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Chapter 19: B. Statistical Process Control 285
EXAMPLE 19.8
Consider the data on computer chips in Table 19.5, Example 19.6. Construct an np chart
for these data and verify whether the process is stable or not.
From the control chart in Figure 19.12 we observe that all the points are well within
the control limits. However, as in Figure 19.10, starting from point number nine, seven
successive points fall below the center line. This indicates that from day nine through
15, the number of nonconforming was relatively low. Investigation to determine the
process conditions on these days should be made so that similar conditions can be
replicated for future use. Otherwise, since all the points of the current data fall within
the control limits, the trial control limits can be extended for use over the next 30 days,
when the control chart should again be reevaluated.
np Chart for Nonconforming Computer Chips
18
16
UCL = 17.01
14
Sample count
12
10
8
6
n – p – = 8.37
4
2
0
Figure 19.12
3 6 9 12 15 18 21 24 27 30
Sample
LCL = 0
np chart for nonconforming computer chips, using trial control limits for
the data in Table 19.5.
Part IV.B.4
c is distributed according to a Poisson probability distribution with parameter
l, where l is the average number of nonconformities per inspection unit. The
Poisson probability distribution is defined as
x
e
p( l l
x)= , x = 0123 , , , ,...
(19.44)
x!
where the mean and the variance of the Poisson distribution are given by l. Now
suppose that we select m samples, with each sample being one inspection unit,
and let the number of nonconformities in these samples be c 1 , c 2 , c 3 , . . . , c m respectively.
Then the parameter l, which is usually unknown, is estimated by