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Ryerson University
Global Management Studies
GMS 401
Kirk Bailey

GMS-401 Learning Curve Solutions from the Exercise Book -complete with full explanations: Page 10 #1 Ryerson Hospital kidney transplants: You are given that L=.92 and Y 1= 6.5 hours. You are asked to find Y8 using 3 different methods: 1. Using the basic Tom Wright formula of Y 2 = Y1 * L and Y 4 = Y2 * L and 3 Y8 = Y4 * L and with a bit of basic algebra Y 8 = Y1 * L Y = Y * L 3 >>>>>> Y = 6.5 * (.92) = 6.5 * .778688 = 5.06 hours 8 1 8 2. Using the chart provided Y8= Y 1 chart coefficient under the .92 units column at unit #8 go to the yellow chart page #3 shown as page 834 and entitled "APPENDIX D LEARNING CURVE CO-EFFICIENTS AND CUMULATIVE TOTALS". Move horizontally across the top of the chart to the .92 column under 92% and move down the column to N = 8. There you will find 0.779 as the required co-efficient. Thus 6.5 * .779 = 5.06 hours. 3. Using the formula shown at the top of the Learning Curve Appendix D referred to above: Y = Y * (N) (LOG L/LOG 2) N 1 (LOG .92/LOG 2) Y8= 6.5 * (8) = 5.06 hours. -------------------------------------------------------------------------------------------------------------- th b) How long will it take for the 100 transplant? There are 2 ways to do this: 1. Use the formula above Y100 = 6.5 (100) (LOG .92/LOG = 3.74 hours using your Stats calculator. 2. Using the supplied chart. Problem: chart ends around N = 92. Solution: ? Wright's basic formula stated that ANY doubling can use the learning rate. Thus we can use the chart to find Y an50then use the doubling property of Learning Curves to find Y 100. Y50 Y *1chart coefficient of units at 92% and 50 units = 6.5 * .625 = 4.0625 Y100 = Y50 L thus: Y 100= 4.0625 * .92 = 3.74 as above. Therefore you have TWO ways of finding any Y value Nou need. -------------------------------------------------------------------------------------------------------------- c) What is the TOTAL time required for the first 15 transplants? That is to say what is the TOTAL of Y1+Y2+Y3+............+Y15. Y1 is known and given as 6.5 hours. We would like to avoid 15 calculations more i.e. Y2 to Y15 inclusive and then have to add all of these up to get a TOTAL. The designers of the Learning Curve chart anticipated such a requirement and provided a totals column to provide an easier and faster way to calculate such an answer. SUM of 1-15 inclusive = 6.5 * 12.044 = 78.286 hours. The 12.044 coefficient is determined by moving horizontally across the chart to 92% as before but moving one more column to the right to the "Total" column and reading down to N=15 where you will find the 12.044 value. Multiply by the 6.5 for Y and y1u have your answer. Note: Learning curve charts such as that given in the formula and charts package plus the chart in the text are based on the time of Y1 being ONE unit of time. Since our 1 is 6.5 hours it means that each coefficient in the chart would need to be multiplied by the same 6.5. We would only multiply out those we actually need. -----------------------------------------------------------------------------
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