Question

In: Operations Management

You’ve just been promoted to a management position at Worcester Corset Candies Company. Congrats! Immediately, you...

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

Solutions

Expert Solution

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.


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