Question

A national pizza chain guarantees delivery of pizza orders within 20 minutes from the time of accepting an order; otherwise, the customer gets the pizza free of charge. Assume that actual delivery times in minutes for a random sample of seven customer orders were: 18, 17, 19, 20, 15, 25, and 30. Given this information,

a. How would you define variation in the pizza delivery process?

b. In the random sample of seven customers, how many customers got a free pizza?

c. What is the accuracy rate of this current delivery process?

d. If this pizza chain wants to be called a Six Sigma operation, what percentage of deliveries should it complete to within 20 minutes from the time of accepting an order?

Answer 1

a.We calculate the variance for the given sample of seven orders.

Using excel function, VAR(18,17,19,20,15,25,30) =26.95

Mean of the delivery times =20.57 minutes

Since the variance is very high,it indicates that the delivery times are spread out and far away from the mean delivery time.Thus ,the pizza chain needs to make improvements to its process and reduce this variance.

b.Number of deliveries with delivery times > 20 is 2 ( 25 and 30 minutes)

Number of customers that got free pizza =2

c.Accuracy rate =Number of deliveries within 20 minutes/Total number of deliveries

=5/7 =71.43 %

d.For the pizza chain to be called a six sigma operation ,the percentage of deliveries to be completed within 20 minutes

=99.9997 %