The following Excel spreadsheet calculates the upper and lower control limits for a continuous variable. Re-create this spreadsheet in Excel. You should develop the spreadsheet so that the results will be recalculated if any of the values in the highlighted cells are changed. Your formatting does not have to be exactly the same, but the numbers should be. (As a test, see what happens if all five observations in Sample 1 are 40. Your new upper and lower control limits for the sample means should be 36.05 and 34.28, respectively.

Central Airlines would like to set up a control chart to monitor its on-time arrival performance. Each day over a 10-day period, Central Airlines chose 30 flights at random and tracked the number of late arrivals in each sample. The results are as follows.

a. Calculate p

b. Set up a p chart to track the proportion of late arrivals. (Note: Each sample consists of 30 observations.)

c. Airline travel is characterized by busy and slow seasons. As a result, what is “normal” during one time of the year wouldn’t be “normal” at some other time. What difficulties might arise as a result of using a single control chart to track the proportion of late arrivals? What could Central Airlines do about this?

$$\begin{array}{rcc} \hline & & \text { NO. OF LATE- } \\ \text { DAY } & \text { SAMPLE SIZE } & \text { ARRIVING FLIGHTS } \\ \hline 1 & 30 & 2 \\ 2 & 30 & 3 \\ 3 & 30 & 4 \\ 4 & 30 & 0 \\ 5 & 30 & 1 \\ 6 & 30 & 6 \\ 7 & 30 & 4 \\ 8 & 30 & 2 \\ 9 & 30 & 3 \\ 10 & 30 & 5 \\ \hline \end{array}$$

BHC produces bags of cement. The stated weight for a bag of cement is 100 lb. Customers will accept an occasional bag weighing as little as 96 lb., as long as the average weight is at least 100 lb. At the same time, BHC doesn’t want to give away cement, so it has set an upper tolerance limit of 104 lb. The current filling process has an actual process mean of 101 lb. and a standard deviation of 0.65 lb.

a. Calculate the process capability index for BHC. In this example, why should we use the process capability index rather than the process capability ratio to assess capability?

b. Can you think of any reason BHC might want a process mean higher than the target value?

Crawford Pharmaceuticals has developed a new drug, Vaxidene. The target amount for a single dose of Vaxidene is 100 mg. Patients can receive as little as 98 mg or as much as 102 mg without experiencing any ill effects. Because of potential liability issues, Crawford has determined that it is imperative that manufacturing be able to provide Six Sigma quality levels. At present, the manufacturing process has a process mean of 100 mg and a standard deviation of 0.25 mg.

a. What are the upper and lower tolerance limits for Vaxidene?

b. Is Crawford’s manufacturing process currently able to meet the dosage specifications at least 99.7% of the time? Show your work.

c. What would the standard deviation for the process have to be in order for Crawford to achieve Six Sigma quality levels?

Suppose Tyler changes its processes so that the average package weight is now 1.5 kg, with a new standard deviation of 0.2 kg. Tyler still markets the packages of bees as weighing 1.4 kg, and the tolerance limits remain as before. Calculate the process capability index for the weight of the bee packages. Is Tyler able to meet the tolerance limits?

EK Chemical Company sells a specialty chemical in packages marked 100 g. In reality, EK has set the process mean at 100.5 g, and the process currently has a standard deviation of 0.50 g. Suppose the customer will accept anywhere from 98 to 102 g, as long as the average package has at least 100 g.

a. Calculate the process capability index for the current manufacturing process. Is the process capable of meeting the tolerance limits more than 99.7% of the time? Explain.

b. Now suppose EK recenters the manufacturing process so that the process mean is exactly 100 g, while the standard deviation remains the same. Calculate the process capability ratio. Is the process still capable of meeting the tolerance limits more than 99.7% of the time? Explain