Control Charts
Using Minitab
Control charts display the process average (center) and process
variability (spread). Process Average is the “expectation” and
Process Variability indicates “risk” associated with the
expectation.
Frequently Used Control Charts
Attribute: Go/no-go Information, sample size of 50 to 100
p-chart (Proportion Defectives)
c-chart (# Defects)
u-chart (Defects/Unit)
Variable: Continuous data, usually measured by the mean
and standard deviation, sample size of 2 to 10
– X-bar and R-charts
– X-bar and s-charts
– X-charts for individuals
2
Attribute Charts in Minitab
Stat / Control charts / Attribute Charts
3
p-Chart
Hour
SampSize
Nonconforming
1
75
17
2
75
18
3
75
18
4
75
16
5
75
20
6
75
22
P C h art o f N o n c o n fo rm in g
0 .4 5
U C L = 0 .4 0 9 7
0 .4 0
P ro p o rt io n
0 .3 5
0 .3 0
_
P = 0 .2 5 8 1
0 .2 5
7
75
24
8
75
19
0 .2 0
9
75
15
0 .1 5
10
75
22
11
75
19
L C L = 0 .1 0 6 5
0 .1 0
1
3
5
7
9
11
13
15
17
19
21
23
25
S a m p le
12
75
24
13
75
12
14
75
22
15
75
20
16
75
20
P charts are used to study the proportion of defectives
in each sample. A “defective” is an attribute that makes
something useless.
Data on non-conforming (defective) chips produced
at a facility
4
c-Chart
Unit
SqFt
Blemishes
1
66
2
2
66
2
6
3
66
0
5
4
66
0
5
66
1
6
66
4
7
66
0
8
66
0
9
66
2
C C h art o f B le m is h e s
1
S a m p le C o u n t
7
U C L = 6 .6 5 0
4
3
_
C = 2 .2
2
1
0
L C L= 0
1
6
11
16
21
26
31
36
41
46
S a m p le
10
66
3
Data are number of blemishes in 66sqft of painted area
C charts are used to display the number of defects in each sample. A
defect is a flaw that is undesirable but does not make the product
useless.
5
U-Chart
U C h art o f B le m is h e s
0 .1 2
1
SqFt
Blemishes
Rate
1
73
5
0.0685
2
70
4
0.0571
3
60
1
0.0167
4
57
1
0.0175
5
58
0
0.0000
6
57
3
0.0526
7
59
1
0.0169
8
52
4
0.0769
9
55
1
0.0182
10
59
2
0.0339
11
67
0
0.0000
12
55
2
0.0364
13
54
1
0.0185
U C L = 0 .1 0 1 7
0 .1 0
S a m p le C o u n t P e r U n it
Unit
0 .0 8
0 .0 6
_
U = 0 .0 3 5 7
0 .0 4
0 .0 2
0 .0 0
LC L= 0
1
6
11
16
21
26
S a m p le
31
36
41
46
T ests p erfo rm ed w ith u n eq u al sam p le sizes
Data are number of blemishes in different areas
U charts are used to display the number of defects per unit of
measurement. Useful when samples are of different sizes.
6
Variable Charts in Minitab
Stat / Control charts / Variable Charts for Subgroups or Individuals
7
XBar-R Charts
Sample
Obs1
Obs2
Obs3
Obs4
Obs5
1
11.991
12.001
12.176
12.004
12.030
X-Bar charts are used to plot
subgroup means.
X b ar-R C h art o f O b s 1 , ..., O b s 5
12.2
3
4
12.065
11.946
12.011
12.018
11.980
12.069
12.223
12.089
12.065
11.955
S a m p le M e a n
2
12.125
12.155
U C L= 1 2 . 1 8 3 2
11.959
12.1
_
_
X= 1 2 . 0 4 5 7
12.111
12.0
12.197
LC L= 1 1 . 9 0 8 2
11.9
1
8
15
22
29
36
43
50
57
64
S a m p le
5
11.783
12.140
12.008
12.076
12.044
U C L= 0 . 5 0 4 1
6
11.962
12.132
12.149
S a m p le R a n g e
0.48
11.991
7
12.163
11.961
11.932
12.115
8
12.053
12.053
11.889
11.975
0.36
12.128
_
R = 0.2384
0.24
11.870
0.12
0.00
1
12.037
LC L= 0
8
15
22
29
36
43
50
57
64
S a m p le
9
12.108
11.942
12.102
11.967
Data represents actual contents in 12 oz soda cans
12.056
R charts are used to plot the range
for each subgroup.
