In: Operations Management
You’ve just been promoted to a management position at Worcester Corset Candies Company. Congrats! Immediately, you get a call that Finance noticed a cost variance in your department. It appears that you are consuming too few ingredients for your scheduled output. A box of Special Mixed Corset Candies is supposed to be 140 ounces, and your annual bonus is paid on how close you manage your department’s per/unit costs. To begin analyzing the process, you ask your fill machine operator to record the weights of 9 candy cartons each hour for the next 11 hours. (HINT: Save yourself a lot of time and do this in Excel). Are all points on the R-chart are within the control limits? Are all points on the X-bar chart are within the control limits? So, manager, is your candy making process considered in control?
Data provided
Batch | Weight 1 | Weight 2 | Weight 3 | Weight 4 | Weight 5 | Weight 6 | Weight 7 | Weight 8 | Weight 9 |
1 | 147 | 136 | 138 | 138 | 131 | 130 | 134 | 148 | 144 |
2 | 148 | 137 | 149 | 134 | 134 | 143 | 144 | 150 | 140 |
3 | 138 | 141 | 130 | 140 | 135 | 132 | 138 | 134 | 133 |
4 | 141 | 143 | 149 | 133 | 143 | 149 | 132 | 135 | 130 |
5 | 135 | 141 | 140 | 139 | 135 | 150 | 136 | 130 | 135 |
6 | 133 | 146 | 142 | 136 | 150 | 140 | 144 | 147 | 150 |
7 | 138 | 137 | 145 | 138 | 134 | 149 | 130 | 131 | 147 |
8 | 144 | 137 | 133 | 149 | 131 | 141 | 143 | 149 | 146 |
9 | 145 | 134 | 149 | 140 | 142 | 130 | 150 | 142 | 148 |
10 | 135 | 146 | 130 | 141 | 135 | 137 | 141 | 140 | 150 |
11 | 149 | 142 | 149 | 143 | 142 | 137 | 134 | 139 | 140 |
Calculating the x bar and Range of the data
Batch | Weight 1 | Weight 2 | Weight 3 | Weight 4 | Weight 5 | Weight 6 | Weight 7 | Weight 8 | Weight 9 | Mean | Range |
1 | 147 | 136 | 138 | 138 | 131 | 130 | 134 | 148 | 144 | 138.44 | 18 |
2 | 148 | 137 | 149 | 134 | 134 | 143 | 144 | 150 | 140 | 142.11 | 16 |
3 | 138 | 141 | 130 | 140 | 135 | 132 | 138 | 134 | 133 | 135.67 | 11 |
4 | 141 | 143 | 149 | 133 | 143 | 149 | 132 | 135 | 130 | 139.44 | 19 |
5 | 135 | 141 | 140 | 139 | 135 | 150 | 136 | 130 | 135 | 137.89 | 20 |
6 | 133 | 146 | 142 | 136 | 150 | 140 | 144 | 147 | 150 | 143.11 | 17 |
7 | 138 | 137 | 145 | 138 | 134 | 149 | 130 | 131 | 147 | 138.78 | 19 |
8 | 144 | 137 | 133 | 149 | 131 | 141 | 143 | 149 | 146 | 141.44 | 18 |
9 | 145 | 134 | 149 | 140 | 142 | 130 | 150 | 142 | 148 | 142.22 | 20 |
10 | 135 | 146 | 130 | 141 | 135 | 137 | 141 | 140 | 150 | 139.44 | 20 |
11 | 149 | 142 | 149 | 143 | 142 | 137 | 134 | 139 | 140 | 141.67 | 15 |
Mean of each Batch = Average of Weight 1 to weight 9
Range of each batch = Max of values between Weight 1 to weight 9 - Min of values between Weight 1 to weight 9
x double bar = Mean of the averages of all batches from 1 to 11 = 140.02
Average range or R bar = Average of all ranges calculated from batch 1 to batch 11 = 17.55
Control Limits of X bar chart:
UCL = X double bar + A_2*R bar = 140.02+0.337*17.55 = 145.93
LCL = X double bar - A_2*R bar = 140.02-0.337*17.55 = 134.10
Control Limts of R bar chart:
UCL = D_4*R bar = 1.816*17.55 = 31.87
LCL = D_3*R bar = 0.184*17.55 = 3.23
A_2, D_3 and D_4 are the control chart constant. The value of these constanct can be found from the Contol Chart constant table.
Now plotting the X bar values (Mean of all batches). The number of batches on x axis and values on y axis.
The upper limit for x bar chart is 145.93 and lower limit is 134.10. No point is beyond these two values. All points are with in the limits. Hence this process is in control as per x bar chart.
Similalry, plotting the R bar chart. With batch number of x axis and the R bar value on the y axis.
The UCL and LCL for R bar chart are 31.87 and 3.23. So no point is lying beyond these two values. Hence the process is in control as per R bar chart as well.