Read the following scenario to answer the questions: "The time it takes from receipt of order by ITL to shipping (the "order-to-ship" time) is too variable for the company to guarantee a fast lead time for delivery to customers. Rick is upset about this variability, since he's received some customer complaints. He has a very reliable trucking company, but he knows he needs to improve his own operations. He goes to talk to Roberto, asking him to ensure that the order-to-ship process does not exceed 3 days. "I'll look into it and get back to you quickly boss," says Roberto. Roberto generates some data on the process (Table 2 below). After some quick analysis of the numbers, Roberto, full of confidence, comes back to Rick the next day and says, "Boss, good news! In the last 60 orders, only 3 orders took longer than 3 days. That's only 5% of all orders. Our average is 2.14 days and we're below 3 days 95% of the time.

That's pretty good!" Roberto responds, "That may be good enough for you, but it's not good enough for our customers. I need this process to be Six Sigma good!" Use the data from Table 2 below and assume the target mean is 1.5 days, the LSL is 0 days, and the USL is 3 days for the order-to-shipment process (see Figure 1 below), and answer the following questions. (10 points)

a. What is the current UCL of the process? (1 point)

b. What is the current LCL of the process? (1 point)

c. Calculate the current Cp. Is the process capable? (2 points)

d. Calculate the current Cpk. Is the process centred? (2 points)

e. Is the current process "Six Sigma" good? Why or why not? (2 points)

f. What would the mean and standard deviation have to be in order to be "Six Sigma" good? (2 points) FIGURE 1: The Capability of the ITL Order-to-Shipment Process