1) [10 points] Which of the Seven QC Tools would be most useful in addressing each of the following situations? Explain your reasoning. a) a. A copy machine suffers frequent paper jams and users are often confused as to how to fix the problem. b) A bank needs to determine how many teller positions, drive-through stations, and ATM machines it needs for a new branch bank in a certain busy location. Its information includes the average numbers and types of customers served by other similar facilities, as well as demographic information to suggest the level of customer traffic in the new facility. c) A contracting agency wants to investigate why they had so many changes in their contracts. They believe that the number of changes may be related to the dollar value of the original contract or the days between the request for proposal and the contract award. 2) [10 points] Over the last year, 1,800 injections were administered at a clinic. Quality is measured by the proper amount of dosage as well as the correct drug. In six instances, the incorrect amount was given, and in three cases, the wrong drug was given. a) What is the epmo metric? b) What sigma level does it correspond to? (You may need to use the Excel template). 3) [10 points] Analysis of customer complaints at an e-commerce retailer revealed the following: Billing errors 537 Shipping errors 2,460 Electronic charge errors 650 Shipping delays 5,372 Packing errors 752 Construct a Pareto diagram and discuss the conclusions you may draw from it. 4) [10 points] Thirty samples of size 4 of the customer waiting time at a call center for a health insurance company resulted in an overall mean of 10.4 minutes and average range of 0.9 minutes. Compute the control limits for x-bar and R-charts. MGMT 3106: Management Science and Operations Management 5) [20 points] Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Webster is concerned whether the filling process for tubes of caulking is in statistical control. The process should be centered on 8 ounces per tube. Six samples of eight tubes are taken and each tube is weighed in ounces. a) Calculate Mean, Average Range, Upper and lower control limits for xBar and R charts. Show all calculations. (You may use Excel tools to verify your answers). b) Plot the xBar and R charts. (You may use Excel tools to plot the charts.) c) Based on the xBar and R charts, discuss whether the process in statistical control or not. 6) [20 points] A sticky scale brings Webster’s attention to whether caulking tubes are being properly capped. If a significant proportion of the tubes aren’t being sealed, Webster is placing their customers in a messy situation. Tubes are packaged in large boxes of 144. Several boxes are inspected and the following numbers of leaking tubes are found: a) Calculate the pbar, standard deviation, upper and lower control limits. Show all calculations. (You may use Excel tools to verify your answers). b) Plot the p-chart. (You may use Excel tools to plot the charts.) c) Based on the p-chart, discuss whether the process in statistical control or not. Tube Number Sample 1 2 3 4 5 6 7 8 1 7.98 8.34 8.02 7.94 8.44 7.68 7.81 8.11 2 8.23 8.12 7.98 8.41 8.31 8.18 7.99 8.06 3 7.89 7.77 7.91 8.04 8.00 7.89 7.93 8.09 4 8.24 8.18 7.83 8.05 7.90 8.16 7.97 8.07 5 7.87 8.13 7.92 7.99 8.10 7.81 8.14 7.88 6 8.13 8.14 8.11 8.13 8.14 8.12 8.13 8.14 Sample Tubes Sample Tubes Sample Tubes 1 3 8 6 15 5 2 5 9 4 16 0 3 3 10 9 17 2 4 4 11 2 18 6 5 2 12 6 19 2 6 4 13 5 20 1 7 2 14 1 Total = 72 MGMT 3106: Management Science and Operations Management 7) [10 points] A fast food franchise tracked the number of errors that occurred in customers’ orders. These included wrong menu item, wrong size drink, lack of condiments, wrong price total, and so on. Some orders may have more than one error. In one week, 1250 orders were filled, and a total of 30 errors were discovered. Find the control limits for a c-chart. 8) [10 points] A specification for a spacer plate used in a machine tool has specifications LSL = 0.05 and USL = 0.10 cm in thickness. A sample of 100 parts found µ = 0.067 and σ= 0.011. Compute and interpret the process capability indexes Cp, Cpl, Cpu, and Cpk
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