# LearningCurvesFromExerciseBookGMS401Fall2012.docx

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Ryerson University

Global Management Studies

GMS 401

Kirk Bailey

Fall

Description

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.
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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.
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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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