Consider a service process such as a fast food drive through window. The target for a customer's waiting time is 3.0 minutes. A manager observes the process and randomly collects a sample of four waiting times each hour over a 12 hour period. The sum of the average waiting time for each of the 12 samples is 35.4. The sum of the range for each of the 12 samples is 18.0. The UCL for the process control chart reporting variability between the sample means is
A) 4.05
B) 3.10
C) 2.15
D) 1.25

Question

Quizplus · Accepted Answer

To calculate the UCL for the process control chart for variability between the sample means, we use the formula UCL = X-double bar + A2R-bar, where X-double bar is the average of sample averages, A2 is a constant based on sample size (A2 = 0.577 for n = 4), and R-bar is the average range of the samples.

Given that the sum of the average waiting time for each of the 12 samples is 35.4, we can calculate the X-double bar as X-double bar = 35.4/12 = 2.95 minutes.

The sum of the range for each of the 12 samples is 18.0, so we can calculate the average range as R-bar = 18.0/12 = 1.5 minutes.

Plugging these values into the formula for UCL, we get UCL = 2.95 + 0.577(1.5) = 2.15 minutes.

Therefore, the answer is choice C) 2.15.

Consider a Service Process Such as a Fast Food Drive