Quality Quiz from Professor Cleary
"B" is the correct answer!
Click here for a more complete video explanation.
Allie Katt might want to consider returning to litter,
or at least reviewing her statistics textbook. This process is definitely
not in control.
This SQCpack chart indicates an out-of-control condition:
"Runs up," which Allie did not notice. Seven X-bars in
a row go progressively higher on the chart. This situation is somewhat
similar to that described in November's Quality Quiz in which we
discussed the situation in which seven X-bars were above the process
(x-bar) and seven R's above R-bar. In both cases, the process would
be declared out of control.
Let us examine the origin of the so-called rule
of 7. To understand the rule of 7, it is useful to illustrate with
a coin-toss example. What is the probability of getting a "heads"
by flipping a coin? The answer, as any student will attest, is 50%.
The chance of getting two "heads" with two coin tosses diminishes to 25%.
The following figure demonstrates this probability graphically:
This is called a probability tree, with four possible outcomes: HH, HT, TH, or TT. One way to respond to the question about the probability of two heads in a row with two flips of the coin is to say that it represents one possibility in four potential outcomes, or a one in four (25%) chance.
A second way to look at the question
is to introduce the probability multiplication rule:
P(A and B) = P(A) x P(B)
The probability that event A and B
occur is equal to the probability of event A taking place times
the probability of event B taking place. In this case, event A is
tossing a “heads” (.5), and event B is getting “heads” again.
P(heads and heads) = P(heads) x P(heads)
= .5 x .5
Introducing the concept of a control
chart and asking about the probability of seeing an increase on
the next sample, one can see that it would be 50% for a process
that is in control. The same would be true for the probability of
to go down on the next sample.
So the probability of two s
in a row going up can be illustrated with a sample space like the
coin flip, except that instead of heads and tails, it represents
X-bar going up or X-bar going down.
Therefore, the probability of getting
two s in a
row going up is .25.
The next question addresses the probability
of not two, but seven s
in a row going up.
A = up,
B = down
The likelihood of getting seven s
in a row going up when the process is in control is .0078
We still haven’t answered the question, “Why 7?” One answer is that when Ford Motor Company began utilizing SPC in process improvement, the company’s SPC manual designated 7. In manufacturing settings, this became somewhat of an industry standard. Statisticians Duncan and Hughes subscribe to 7, while AT&T and Western Electric insist on 8.
SQCpack or CHARTrunner users don’t have to worry about any of this, of course, since the software has built-in rules about 7 points above or below the process average. A user can change the out-of-control rules, either creating customized rules or selecting from more than 15 of the most commonly-used out-of-control tests. There are a number of out-of-control tests that are especially appropriate for healthcare applications, for example.
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