Chapter 21
21.1Chance variation is caused by a number of randomly occurring events that are part of the
production process and that in general cannot be eliminated without changing the process.
21.5
0124.)9938.1(2)5.2|z(|P=−==
0124.
1
0456.
1
21.9 ARL =
0026.
1
= 385
Number of units = Production
ARL = 100(385) = 38,500
21.12 Number of units = Production
ARL = 50(385) = 19,250
21.15 Sampling 3 units per hour means that on average we will produce 38,500 units before
erroneously concluding that the process is out of control when it isn’t. Sampling 2 units per half
21.16 Number of units = Production
ARL = 2000(385) = 770,000
21.19 Number of units = Production
ARL = 4000(385) = 1,540,000
21.20a From Beta-mean spreadsheet,
= .3659
21.22 Sampling 10 units per half hour means that on average we will produce 770,000 units before
erroneously concluding that the process is out of control when it isn’t. Sampling 20 units per hour
x
Lower control limit =
n
S3
x−
= 453.6 − 3
4
5.12
= 434.85
4
5.12
21.24 Centerline =
x
= 181.1
Lower control limit =
n
S3
x−
= 181.1 − 3
9
0.11
= 170.1
9
21.25 a Centerline =
x
= 13.3
Lower control limit =
n
S3
x−
= 13.3 − 3
4
8.3
= 7.6
4
21.26a S Chart
1
2
3
A B C D
Statistical Process Control
Data
x
Chart
6
8
10
12
1
2
3
A B C D
Statistical Process Control
Data
21.27a S Chart
15
20
25
1
2
A B C
Statistical Process Control
0.14
0.16
0.18
0.2
1
2
A B C D E F G
Statistical Process Control
21.28
96
96.1
96.2
1
2
3
A B C
Statistical Process Control
AEU
0.0025
0.003
0.0035
1
2
A B C
Statistical Process Control
0.439
0.44
0.441
0.442
21.30
1
2
3
A B C
Statistical Process Control
Volume
1.2
1.4
1.6
1.8
2
1
2
3
A B C
Statistical Process Control
Volume
21.31
4317.
3
092.10003871.1001
3
CenterlinelimitcontrolUpper
n
S=
−
=
−
=
9653.S;4317.
5
S==
21.32
1
1.5
2
1
2
3
A B C
Statistical Process Control
Headrest
2
2.5
1
2
3
4
A B C D
Statistical Process Control
Headrest
Upper control limit 241.3248
240
241
242
21.33
21.34
1
2
3
7
A B C D
Statistical Process Control
Nuts
Pattern Test #1 Failed at Points: 21
4
5
6
1
2
A B C D
Statistical Process Control
21.35
10
12
14
1
2
A B C
Statistical Process Control
0.004
0.005
1
2
3
A B C
Statistical Process Control
Headers
4.984
4.986
4.988