Problem 4:

a. According to the customers specification given to the manufacturer, the length of a shoe should not deviate from the correct size by more than 1 mm. In the manufacturing process, the standard deviation of this length is 0.32 mm and the mean is equal to the correct size. Find the capability ratio of this process for three standard deviations. Is this process capable? (5 points)

b. A local fast-food restaurant has told its employees that the maximum amount for order time should be 2.75 minutes. Ordering time data was collected for five randomly selected customers per day for 10 days. (5 points)

c. Construct Upper and Lower Control Limits of a X bar and range chart.

Mean Range 1.4 2.22 1.45 0.4 1.72 0.6 0.6 1.56 1.92 0.9 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 1.71 0.5 3.20 2.5 2.37 1.3 1.89 0.6 1.30 0.2 i = 1.934 R = 0.9