16-11 OTHER SPC PROBLEM-SOLVING TOOLS 639Sample Diameter Sample Diameter
1 9.94 14 9.99
2 9.93 15 10.12
3 10.09 16 9.81
4 9.98 17 9.73
5 10.11 18 10.14
6 9.99 19 9.96
7 10.11 20 10.06
8 9.84 21 10.11
9 9.82 22 9.95
10 10.38 23 9.92
11 9.99 24 10.09
12 10.41 25 9.85
13 10.36appear to be operating in a state of statistical control at the de-
sired target level?
16-40. The concentration of a chemical product is meas-
ured by taking four samples from each batch of material. The
average concentration of these measurements is shown for the
last 20 batches in the following table:Batch Concentration Batch Concentration
1 104.5 11 95.4
2 99.9 12 94.5
3 106.7 13 104.5
4 105.2 14 99.7
5 94.8 15 97.7
6 94.6 16 97.0
7 104.4 17 95.8
8 99.4 18 97.4
9 100.3 19 99.0
10 100.3 20 102.6(a) Suppose that the process standard deviation is 8 and
that the target value of concentration for this process is- Design a CUSUM scheme for the process. Does the
process appear to be in control at the target?
(b) How many batches would you expect to be produced with
off-target concentration before it would be detected by the
CUSUM control chart if the concentration shifted to 104?
Use Table 16-9.
16-41. Consider a standardized CUSUM with H5 and
K 1 2. Samples are taken every two hours from the
process. The target value for the process is 0 50 and
2. Use Table 16-9.
(a) If the sample size is n1, how many samples would be
required to detect a shift in the process mean to 51 on
average?
(b) If the sample size is increased to n4, how does this af-
fect the average run length to detect the shift to 51
that you determined in part (a)?
16-42. A process has a target of 0 100 and a standard
deviation of 4. Samples of size n1 are taken every two
hours. Use Table 16-9.
(a) Suppose the process mean shifts to 102. How many
hours of production will occur before the process shift is
detected by a standardized CUSUM with H5 and
K 1 2?
(b) It is important to detect the shift defined in part (a) more
quickly. A proposal is made to reduce the sampling
frequency to 0.5 hour. How will this affect the CUSUM
control procedure? How much more quickly will the shift
be detected?
(c) Suppose that the 0.5 hour sampling interval in part (b) is
adopted. How often will false alarms occur with this new
sampling interval? How often did they occur with the old
interval of two hours?
(d) A proposal is made to increase the sample size to n4 and
retain the two-hour sampling interval. How does this sug-
gestion compare in terms of average detection time to the
suggestion of decreasing the sampling interval to 0.5 hour?
16-11 OTHER SPC PROBLEM-SOLVING TOOLSWhile the control chart is a very powerful tool for investigating the causes of variation in a
process, it is most effective when used with other SPC problem-solving tools. In this section
we illustrate some of these tools, using the printed circuit board defect data in Example 16-4.
Figure 16-17 shows a Uchart for the number of defects in samples of five printed circuit
boards. The chart exhibits statistical control, but the number of defects must be reduced. The
average number of defects per board is 8 5 1.6, and this level of defects would require ex-
tensive rework.
The first step in solving this problem is to construct a Pareto diagramof the individual de-
fect types. The Pareto diagram, shown in Fig. 16-22, indicates that insufficient solder and solder
balls are the most frequently occurring defects, accounting for (109160) 10068% of thec 16 .qxd 5/8/02 9:58 PM Page 639 RK UL 6 RK UL 6:Desktop Folder: