Question

A restaurant is improving its processes, and is currently focusing on the final bill presented to customers. the manager samples 50 bills per day for 12 days, and checks to see how many are incorrect using a z-value of 3.

day 1 2 3 4 5 6 7 8 9 10 11 12
incorrect bills 1 3 2 1 4 8 2 1 1 3 1 4

is the billing process consistent (in other words, is it in control), or do special cause events appear to be present?

Answer 1

To determine if a restaurant's billing process is consistent, the average number of incorrect bills and control limits need to be calculated based on a sample of data. By comparing the actual number of incorrect bills to the control limits, we can identify the presence of special cause events.

Step-by-step explanation:

The manager of the restaurant is focusing on the final bill presented to customers to improve the billing process. To assess the consistency of the billing process, the manager samples 50 bills per day for 12 days and checks the number of incorrect bills. The data is provided in the question:

Day: 1 2 3 4 5 6 7 8 9 10 11 12
Incorrect Bills: 1 3 2 1 4 8 2 1 1 3 1 4

To determine if special cause events are present, we can calculate the average number of incorrect bills and use statistical process control methods. We can calculate the average as (1 + 3 + 2 + 1 + 4 + 8 + 2 + 1 + 1 + 3 + 1 + 4) / 12 = 2.25. Next, we can calculate the standard deviation and control limits using the formulas:

Standard Deviation = √ [ (1-2.25)^2 + (3-2.25)^2 + (2-2.25)^2 + ... ] / (12-1)

Control Limits = Average ± (3 × Standard Deviation)

We can then compare the actual number of incorrect bills to the control limits to determine if there are any special cause events present.