Applied Statistics and Probability for Engineers

614 CHAPTER 16 STATISTICAL QUALITY CONTROL

16-1. An extrusion die is used to produce aluminum rods.

The diameter of the rods is a critical quality characteristic. The

following table shows and rvalues for 20 samples of five

rods each. Specifications on the rods are 0.5035 0.0010 inch.

The values given are the last three digits of the measurement;

that is, 34.2 is read as 0.50342.

x

(a) Using all the data, find trial control limits for and R

charts, construct the chart, and plot the data.

(b) Use the trial control limits from part (a) to identify

out-of-control points. If necessary, revise your control

limits, assuming that any samples that plot outside the

control limits can be eliminated.

16-2. Twenty-five samples of size 5 are drawn from a

process at one-hour intervals, and the following data are

obtained:

(a) Find trial control limits for and Rcharts.

(b) Repeat part (a) for and Scharts.

16-3. The pull strength of a wire-bonded lead for an inte-

grated circuit monitored. The following table provides data for

20 samples each of size three.

(a) Use all the data to determine trial control limits for

and Rcharts, construct the control limits, and plot the

data.

X

X

X

a

25

i 1

xi362.75 (^) a
25
i 1
ri8.60 (^) a
25
i 1
si3.64
X
(b) Use the control limits from part (a) to identify out-of-control
points. If necessary, revise your control limits assuming that
any samples that plot outside of the control limits can be
eliminated.
(c) Repeat parts (a) and (b) for Xand Scharts.
16-4. Samples of size n6 are collected from a process
every hour. After 20 samples have been collected, we calcu-
late and
(a) Find trial control limits for and Rcharts.
(b) If , determine trial control limits for and S
charts.
16-5. Control charts for and Rare to be set up for an im-
portant quality characteristic. The sample size is n5, and
and rare computed for each of 35 preliminary samples. The
summary data are
(a) Find trial control limits for and Rcharts.
(b) Assuming that the process is in control, estimate the
process mean and standard deviation.
16-6. Control charts are to be constructed for samples of size
n4, and and sare computed for each of 20 preliminary sam-
ples as follows:
a
20
i 1
xi (^4460) a
20
i 1
si271.6
x
X
a
35
i 1
xi (^7805) a
35
i 1
ri 1200
x
X
sc 4 1.5 X
X
x20.0 r d 2 1.4.
EXERCISES FOR SECTION 16-5
Sample r
1 34.2 3
2 31.6 4
3 31.8 4
4 33.4 5
5 35.0 4
6 32.1 2
7 32.6 7
8 33.8 9
9 34.8 10
10 38.6 4
11 35.4 8
12 34.0 6
13 36.0 4
14 37.2 7
15 35.2 3
16 33.4 10
17 35.0 4
18 34.4 7
19 33.9 8
20 34.0 4
x
Sample Number x 1 x 2 x 3
1 15.4 15.6 15.3
2 15.4 17.1 15.2
3 16.1 16.1 13.5
4 13.5 12.5 10.2
5 18.3 16.1 17.0
6 19.2 17.2 19.4
7 14.1 12.4 11.7
8 15.6 13.3 13.6
9 13.9 14.9 15.5
10 18.7 21.2 20.1
11 15.3 13.1 13.7
12 16.6 18.0 18.0
13 17.0 15.2 18.1
14 16.3 16.5 17.7
15 8.4 7.7 8.4
16 11.1 13.8 11.9
17 16.5 17.1 18.5
18 18.0 14.1 15.9
19 17.8 17.3 12.0
20 11.5 10.8 11.2
c 16 .qxd 5/8/02 9:58 PM Page 614 RK UL 6 RK UL 6:Desktop Folder: