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39.4 A plastic extrusion process produces round extrudate with a mean diameter = 28.6 mm. The process
is in statistical control and the output is normally distributed with standard deviation = 0.53 mm.
Determine the process capability.
Solution
: Process capability
PC
=
μ
± 3
σ
= 28.6 ± 3(0.53) =
28.6
±
1.59 mm
The upper and lower limits of the process capability range are: 27.01 to 30.19 mm.
42.8 Ten samples of size
n
= 8 have been collected from a process in statistical control, and the dimension of
interest has been measured for each part. The calculated values of
x
for each sample are (mm) 9.22, 9.15, 9.20, 9.28, 9.19, 9.12, 9.20, 9.24, 9.17, and 9.23. The values of
R
are (mm)
0.24, 0.17, 0.30, 0.26, 0.26, 0.19, 0.21, 0.32, 0.21, and 0.23, respectively. (a) Determine the values of the
center, LCL, and UCL for the
x
and
R
charts. (b) Construct the control charts and plot the sample data on the charts.
Solution
:
x
=
Σ
x
/m =
Σ
x
/
10
= (9.22 + 9.15 + 9.20 + 9.28 + 9.19 + 9.12 + 9.20 + 9.24 + 9.17 + 9.23)/10 = 9.20
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