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And bar chartlclwithin controlcontrol chart constant tabled

Note Refer last sheet for Control chart constant

Useful Formula
X bar R bar
UCL = X double bar + A2 * R bar UCL =

X bar--->

A2 =
LCL = X double bar - A2 * R bar LCL =
CL =
CL =

R bar

 D3 =

Process is stable/within cont
R UCL

3

 CL 4

LCL
2
Note Refer last sheet for Control chart constant
X bar
Sample Mean
UCL CL

LCL
1 3.06 0.42 3.181 3.1

3.019
2 3.15 0.50 3.181 3.1
3 3.11 0.41 3.181 3.1
4 3.13 0.46 3.181 3.1
5 3.06 0.46 3.181 3.1
6 3.09 0.45 3.181 3.1

3.019
X - double bar------> 3.1 0.45

<---R bar
X bar
3.181

b. Is the process in control?

 LCL 3.019

LCL
R bar control chart
X bar R chart
Mean UCL CL
Range
CL

3.2

 0.80

3.15
0.50
0.40

0.30
0.20

2.95

 0.10
2.9 1 2 3 4 5 6
2

5

b. Process is within control

A2=0.18 D3 = 0.41

D4 = 1.59Useful Formula
X bar R bar
UCL R chart UCL =

X double bar + A2 *

 UCL =
CL LCL
X double bar - A2 * R LCL =
0.7155 0.45 0.185 CL =
CL =

R bar
0.7155 0.45

0.185
0.7155 0.45
0.7155 0.45
0.7155 0.45
0.7155 0.45

No. of Lines
Note

x bar

r Control
st
CL
1 1010 991 985 986 993.0 25

1014.94
2 995 996 1009 994 998.5 15
3 990 1003 1015 1008 1004.0 25

999.10
4 1015 1020 1009 998 1010.5 22

1014.94
5 1013 1019 1005 993 1007.5 26
6 994 1001 994 1005 998.5 11

999.10
7 989 992 982 1020 995.8 38

1014.94
8 1001 986 996 996 994.8 15
9 1006 989 1005 1007 1001.8 18

999.10
10 992 1007 1006 979 996.0 28

1014.94
11 996 1006 997 989 997.0 17
12 1019 996 991 1011 1004.3 28

999.10
13 981 991 989 1003 991.0 22

1014.94
14 999 993 988 984 991.0 15
15 1013 1002 1005 992 1003.0 21

999.10
999.1

21.73333
X double bar R bar X bar
b. Is the process in control? LCL

X bar control chart

 R bar control chart R R-Chart CL 1 0 1
60 1 2 3 4
UCL
50 5 6 7 8 9
40
30
20
10
0

X bar

R bar
UCL = X double bar + A2 *
X bar---> A2 =
LCL =

X double bar - A2 * R

LCL =
R bar---> D4 =
CL =

R bar

 D3 = 0

b. Process is within control

A2, D4 and D3

X bar

 R bar
LCL UCL CL LCL
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00
983.26 49.60 21.73 0.00

Following is the data from Chicago Hospital COVID 19 inspection carried in 5 shifts. Samples of five observat have been taken, and the results are as listed. Using factors from following table , determine upper and lower co for mean and range charts, and decide if the process is in control.
R bar
UCL =

D4 * R bar D3 * R bar
LCL =

X double bar - A2 *
X bar---> A2 =

0.577
R bar---> D4 =

2.114

X bar control chart R bar control chart

X Bar

 x bar UCL CL
18
16
14

98

 12

96

 10
8
6

vations = 5
A2, D4 and D3

R UCL CL

18
16
14
12
10
8
6
4
2

A quality engineer at an automotive parts plant monitors the lengths of camshafts. Five samples of n = 50 obser The engineer measures five camshafts from each machine during each shift.Using factors from following table , control limits for mean and range charts, and decide if the process is in control. (Some observations are missin

X bar

 R bar
X double bar + A2 * R bar

X double bar - A2 * R bar

 LCL =

D3 * R bar
X bar---> A2 =
R bar---> D4 =

2.114
Sample 1 2 3 4 5 x bar R UCL

39 100.6 98.8 101.8 99.9 97.9 100.4 3.1

100.98
40 99.3 99.8 100.9 99.9 1.6
41 100.0 101.8 101.5 98.6 100.5 3.2
42 100.9 98.8 99.0 99.2 99.5 2.1
43 99.0 100.1 99.7 97.9 98.9 2.3
44 100.1 99.9 99.8 101.0 101.0 100.3 1.1

100.98
45 100.0 98.2 100.7 99.5 99.5 99.6 2.6

100.98
46 100.3 99.0 100.1 101.0 101.0 100.3 2.0
47 100.1 98.4 101.7 100.6 100.6 100.1 3.2
48 100.1 99.7 98.8 99.5 1.3
49 99.9 98.6 100.0 99.9 2.0
50 101.2 99.5 100.7 100.4 1.7

100.98
99.9 1.9

X double bar R bar

97.5

R

LCL 98.84 LCL 0.00

samples of n = 50 observations have been obtained.
rs from following table , determine upper and lower
observations are missing)
CL LCL UCL CL LCL

99.91 98.84 3.93 1.9
99.91 98.84 3.93 1.9
99.91 98.84 3.93 1.9
99.91 98.84 3.93 1.9
99.91 98.84 3.93 1.9

0
99.91 98.84 3.93 1.9

0
99.91 98.84 3.93 1.9
99.91 98.84 3.93 1.9
99.91 98.84 3.93 1.9
99.91 98.84 3.93 1.9
99.91 98.84 3.93 1.9

0
99.91 98.84 3.93 1.9

0
Sample size (n) A2 D3

D4
2 1.88 0

3.267
3 1.023 0
4 0.729 0
5 0.577 0
6 0.483 0
7 0.419 0.076

1.924
8 0.373 0.136

1.864
9 0.337 0.184
10 0.308 0.223
11 0.285 0.256
12 0.266 0.283
13 0.249 0.307

1.693
14 0.235 0.328

1.672
15 0.223 0.347
16 0.212 0.363
17 0.203 0.378
18 0.194 0.391
19 0.187 0.403

1.597
20 0.180 0.415

1.585
21 0.173 0.425
22 0.167 0.434
23 0.162 0.443
24 0.157 0.451
25 0.153 0.459

1.541
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