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Unformatted text preview: is set at 2 to 6. The subgroup size should be made uniform. The
letter “k” represents the number of subgroups made by data classification. Normally, 20 to
25 subgroups are supplied.
A Roadmap to Quality 23 Unit 9  Problem solving 0587581_unit 9.qxd 09/09/2005 11:55 Page 24 In this example, numbers are set as follows:
Subgroup size
n=3
Number of data items in a subgroup
k = 30
Number of all data items
N = n x k = 90
Step 3. Calculate the average for subgroups
Calculate the average (represented by –) for respective subgroups. The value – is calculated
x
x
using the following formula:
– = (X + X + ... + X )/n
x
1
2
n
–
The value “x” should be calculated to three decimal places after the measured values, then
rounded off. For example, the value for subgroup 1 is calculated as follows.
– = (0.42 + 0.40 + 0.41)/3 = 0.410
x
–
The average “x ” for all subgroups should be calculated in the same manner. Calculated
averages should be arranged as shown in Figure 9.8b.
Figure 9.8b Calculation table for –R control charts: Amount of steam consumed in drying
x
synthetic rubber B over a period of one month. An –R control chart is prepared based on
x
this data (page 25).
Step 4. Calculate
Calculate “R”, range per subgroup, where R = [maximal value within the subgroup] –
[minimal value within the subgroup]
For example, the value for subgroup 1 is calculated as follows:
R = 0.42  0.40 = 0.02
Range “R” for all subgroups should be calculated in the same manner. Calculated values
should be arranged as shown in Figure 9.8b.
Step 5. Calculate =
x
–
Add up the value “x“ for all subgroups and divide this total by “k”, the number of
data items in a subgroup.
–
= = (– + – + ... +x )/k
x
x1
x2
k
–
Value “x” should be calculated to four decimal places after the measured value.
For example, the value for data presented in Figure 9.8b is calculated as follows:
= = 13.165/30 = 0.4388
x
–
Step 6. Calculate R
Add up the value “R” for all subgroups and divide this total by “k”, the number of
–
data items in a subgroup. The resulting figure is value “R”
–
R= (R1+ R2 + ... + Rk)/k
–
Value “R“ should be calculated to four decimal places after the measured values.
For example, the value for data presented in Figure 9.8b is calculated as follows:
–
R = 4.27/30 = 0.1423
Figure 9.8c Coefficient table for calculating the control lines of control charts (page 26) Unit 9  Problem solving 24 A Roadmap to Quality 0587581_unit 9.qxd 09/09/2005 11:55 Page 25 Figure 9.8b Calculation table for –R control charts
x Subgroup
number (date) Morning
shift Midday
shift Night
shift Average Range R 1 0.42 0.40 0.41 0.410 0.02 2 0.48 0.53 0.47 0.493 0.06 3 0.46 0.88 0.66 0.667 0.42 4 0.50 0.44 0.46 0.467 0.06 5 0.33 0.23 0.30 0.287 0.10 6 0.60 0.40 0.36 0.453 0.24 7 0.41 0.35 0.51 0.423 0.16 8 0.41 0.40 0.45 0.420 0.05 9 0.55 0.59 0.42 0.520 0.17 10 0.28 0.50 0.45 0.410 0.22 11 0.56 0.43 0.50 0.497 0.13 12 0.43 0.40 0.45 0.427 0.05 13 0.45 0.36 0.41 0.407 0.09 14 0.44 0.53 0.48 0.483 0.09 15 0.45 0.51 0.29 0.417 0.22 16 0.14 0.30 0.62 0.353 0.48 17 0.47 0.62 0.46 0.517 0.16 18 0.45 0.32 0.57 0.447 0.25 19 0.49 0.43 0.48 0.467 0.06 20 0.49 0.65 0.50 0.547 0.16 21 0.52 0.49 0.48 0.497 0.04 22 0.44 0.68 1.19 0.770 0.75 23 0.48 0.36 0.36 0.400 0.12 24 0.39 0.35 0.34 0.360 0.05 25 0.32 0.30 0.30 0.307 0.02 26 0.35 0.36 0.35 0.353 0.01 27 0.40 0.40 0.38 0.393 0.02 28 0.36 0.35 0.37 0.360 0.02 29 0.31 0.30 0.33 0.313 0.03 30 0.29 0.30 0.31 0.300 0.02 Total 13.165 4.27 A Roadmap to Quality 25 Unit 9  Problem solving 0587581_unit 9.qxd 09/09/2005 11:55 Page 26 Figure 9.8c Coefficient table for calculating the control lines of control charts Control chart types –
x ~
x Subgroup size (n) A2 m3A2 D3 D4 2 1.880 1.880  3.267 3 1.023 1.187  2.575 4 0.729 0.796  2.282 5 0.577 0.691  2.115 6 0.483 0.549  2.004 7 0.419 0.509 0.076 1.924 8 0.373 0.432 0.136 1.864 9 0.337 0.412 0.184 1.816 10 0.308 0.363 0.223 1.777 R Note: Columns denoted by “” are disregarded.
–
Step 7. Calculate control lines of xR control charts
– Control Charts
x
CL: Central Line
CL = =
x
UCL: Upper Control Limit
–
UCL = = + A2 R
x
LCL: Lower Control Limit
–
LCL = =  A2 R
x
R Control Charts
–
CL; R
–
UCL = D4 R
–
LCL = D3 R
(When n<=6, there is no need to consider LCL)
Values A2, D3 and D4 are numbers fixed by “n”, the subgroup size (see Figure 9.8c). For
example, control lines for the control charts presented in Figure 9.8c are calculated as
follows:
– Control Chart
x
CL = = = 0.4388
x
–
UCL = = + A2R (when n = 3, A2 = 1.023)
x
= 0.4388 + 0.145573 = 0.584373
Rounded off to 0.5844 (two more decimal places after the measured values)
–
LCL = =  A2R
x
= 0.4388  0.145573 = 0.293227
Rounded off to 0.2932
Unit 9  Problem solving 26 A Roadmap to Quality 0587581_unit 9.qxd 09/09/2005 11:55 Page 27 R Control Chart
–
1. CL = R= 0.1423
–
2. UCL = D4R (when n = 3...
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This note was uploaded on 10/07/2013 for the course MKT marketing taught by Professor Anamika during the Spring '12 term at Punjab Engineering College.
 Spring '12
 anamika
 Marketing

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