MBA Operations Management Student Name _______________________. Skill Builder Exercise #3 Problem 1. The production manager at Sunny Soda, Inc., is interested in tracking the quality of the company's 12-ounce bottle filling line. The bottles must be filled within the tolerances set for this product because the dietary information on the label shows 12 ounces as the serving size. The design specification for the product calls for a fill level of 12.000.10 ounces. The manager collected the following sample data (in fluid ounces per bottle) on the production process. Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 12.00 11.91 11.89 12.10 12.08 11.94 12.09 12.01 12.00 11.92 11.91 12.01 11.98 12.02 12.00 Observation 2 3 11.97 12.10 11.94 12.10 12.02 11.97 12.09 12.05 11.92 12.12 11.98 12.06 12.00 12.00 12.04 11.99 11.96 11.97 11.94 12.09 11.99 12.05 12.00 12.06 11.99 12.06 12.00 12.05 12.05 12.01 4 12.08 11.96 11.99 11.95 12.05 12.08 12.03 11.95 12.03 12.00 12.10 11.97 12.03 11.95 11.97 a) (10 points) Calculate control limits for R-chart and draw the R-chart. b) (10 points) Calculate control limits for x -chart and draw the x -chart. c) (10 points) From the charts, is the process in control? And why? d) (20 points) Assuming the population mean and standard deviation of the bottle filling line are 12.01 ounces and 0.023 ounces, respectively. Is the process capable of producing products that comply with the design specifications? Explain. Problem2: An insurance company wants to design a control chart to monitor whether insurance claim forms are being completely correctly. The company intends to sue the chart to see if improvements in the design of the form are effective. To start the process the company collected data on the number of incorrectly completed claim forms over the past 10 days. The insurance company processes thousands of these forms each day, and due to the high cost of inspecting each form, only a small representative sample was collected each day. The data and analysis are shown in the table: Sample Number Inspected 1 2 3 4 5 6 7 8 9 10 300 300 300 300 300 300 300 300 300 300 # of Forms Completed Incorrectly 10 8 9 13 7 7 6 11 12 8 a) (20 points) Assume that the process is \"in control\" during past 10 days. Calculate the mean proportion and standard deviation. Mean proportion: ___________________ Standard deviation: ___________________ b) (30 points) Calculate the upper control limit and the lower control limit (use a multiple of 3 times sigma for the control limits) and draw the control chart. Is the process in control? And why? UCL: ____________________ LCL: _____________________
