Customer expectations on pizza delivery are such that most people are happy with a 20 minute delivery and very upset if it takes more than 40 minutes. You have observed the delivery time for a random sample of customers for two days as follows:
DayDelivery number 1 2 3 4 5 6 7 8 9 10
Day 1 15 23 22 28 34 10 50 20 37 41
Day 2 32 21 27 40 12 45 41 22 35 31
• Using an USL of 40 and an LSL of 20, calculate both Cp and Cpk where Cp = (USL-LSL)/6*σ and Cpk = Minimum of (USL-μ)/3σ and (μ-LSL)/3σ. Note that to calculate the mean (μ) and standard deviation (σ), you could use delivery time data on day 1, day 2 or both days. I would use all 20 data points, but it's your call.
b) Based on your answer in (a), is the process capable?
c) Suggest the upper and lower control limits (UCL and LCL) of a control chart that would monitor the pizza delivery process?
Note that control limits, UCL and LCL are defined as UCL = (μ+3σ) and LCL = (μ-3σ) and represent data ranges within which we conclude that the process has no aberrant behavior (assignable cause).