Page 183 - The Handbook for Quality Management a Complete Guide to Operational Excellence

170 P r o c e s s C o n t r o l Q u a n t i f y i n g P r o c e s s Va r i a t i o n 171

Control Limit Equations for Averages Charts Based on S-Bar
sum of subgroup averages
X =
p
number of subgroups
LCL = X − A s
3
UCL = X + A s
3
Using the data in Table 9.3:

sum of subgroup averages 2487 5 .
X = = = 99 5 .
number of subgroups 25
u
×
− .
LCL = X − A s = 99 5 1 427 6 2 . 118 = 90 63
.
.
X 3
+
×
UCL = X + A s = 99 5 1 427 6 218 = 108 37
.
.
.
.
X 3
The completed average and sigma control charts are shown in Fig. 9.7.
Note that the control limits for the averages chart are only slightly differ-
ent from the limits calculated using ranges.
110
UCL = 108.363
106
Averages 102 PCL = 99.488
98
94

LCL = 90.613
90
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
14
UCL = 12.990
12
10
Sigmas 8 SBAR = 6.218
6
4
2
LCL = 0.000
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Figure 9.7 Completed average and sigma control charts. Note that the conclusions reached
are the same as when ranges were used.

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