Controls

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Assignment 1: Discussion

You are working with a company selling building material to builders. You predict the quarterly purchases of customers based on their current purchases by using a linear regression model. These predictions, however, are not very accurate. Discuss at least three reasons why these predictions may not be accurate and offer three ways in which you can increase the likelihood of accurately predicting your customers’ purchases.
Post your response to the Discussion Area by Friday, March 8, 2013.

 Assignment 2: Controls

As a quality analyst you are also responsible for controlling the weight of a box of cereal. The Operations Manager asks you to identify the ways in which statistical quality control methods can be applied to the weights of the boxes. Provide your recommendations to the Operations Manager in a two-three page report. Using the data provided in the Doc Sharing area labeled M4A2Data, create Xbar and R charts.

Your report should indicate the following along with valid justifications of your answers:

  1. The control limits of the weights of the boxes.
  2. Nonrandom patterns or trends, if any.
  3. If the process is in control.
  4. The appropriate action if the process is not in control.

Submit your handout and summary to the M4: Assignment 2 Dropbox by Monday, March 11, 2013.

Data and Answers

As a quality analyst you are also responsible for controlling the weight of a box of cereal. The Operations Manager asks you to identify the ways in which statistical quality control methods can be applied to the weights of the boxes. Provide your recommendations to the Operations Manager in a two-page report. Using the data provided in the Doc Sharing area, create Xbar and R charts.
Your report should indicate the following along with valid justifications of your answers:
The control limits of the weights of the boxes.
Nonrandom patterns or trends, if any.
If the process is in control.
The appropriate action if the process is not in control.
Sample Box 1 Box 2 Box 3 Sample Means Maximum Minimum Sample Range
1 6.300 6.280 6.260 6.280 6.300 6.260 0.040
2 6.320 6.320 6.330 6.323 6.330 6.320 0.010
3 6.290 6.330 6.360 6.327 6.360 6.290 0.070
4 6.300 6.290 6.340 6.310 6.340 6.290 0.050
5 6.295 6.315 6.390 6.333 6.390 6.295 0.095
6 6.292 6.319 6.330 6.314 6.330 6.292 0.038
7 6.289 6.323 6.400 6.337 6.400 6.289 0.111
8 6.286 6.327 6.471 6.361 6.471 6.286 0.185
9 6.283 6.331 6.498 6.371 6.498 6.283 0.215
10 6.280 6.335 6.525 6.380 6.525 6.280 0.245
11 6.277 6.339 6.390 6.335 6.390 6.277 0.113
12 6.274 6.343 6.400 6.339 6.400 6.274 0.126
See all the other sheets in this file.
(a) The control limits are: (a) For Mean weight, LCL = 6.3087 ounces, UCL = 6.3696 ounces and (b) For Range, LCL = 0.0324 ounes, UCL = 0.1964 ounce
(b) At the time measurements were taken on the 5th through 9th samples, the mean weights and the range of weights appears to have been increasing in a somewhat linear pattern. It appears that the filling machine has gradually gone off setting during this period. This is the only non-random variation observed at the time of taking the 12 measurements.
(c ) The process is not in control since we see points lying outside the control limits in both x-bar chart and R chart.
(d) Corrective action in terms of resetting the machine is required. Trials should be run and again more samples drawn to check if the process has come under control.
See all the sheets for the calculations and tables. The process is in statistical control.

XBar Chart

1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 10 10 10
11 11 11 11
XBar
LCL-X
Center-X
UCL-X
Sample Mean
Control Chart Calculations
LCL
XBar
UCL
6.3233333333
6.3087307879
6.3391515152
6.3695722424
6.3266666667
6.3087307879
6.3391515152
6.3695722424
6.31
6.3087307879
6.3391515152
6.3695722424
6.3333333333
6.3087307879
6.3391515152
6.3695722424
6.3136666667
6.3087307879
6.3391515152
6.3695722424
6.3373333333
6.3087307879
6.3391515152
6.3695722424
6.3613333333
6.3087307879
6.3391515152
6.3695722424
6.3706666667
6.3087307879
6.3391515152
6.3695722424
6.38
6.3087307879
6.3391515152
6.3695722424
6.3353333333
6.3087307879
6.3391515152
6.3695722424
6.339
6.3087307879
6.3391515152
6.3695722424

RChart

1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 10 10 10
11 11 11 11
Range
LCL-R
Center-R
UCL-R
Sample Range
Control Chart Calculations
LCL
RBar
UCL
0.01
0.0323649091
0.1143636364
0.1963623636
0.07
0.0323649091
0.1143636364
0.1963623636
0.05
0.0323649091
0.1143636364
0.1963623636
0.095
0.0323649091
0.1143636364
0.1963623636
0.038
0.0323649091
0.1143636364
0.1963623636
0.111
0.0323649091
0.1143636364
0.1963623636
0.185
0.0323649091
0.1143636364
0.1963623636
0.215
0.0323649091
0.1143636364
0.1963623636
0.245
0.0323649091
0.1143636364
0.1963623636
0.113
0.0323649091
0.1143636364
0.1963623636
0.126
0.0323649091
0.1143636364
0.1963623636

ForCharts

Number XBar Range LCL-R Center-R UCL-R LCL-X Center-X UCL-X
1 6.3233333333 0.01 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
2 6.3266666667 0.07 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
3 6.31 0.05 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
4 6.3333333333 0.095 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
5 6.3136666667 0.038 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
6 6.3373333333 0.111 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
7 6.3613333333 0.185 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
8 6.3706666667 0.215 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
9 6.38 0.245 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
10 6.3353333333 0.113 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424
11 6.339 0.126 0.0323649091 0.1143636364 0.1963623636 6.3087307879 6.3391515152 6.3695722424

Calculations

Control Chart Calculations
Control Chart Factors Table.
Data Subgroup size D3 D4 A2
Sample/Subgroup Size 12 2 0 3.267 1.880
3 0 2.575 1.023
R Chart Intermediate Calculations 4 0 2.282 0.729
RBar 0.1143636364 5 0 2.114 0.577
D3 Factor 0.283 6 0 2.004 0.483
D4 Factor 1.717 7 0.076 1.924 0.419
8 0.136 1.864 0.373
R Chart Control Limits 9 0.184 1.816 0.337
Lower Control Limit 0.0323649091 10 0.223 1.777 0.308
Center 0.1143636364 11 0.256 1.744 0.285
Upper Control Limit 0.1963623636 12 0.283 1.717 0.266
13 0.307 1.693 0.249
XBar Chart Intemediate Calculations 14 0.328 1.672 0.235
Average of Subgroup Averages 6.3391515152 15 0.347 1.653 0.223
A2 Factor 0.266 16 0.363 1.637 0.212
A2 Factor * RBar 0.0304207273 17 0.378 1.622 0.203
18 0.391 1.609 0.194
XBar Chart Control Limits 19 0.404 1.596 0.187
Lower Control Limit 6.3087307879 20 0.415 1.585 0.180
Center 6.3391515152 21 0.425 1.575 0.173
Upper Control Limit 6.3695722424 22 0.435 1.565 0.167
23 0.443 1.557 0.162
24 0.452 1.548 0.157
25 0.459 1.541 0.153
26 Factor value not available. Possible error in sample/subgroup size. Factor value not available. Possible error in sample/subgroup size. Factor value not available. Possible error in sample/subgroup size.
Factor value not available. Possible error in sample/subgroup size.
 
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