Hartford Simsack needed a vacation. The quality manager was suffering the effects of stress derived not only from
the pressures of running his quality department and keeping his past prison record from surfacing among his customers but also from his frantic efforts to appear to understand statistics in spite
of his limited experience. When he took this position with Greer Grate & Gate, the only normal distribution he knew was among his fellow inmates--definitely an abnormal distribution--and the
only probability he understood was that he likely wouldn't be let off parole for a while. In spite of this limited background, Simsack had managed to both exploit the
knowledge of his professor at the community college where he was taking a beginning statistics course and successfully fool his subordinates about his level of knowledge. But it wasn't easy to
keep up the facade of a statistician when there was so little behind it, and he was definitely stressed out. Simsack felt tired and confused by the questions that people had
left for him on his work e-mail and voicemail. Fortunately, there was an easy one among the inquiries, or at least that was Simsack's feeling when a supplier asked for a capability study. You
will remember that Ms. X. Trusion of Rhott Iern Products had requested capability data earlier, so Simsack had at least had some experience with the concept. X. Trusion's colleague,
Bendon Brake, was looking for more current data. From his prior experience, Simsack knows, for example, that he needs to do an X-bar and R chart to establish whether the
process is in control. Indeed, the chart reflects process stability, with a sample size of four. After examining the chart, Simsack recalls the warnings of his statistics professor--Dr. Stan
Deviation--that one must check for normalcy of the data, so he has used software to check this distribution. "Aha!" he exclaims knowingly. "The specification
limits on this chart seem to be exactly equal to the control limits. What luck: Everything is fine. Because the control limits and spec limits are the same, the Cpk value is equal to 1." He
leaves a message to that effect for Brake. After smugly explaining his solution to the capability question on Brake's voicemail, Simsack decides he's earned a break from the
demands that are made on him, so he visits Dr. Deviation. He casually shares his interpretation of the Rhott Iern data, adding triumphantly, "When I saw that the spec limits
and control limits coincided, of course there was no question about the Cpk." As we may have already noticed, Simsack's statistical knowledge is grounded in fear of
discovery rather than in genuine interest in learning--or even in common sense. So his conclusion is subject to scrutiny, at the very least. What do you think Deviation will want him to
understand about his process? "You idiot!" Deviation exclaims, then quickly regains his composure and begins to explain the
differences between control limits and specification limits, his voice shaking only slightly as he struggles to control his response. "Control limits are recorded on
control charts," the professor says in his Dick-and-Jane voice. "Ri-i-ight?" Simsack nods, still shocked by the response of his respected professor to what he
had thought was a glory moment. "Control charts display averages, not individual values," Deviation continues. "This is why 99.73 percent of the averages can be
expected to fall within the upper and lower control limits. If, indeed, control limits and spec limits are the same, with a sample size of four, one would find a number of points (approximately
13%) outside spec and a Cpk, by definition, less than 1. "On the other hand, spec limits reflect individual parts, not averages. They are sometimes referred to as the
'voice of the customer,' while control limits are the 'voice of the process.' Just because a process is in control doesn't mean that it's capable. Spec limits are ways of identifying the
relationship of individual values to engineering or design specifications. They are created by designers of a product or process rather than by the data itself."
Chastened, Simsack resists the impulse to take notes, or even to make any clever comments. He will attempt to salvage his dignity when he runs to his car and writes everything down as if he
has really understood. About the author Michael J. Cleary, Ph.D., is founder and
president of PQ Systems Inc. He has published articles on quality management and statistical process control in a variety of academic and professional journals. E-mail Cleary at mcleary@qualitydigest.com. |
