Quality Quiz
Last month, Bjorn Luzer found himself
stumped by the first question he encountered about sample sizes, but
since that time he has reviewed everything he can find in order to avoid
future embarrassment among his colleagues or worse, wrath from his boss.
While he is loudly explaining his theories about sample size to Rock
deBote, his boss, one of the inspectors at Iffy Products approaches to
ask how to frame a capability study. This inspector, Norm L. Kurv, makes
Bjorn a little nervous, since he seems to know more about statistics
than Bjorn himself. And now here he is, doing a capability study for one
of the product parts that he holds in his hand.
'I got the specification limits, used a control chart to be sure that
the process is in control, and made a histogram that seems to form a
normal distribution, ' Norm reports. He is particularly adept at noting
normal distributions. His calculation of the Cpk matches what Bjorn
himself finds when he enters the same data into SQCpack 2000, Bjorn congratulates Norm, but realizes that he better get rid of him
before he asks another question.
Sure enough, as he is leaving, Norm turns to Bjorn Luzer and asks about
the calculation of the estimated sigma:
Norm noted that the table shows the value of d2 becoming smaller as the
sample size becomes larger, and turned to Bjorn to discover the basis
for this:
d2 1.128
1.693
2.059
2.326
n
2
3
4
5
Rock DeBote finds the question to be an interesting one, and turns to
Bjorn for a response.
'Well, it's clear that they go up together because of correlation.
They are correlated. And besides, the rsquared (r^{2}) is equal
to .89. ' He breathes a sigh of relief. Is Bjorn Luzer off the
hook?
A) Yes. He has hit a lucky answer.
B) No. Without further study of capability, he will
continue to disseminate misinformation such as this.
