased.

    Time passed quickly and Patty was soon in front of the 35 students in the class.  The topic was Cpk as the most important metric to determine the quality of a lot of material or product.   She asked the students if it was OK to average Cpks from different lots.  A student raised her hand.

    “Yes Emily.” said Patty. (Patty had ask the students to use nametags.)

    “No, Professor Coleman. One can’t average Cpks. The reason being that Cpk goes as one over the standard deviation and standard deviation is a squared term.  So one can’t average two lots and get the same result as taking the Cpk of all of the two lot data.

    Patty responded, “Emily is 100% correct.  Remember, when you get out in the working world, to always check to see that your suppliers are not averaging Cpks.  This might happen when half of the lot is below the spec, say the Cpk is 1.4 and the spec is 1.5 and the other half is over the spec, say 1.7.  The supplier will say that the lot is in spec because the average Cpk is 1.55.  This isn’t necessarily so, as Emily points out.  You should only accept a calculation of Cpk for the entire lot.”

    Patty chuckled that Emily thought she was a Professor, at Ivy U. Right!

    The class continued to go well and Patty began to relax.  As the class began to end, she mentioned another important point.

    “What important criteria must the data have to be considered acceptable to calculate Cpk?” Patty asked.

    There was a bit of murmuring and finally a boy (man?) raised his hand.  He looked 12 years old to Patty.

    “Yes, William,” Patty acknowledged him.

    “Dr. Coleman, I think the data must be normal,” William answered.

    “Dr. Coleman?” Patty thought.

    “Absolutely correct, William,” Patty responded.

    “Class, remember this point when you get out into industry.  Almost no one checks to see that the data are normal before calculating Cpk. The data must be normal to calculate Cpk.  I can’t tell you how many times I have rejected a lot of incoming material because the Cpk was calculated from non-normal data.  In some cases non-normal data can be transformed so that the data are normal, “ Patty continued.

    “Professor, how do we know if the data are normal?” a student named Kathy asked.

    “Stay tuned for the next lecture,” Patty chuckled and dismissed the class.

    As she was gathering her laser pointer, lap top etc., a number of students came to talk to her.  Emily was with a group of about 6 of them.

    “Professor, we just wanted to tell you that we are thrilled to have you as our instructor.  We appreciate your practical, real world perspective on statistics,” Emily said.

    Patty responded warmly and was close to being choked up by this show of respect and appreciation.  She decided she would walk to The Professor’s office to tell him how it went.

    On the way out, she heard one of the male students say to his friend, “You know, she is quite attractive for an older woman.”

    Patty didn’t know whether to laugh or cry.


    Dr. Ron