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A B C D E F G H
1 As a quality analyst you are also responsible for controlling the weight of a box of cereal. The Operations Manager ask
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3 Your report should indicate the following along with valid justifications of your answers:
4 a. The control limits of the weights of the boxes.
5 b. Nonrandom patterns or trends, if any.
6 c. If the process is in control.
7 d. The appropriate action if the process is not in control.
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10 Sample Box 1 Box 2 Box 3 Sample Means Maximum Minimum
11 1 6.300 6.280 6.260 6.280 6.300 6.260
12 2 6.320 6.320 6.330 6.323 6.330 6.320
13 3 6.290 6.330 6.360 6.327 6.360 6.290
14 4 6.300 6.290 6.340 6.310 6.340 6.290
15 5 6.295 6.315 6.390 6.333 6.390 6.295
16 6 6.292 6.319 6.330 6.314 6.330 6.292
17 7 6.289 6.323 6.400 6.337 6.400 6.289
18 8 6.286 6.327 6.471 6.361 6.471 6.286
19 9 6.283 6.331 6.498 6.371 6.498 6.283
20 10 6.280 6.335 6.525 6.380 6.525 6.280
21 11 6.277 6.339 6.390 6.335 6.390 6.277
22 12 6.274 6.343 6.400 6.339 6.400 6.274
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24 See all the other sheets in this file.
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26 (a) The control limits are: (a) For Mean weight, LCL = 6.3087 ounces, UCL = 6.3696 ounces and (b) For Range,
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28 (b) At the time measurements were taken on the 5th through 9th samples, the mean weights and the range
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30 (c ) The process is not in control since we see points lying outside the control limits in both x-bar chart and R
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32 (d) Corrective action in terms of resetting the machine is required. Trials should be run and again more samp
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A B C D E F G H
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59 See all the sheets for the calculations and tables. The process is in statistical control.
I J K L M N O P Q
Operations Manager asks you to identify the ways in which statistical quality control methods can be applied to the weigh
of cereal. The 1
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10 Sample Range
11 0.040
12 0.010
13 0.070
14 0.050
15 0.095
16 0.038
17 0.111
18 0.185
19 0.215
20 0.245
21 0.113
22 0.126
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UCL = 6.3696 ounces and (b) For Range, LCL = 0.0324 ounes, UCL = 0.1964 ounce
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mples, the mean weights and the range of weights appears to have been increasing in a somewhat linear pattern. It appears that the filling
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control limits 30 both x-bar chart and R chart.
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als should be 32 and again more samples drawn to check if the process has come under control.
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I J K L M N O P Q
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R S T U V W X Y Z
ds can be applied to the weights of the boxes. Provide your recommendations to the Operations Manager in a report. Using the data pro
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ttern. It appears that the filling machine has gradually gone off setting during this period. This is the only non-random variation observed
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R S T U V W X Y Z
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AA AB AC AD AE AF
nager in a report. Using the data provided create Xbar and R charts.
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nly non-random variation observed at the time of taking the 12 measurements.
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Control Chart Calculations
6.39
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6.37 UCL
6.36
Sample Mean
6.35
XBar
LCL-X
6.34 XBar Center-X
UCL-X
6.33
6.32
6.31
LCL
6.3
0 2 4 6 8 10 12
Control Chart Calculations
0.3
0.25
0.2
UCL
Sample Range
Range
0.15
LCL-R
Center-R
RBar UCL-R
0.1
0.05
LCL
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0 2 4 6 8 10 12
Number XBar Range LCL-R Center-R UCL-R LCL-X Center-X UCL-X
1 6.323333 0.01 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
2 6.326667 0.07 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
3 6.31 0.05 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
4 6.333333 0.095 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
5 6.313667 0.038 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
6 6.337333 0.111 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
7 6.361333 0.185 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
8 6.370667 0.215 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
9 6.38 0.245 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
10 6.335333 0.113 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
11 6.339 0.126 0.032365 0.114364 0.196362 6.308731 6.339152 6.369572
A B C D E F G H
1 Control Chart Calculations
2 Control Chart Factors Table.
3 Data Subgroup size D3 D4 A2
4 Sample/Subgroup Size 12 2 0 3.267 1.880
5 3 0 2.575 1.023
6 R Chart Intermediate Calculations 4 0 2.282 0.729
7 RBar 0.114363636 5 0 2.114 0.577
8 D3 Factor 0.283 6 0 2.004 0.483
9 D4 Factor 1.717 7 0.076 1.924 0.419
10 8 0.136 1.864 0.373
11 R Chart Control Limits 9 0.184 1.816 0.337
12 Lower Control Limit 0.032364909 10 0.223 1.777 0.308
13 Center 0.114363636 11 0.256 1.744 0.285
14 Upper Control Limit 0.196362364 12 0.283 1.717 0.266
15 13 0.307 1.693 0.249
16 XBar Chart Intemediate Calculations 14 0.328 1.672 0.235
17 Average of Subgroup Averages 6.339151515 15 0.347 1.653 0.223
18 A2 Factor 0.266 16 0.363 1.637 0.212
19 A2 Factor * RBar 0.030420727 17 0.378 1.622 0.203
20 18 0.391 1.609 0.194
21 XBar Chart Control Limits 19 0.404 1.596 0.187
22 Lower Control Limit 6.308730788 20 0.415 1.585 0.180
23 Center 6.339151515 21 0.425 1.575 0.173
24 Upper Control Limit 6.369572242 22 0.435 1.565 0.167
25 23 0.443 1.557 0.162
26 24 0.452 1.548 0.157
27 25 0.459 1.541 0.153
28 value Factornot available. Possible erro
value value not available. in sam
26 Factor Factornot available. Possible errorPossib
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30 Factor value not available. Possible error in sample/subgroup siz
I J K L M
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Factor value not available. Possible error in sample/subgroup size.
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sible error in sample/subgroup size.
