Question

Your client is a large quick service restaurant chain. They want to monitor drive through times that are longer than 90 seconds. Every day for 6 days they time 150 orders and record the number that are greater than 90 seconds. The number of orders that were longer than 90 seconds for each of the 9 days is: 6,8,12,9,7,2,15,8, and 11 . You are asked to develop a three-sigma control chart for the order process. What are the appropriate upper and lower control limits? A new store has opened, and they want to evaluate its drive through performance. Measures from the new store are: 12,16,11,13, and 14. Graph the chart and comment on the new store's performance.

Answer 1

To create a three-sigma control chart for the large quick service restaurant chain, calculate the mean and standard deviation from the provided times. then use these to find the upper and lower control limits. the new store's performance should be compared against these control limits on the chart.

Step-by-step explanation:

To develop a three-sigma control chart to monitor drive through times for your client, a large quick service restaurant chain, we first need to calculate the average and standard deviation of the data provided. The numbers of orders taking longer than 90 seconds over the 9 days are: 6, 8, 12, 9, 7, 2, 15, 8, and 11. Calculating the mean (μ) gives us (6+8+12+9+7+2+15+8+11)/9 = 8.44 (repeating this should exclude the sixth day as the question mentions 6 days but provides 9 data points). The standard deviation (σ), assuming a sample standard deviation due to the sample size, must be calculated based on this data.

Once the standard deviation is calculated, the upper control limit (UCL) and the lower control limit (LCL) can be determined using the following formulas: UCL = μ + 3σ and LCL = μ - 3σ. for the new store's performance, you would graph the number of orders taking longer than 90 seconds on a chart with the previously calculated UCL and LCL. If the data points for the new store lie within these limits, the process could be considered in control. If they lie outside these limits, this could indicate a potential problem with the process at the new store.