Sample Size, or Number of measurements in each Subgroup: • Number of Subgroups: • Subgroup Mean(X-Bar)
Question 1 Data:
A drive-in restaurant is running a new promotion, the "Route 44," named after an interstate
that runs through their primary market area. The drink is promoted as 44 ounces of pure
carbonated pleasure but the regional manager, being somewhat of a quality expert, wantsto
make sure that the company's drink process can deliver 44 ounces. He decidesstatistical
quality control is the best way to monitor their process.
For ten consecutive days he purchases five Route 44 drinks from franchise locations on his
way to headquarters and turns them over to the testing lab for volume analysis. The data
appear in the table, all amounts are in fluid ounces as measured by the testing lab.
Drinks
← Sample Readings →
Subgroup ↓ Drink 1 Drink 2 Drink 3 Drink 4 Drink 5 Mean Range
D 1 43.51 42.47 42.15 43.15 44.14
A 2 42.94 44.90 42.72 43.68 43.71
Y 3 42.05 44.65 45.37 42.43 45.32
S 4 41.72 45.94 46.68 43.13 42.62
5 44.98 45.39 43.30 44.52 43.44
6 43.83 44.44 44.94 45.74 45.83
7 43.76 44.65 45.41 44.73 45.41
8 45.53 45.18 45.65 43.11 46.08
9 43.42 44.16 45.53 44.23 46.63
10 43.56 44.10 44.04 45.56 45.06
Since the regional manager is somewhat of a quality expert, he needs your help in
formulating a control chart that will monitor the process performance to target.
Develop the appropriate metrics:
• Sample Size, or Number of measurements in each Subgroup:
• Number of Subgroups:
• Subgroup Mean(X-Bar)
• Grand Mean (Double X-Bar)
• Subgroup Range (R)
• Average Range (R-Bar)
• Calculate and Chartthe “Mean” and “Range”Upperand Lower
control limits
Notice any trends in the charts?
What could it mean? Or, future reading predictions?
Formulas for X-bar and range charts Above, and Statistical Constants below:
Subgroup Size A2 d2 D3 D4
2 1.880 1.128 ----- 3.268
3 1.023 1.693 ----- 2.574
4 0.729 2.059 ----- 2.282
5 0.577 2.326 ----- 2.114
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