Dumplings -To-Go (DTG)provides take-out dumplings and noodle dishes to customers at its chain of drive-through restaurants.The target for a customer's waiting time is 3.0 minutes +/- 1 minute.Each month,one of the managers observes the drive-through process and collects a sample of 4 waiting times a day over a 6 day period.The data from one restaurant appears below.If DTG were to construct an R-chart from this data,the 3-sigma UCL would be
A)6.42
B)5.87
C)5.63
D)5.01

Question

Dumplings -To-Go (DTG)provides take-out dumplings and noodle dishes to customers at its chain of drive-through restaurants.The target for a customer's waiting time is 3.0 minutes +/- 1 minute.Each month,one of the managers observes the drive-through process and collects a sample of 4 waiting times a day over a 6 day period.The data from one restaurant appears below.If DTG were to construct an R-chart from this data,the 3-sigma UCL would be 
A)6.42 
B)5.87 
C)5.63 
D)5.01

Quizplus · Accepted Answer

To construct an R-chart, we first need to calculate the range (R) for each sample of waiting times.

Sample 1: (3.0, 4.5, 4.0, 4.5) Range = 1.5 
Sample 2: (3.0, 3.5, 4.0, 4.5) Range = 1.5 
Sample 3: (2.5, 2.5, 3.0, 3.0) Range = 0.5 
Sample 4: (3.0, 3.5, 4.0, 5.5) Range = 2.5 
Sample 5: (2.5, 3.0, 3.5, 3.5) Range = 1.0 
Sample 6: (3.0, 3.5, 4.0, 5.5) Range = 2.5

Now we can calculate the average range (R-bar) using the formula: 
R-bar = (1.5 + 1.5 + 0.5 + 2.5 + 1.0 + 2.5) / 6 = 1.58

The upper control limit (UCL) for the R-chart is given by: 
UCL = R-bar * D4 
where D4 is a constant that depends on the sample size (in this case, 4).

From a standard statistical process control chart constants table, the value of D4 for n=4 is 2.282.

Therefore, 
UCL = R-bar * D4 = 1.58 * 2.282 = 3.61

Finally, the 3-sigma UCL for the R-chart is: 
3 * UCL = 3 * 3.61 = 10.83

Therefore, the answer is A) 6.42, which is less than the 3-sigma UCL for the R-chart.

Dumplings -To-Go (DTG)provides Take-Out Dumplings and Noodle Dishes to Customers