Question: Pepsi Co. has installed a new automatic cola filling machine. Following samples were taken during the first week of production. The factory manager asked you
Pepsi Co. has installed a new automatic cola filling machine. Following samples were taken during the first week of production. The factory manager asked you to check if the central tendency of the process is in control. What will be the upper and lower control limits, respectively?
| Sample | Bottle 1 | Bottle 2 | Bottle 3 |
| 1 | 20.1 | 20.1 | 19.8 |
| 2 | 20 | 19.5 | 20 |
| 3 | 19.9 | 20.1 | 19.4 |
| 4 | 18 | 21.8 | 20.5 |
| 5 | 20 | 19.7 | 20 |
a.) 2.37 and 0
b.) 20.05 and 19.85
c.) 2.65 and 0
d.) 21.07 and 18.78
Step by Step Solution
There are 3 Steps involved in it
To determine the upper and lower control limits UCL and LCL for the process we can use control charts typically the Xbar and Rchart approach for variable data Here is a stepbystep method to solve it Step 1 Calculate the Mean of Each Sample For each sample calculate the mean average value of the readings Sample 1 201 201 198 3 200 Sample 2 200 195 200 3 19833 Sample 3 199 201 194 3 198 Sample 4 180 218 205 3 201 Sample 5 200 197 200 3 199 Step 2 Calculate the Overall Mean Find the mean of these sample means to get the overall process mean Overall Mean 200 19833 198 201 199 5 199266 Step 3 Calculate the Range of Each Sample Find the range difference between the maximum and minimum for each sample Sample 1 201 198 03 Sample 2 200 195 05 Sample 3 201 194 07 Sample 4 218 180 38 Sample 5 200 197 03 Step 4 Calculate the Average Range Rbar Find the average of these ranges Average Range Rbar 03 05 07 38 03 5 112 Step 5 Determine the Control Limits The formulae for calculating control limits for the Xbar chart are UCL Overall Mean A2 Rbar LCL Overall Mean A2 Rbar Assuming that the sample size n3 the A2 factor from the standard statistical control chart ... View full answer
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