4.1.
n
= 15;
x
= 8.2535 cm;
σ
= 0.002 cm
(a)
μ
0
= 8.25,
α
= 0.05
Test
H
0
:
μ
= 8.25 vs.
H
1
:
μ
≠
8.25.
Reject
H
0
if 
Z
0
 >
Z
α
/2
.
0
0
8.2535
8.25
6.78
0.002
15
x
Z
n
μ
σ


=
=
=
Z
α
/2
=
Z
0.05/2
=
Z
0.025
= 1.96
Reject
H
0
:
μ
= 8.25, and conclude that the mean bearing ID is not equal to 8.25 cm.
(b)
P
value = 2[1

Φ
(
Z
0
)] = 2[1

Φ
(6.78)] = 2[1

1.00000] = 0
(c) sqrt means square root.
8.25351.96(0.002/sqrt(15))
<=
μ
<=
8.2535+1.96(0.002/sqrt(15))
8.2525
<=
μ
<=
8.2545
5.1
“Chance” or “common” causes of variability represent the inherent, natural variability of a
process  its background noise.
Variation resulting from “assignable” or “special” causes
represents generally large, unsatisfactory disturbances to the usual process performance.
Assignable cause variation can usually be traced, perhaps to a change in material, equipment, or
operator method.
A Shewhart control chart can be used to monitor a process and to identify occurrences of
assignable causes.
There is a high probability that an assignable cause has occurred when a plot
point is outside the chart's control limits.
By promptly identifying these occurrences and acting
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 Fall '06
 PALMER
 Control Chart, Plot Point, 3sigma limits, mean bearing ID, Shewhart control

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