8
XBar-S Charts
X-Bar charts are used to plot subgroup means.
Sample
Obs1
Obs2
Obs3
Obs4
Obs5
1
11.991
12.001
12.176
12.004
12.030
2
12.065
12.018
12.223
11.955
11.959
3
11.946
11.980
12.089
12.125
4
12.011
12.069
12.065
12.155
5
11.783
12.140
12.008
12.076
12.0
6
11.962
12.132
12.149
11.991
11.9
S charts are used to plot the standard deviation of
each subgroup.
X b ar-S C h art o f O b s 1 , ..., O b s 5
S a m p le M e a n
12.2
U C L= 1 2 . 1 8 3 2
12.111
12.1
12.197
_
_
X= 1 2 . 0 4 5 7
12.044
LC L= 1 1 . 9 0 8 2
12.128
1
8
15
22
29
36
43
50
57
64
S a m p le
7
12.163
11.961
11.932
12.115
8
12.053
12.053
11.889
11.975
11.870
9
12.108
11.942
12.102
S a m p le S t D e v
0.20
11.967
U C L= 0 . 2 0 1 3
12.037
0.15
_
S= 0 . 0 9 6 3
12.056
0.10
0.05
0.00
LC L= 0
1
8
15
22
29
36
43
50
57
64
S a m p le
9
Is the Process in Control?
XBar-S Chart
X (individual) Chart
X b ar-S C h art o f O b s 1 , ..., O b s 5
I C h art o f S o d aC an s
12. 1
1 2 .3
__
X= 12. 0457
12. 0
1 2 .2
LC L= 11. 9082
11. 9
1
8
15
22
29
36
43
50
57
64
S a m p le
0. 20
S a m p le S t D e v
1 2 .4
UC L= 12. 1832
UC L= 0. 2013
0. 15
_
S= 0. 0963
0. 10
In d iv id u a l V a lu e
S a m p le M e a n
12. 2
U B= 1 2 .2
1 2 .1
_
X= 1 2 .0 4 5 7
1 2 .0
1 1 .9
LB= 1 1 .9
1 1 .8
0. 05
1
1 1 .7
0. 00
LC L= 0
1
8
15
22
29
36
S a m p le
43
50
57
64
1
36
71
106
141
176
211
246
281
316
O b se rva tio n
10
Process Capability
P ro c es s C ap ab ility o f S o d aC an s
LS L
USL
P ro c e ss D at a
1 1 .9
LS L
T arg e t
*
USL
1 2 .2
S am p le M e an
1 2 .0 4 5 7
S am p le N
350
S t D e v ( W it h in )
0 .1 0 2 5 0 1
S t D e v ( O v e rall)
0 .1 0 3 5 2 8
W it h in
O v e rall
P o t e n t ial ( W it h in ) C ap ab ilit y
Cp
0 .4 9
CP L
0 .4 7
CP U
0 .5 0
Cp k
0 .4 7
O v e rall Cap ab ilit y
Pp
0 .4 8
PPL
0 .4 7
PPU
0 .5 0
Ppk
0 .4 7
Cp m
1 1 .8
1 1 .9
1 2 .0
1 2 .1
O b se rv e d P e rfo rm an c e
E x p . W it h in P e rfo rm an c e
P P M < LS L
7 4 2 8 5 .7 1
P P M < LS L
7 7 5 6 7 .8 6
P P M < LS L
PPM > USL
7 7 1 4 2 .8 6
PPM > USL
6 6 1 3 7 .5 5
PPM > USL
P P M T o t al
1 5 1 4 2 8 .5 7
P P M T o t al
1 4 3 7 0 5 .4 1
1 2 .2
*
1 2 .3
E x p . O v e rall P e rfo rm an c e
P P M T o t al
7 9 6 3 6 .6 8
6 8 0 7 8 .2 0
1 4 7 7 1 4 .8 8
Process capability refers to the ability of a process to produce a defect-free product or
service in a controlled manner of production or service environment
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