Chapter 10  Quality Control
101
3.
a. n = 20
A
2
= 0.18
=
X = 3.10 Mean Chart:
=
X
±
A
2
−
R
= 3.1
±
0.18(0.45)
D
3
= 0.41
−
R
= 3.1
±
.081
= 0.45
D
4
= 1.59
Hence, UCL is 3.181
and LCL is 3.019. All means are within these limits.
Range Chart: UCL is D
4
−
R
= 1.59(0.45) = .7155
LCL is D
3
−
R = 0.41(0.45) = .1845
In control since all points are within these limits.
9.
100
)
946
(.
054
.
96
.
1
054
.
n
)
p
1
(
p
z
p
are
limits
Control
054
.
)
100
(
16
87
ns
observatio
of
number
total
defectives
of
number
total
p
±
=
−
±
=
=
=
.
044
.
054
.
±
=
Hence, UCL = 0.10
LCL = 0.01
Note that observations must be converted to fraction defective, or control limits must be
converted to number of defectives. In the latter case, the upper control limit would be 10
defectives and the lower control limit would be 1 defective. Even though all points are within
these limits, the process appears to be out of control because 75% of the values are above 4%.
23.
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 Spring '12
 KIM
 Management, Standard Deviation, Control Chart, USL, LSL

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