This preview shows pages 1–3. Sign up to view the full content.
Section 167
1618.
a)
The natural tolerance limits are
100 18
±
.
40
1.1111
63
6
USL LSL
PCR
σ
−
==
=
Since the mean of the process is centered at the nominal dimension,
1.1111
k
PCR
PCR
Since the process natural tolerance limits lie inside the specifications, very few defective units will be
produced.
The fraction defective is
2 ( 20/ 6)
0.0858%
Φ−
=
b)
The natural tolerance limits are
106
18
±
.
40
1.1111
6
USL LSL
PCR
−
=
Since the mean of the process is not centered at the nominal dimension,
14 26
min
,
0.7778
18 18
k
PCR
⎡⎤
⎢⎥
⎣⎦
The small PCRK indicates that the process is likely to produce units outside the specification limits.
The fraction defective is
( ) ( )
(
)
(
)
14/ 6
26/ 6
0.0098+0=0.0098
PX L
SL PX U
SL PZ
PZ
<+>=<
−
+>
=
1619
a)
12
1.5
66
USL
LSL
PCR
σσ
−
=
so
1.3333
=
b) (20+32)/2=26 When the process is centered at the nominal dimension, the fraction defective is minimized
for any
.
1616
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 1620
a) The natural tolerance limits are
20 6
±
.
20
1.6667
61
2
USL LSL
PCR
σ
−
==
=
Since the mean of the process is centered at the nominal dimension,
1.6667
k
PCR
PCR
Since the process natural tolerance limits lie inside the specifications, very few defective units will
be produced.
The fraction defective is
2(1
0
/
2
) 0
Φ−
=
b) The natural tolerance limits is
23 6
±
.
20
1.6667
2
USL LSL
PCR
−
=
Since the mean of the process is not centered at the nominal dimension,
13 7
min
,
1.1667
66
k
PCR
⎡⎤
⎢⎥
⎣⎦
The fraction defective is
00023
.
0
00023
.
0
0
)
2
/
7
(
)
2
/
13
(
)
(
)
(
=
+
=
>
+
−
<
=
>
+
<
Z
P
Z
P
USL
X
P
LSL
X
P
c) The measure of actual capability decreases and the fraction defective increases when the
process mean is shifted from the center of the specification limits.
1621
a) If the process uses 66.7% of the specification band, then 6
σ
= 0.667(USLLSL). Because the process is
centered
LSU
USL
USL
LSL
USL
−
=
−
=
−
=
−
=
−
=
μμ
μ
5
.
4
)
(
667
.
0
)
(
677
.
0
)
(
667
.
0
3
5
.
1
3
5
.
4
,
3
5
.
4
min
=
⎥
⎦
⎤
⎢
⎣
⎡
=
=
K
PCR
PC
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/12/2009 for the course IND E 315 taught by Professor Kailashkapur during the Spring '09 term at University of Washington.
 Spring '09
 KAILASHKAPUR

Click to edit the document details