Exam 16: Learning Curve Analysis

What are the three major assumptions of the learning curve?

The learning rate depends on factors such as ________ and ________.

Which one of the following statements is TRUE about the relationship between learning curves and competitive strategy?

The estimated time to produce the first unit is 100 hours.If a 90 percent learning rate is applicable,what is the estimated time of producing the tenth unit? Refer to the copy of Table G.1 above.

Two contract labor companies are competing for work being outsourced by Febrero SpA.One contractor,Terza,has a learning rate governed by a tripling of output at a 90% rate and the other contractor,Segundo,has a learning rate governed by the conventional doubling of output at a 90% rate.Both Terza and Segundo take 20 minutes to complete the first unit they are given for bid estimation purposes.How many more units must Terza make than Segundo before their time per unit drops below 15 minutes?

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit 80\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.53718 37 0.43976 2 0.90000 20 0.52425 38 0.43634 3 0.83403 21 0.51715 39 0.43304 4 0.78553 22 0.51045 40 0.42984 5 0.74755 23 0.50410 64 0.37382 6 0.71657 24 0.49808 128 0.30269 7 0.69056 25 0.49234 256 0.24405 8 0.66824 26 0.48688 512 0.19622 9 0.64876 27 0.48167 600 0.18661 10 0.63154 28 0.47668 700 0.17771 11 0.61613 29 0.47191 800 0.17034 12 0.60224 30 0.46733 900 0.16408 13 0.58960 31 0.46293 1,000 0.15867 14 0.57802 32 0.45871 1,200 0.14972 15 0.56737 33 0.46464 1,400 0.14254 16 0.55751 34 0.45072 1,600 0.13660 17 0.54834 35 0.44694 1,800 0.13155 18 0.53979 36 0.44329 2,000 0.12720 90\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.73545 37 0.67091 2 0.95000 20 0.73039 38 0.66839 3 0.91540 21 0.72559 39 0.66595 4 0.88905 22 0.72102 40 0.66357 5 0.86784 23 0.71666 64 0.62043 6 0.85013 24 0.71251 128 0.56069 7 0.83496 25 0.70853 256 0.50586 8 0.82172 26 0.70472 512 0.45594 9 0.80998 27 0.70106 600 0.44519 10 0.79945 28 0.69754 700 0.43496 11 0.78991 29 0.69416 800 0.42629 12 0.78120 30 0.69090 900 0.41878 13 0.77320 31 0.68775 1,000 0.41217 14 0.76580 32 0.67471 1,200 0.40097 15 0.75891 33 0.68177 1,400 0.39173 16 0.75249 34 0.67893 1,600 0.38390 17 0.74646 35 0.67617 1,800 0.37711 18 0.74080 36 0.67350 2,000 0.37114 -Suppose the average time for the first 1,000 units you have manufactured is 2.375 minutes.Your rate of learning is 90 percent,and you need to find the total time required to manufacture the next 1,000 units.Refer to the copy of Table G.1 above.The total time is:

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit 80\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.53718 37 0.43976 2 0.90000 20 0.52425 38 0.43634 3 0.83403 21 0.51715 39 0.43304 4 0.78553 22 0.51045 40 0.42984 5 0.74755 23 0.50410 64 0.37382 6 0.71657 24 0.49808 128 0.30269 7 0.69056 25 0.49234 256 0.24405 8 0.66824 26 0.48688 512 0.19622 9 0.64876 27 0.48167 600 0.18661 10 0.63154 28 0.47668 700 0.17771 11 0.61613 29 0.47191 800 0.17034 12 0.60224 30 0.46733 900 0.16408 13 0.58960 31 0.46293 1,000 0.15867 14 0.57802 32 0.45871 1,200 0.14972 15 0.56737 33 0.46464 1,400 0.14254 16 0.55751 34 0.45072 1,600 0.13660 17 0.54834 35 0.44694 1,800 0.13155 18 0.53979 36 0.44329 2,000 0.12720 90\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.73545 37 0.67091 2 0.95000 20 0.73039 38 0.66839 3 0.91540 21 0.72559 39 0.66595 4 0.88905 22 0.72102 40 0.66357 5 0.86784 23 0.71666 64 0.62043 6 0.85013 24 0.71251 128 0.56069 7 0.83496 25 0.70853 256 0.50586 8 0.82172 26 0.70472 512 0.45594 9 0.80998 27 0.70106 600 0.44519 10 0.79945 28 0.69754 700 0.43496 11 0.78991 29 0.69416 800 0.42629 12 0.78120 30 0.69090 900 0.41878 13 0.77320 31 0.68775 1,000 0.41217 14 0.76580 32 0.67471 1,200 0.40097 15 0.75891 33 0.68177 1,400 0.39173 16 0.75249 34 0.67893 1,600 0.38390 17 0.74646 35 0.67617 1,800 0.37711 18 0.74080 36 0.67350 2,000 0.37114 -Given that the third unit took 100 minutes and the rate of learning is 80 percent,how much time will it take to build unit 96? Refer to the copy of Table G.1 above.

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit 80\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.53718 37 0.43976 2 0.90000 20 0.52425 38 0.43634 3 0.83403 21 0.51715 39 0.43304 4 0.78553 22 0.51045 40 0.42984 5 0.74755 23 0.50410 64 0.37382 6 0.71657 24 0.49808 128 0.30269 7 0.69056 25 0.49234 256 0.24405 8 0.66824 26 0.48688 512 0.19622 9 0.64876 27 0.48167 600 0.18661 10 0.63154 28 0.47668 700 0.17771 11 0.61613 29 0.47191 800 0.17034 12 0.60224 30 0.46733 900 0.16408 13 0.58960 31 0.46293 1,000 0.15867 14 0.57802 32 0.45871 1,200 0.14972 15 0.56737 33 0.46464 1,400 0.14254 16 0.55751 34 0.45072 1,600 0.13660 17 0.54834 35 0.44694 1,800 0.13155 18 0.53979 36 0.44329 2,000 0.12720 90\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.73545 37 0.67091 2 0.95000 20 0.73039 38 0.66839 3 0.91540 21 0.72559 39 0.66595 4 0.88905 22 0.72102 40 0.66357 5 0.86784 23 0.71666 64 0.62043 6 0.85013 24 0.71251 128 0.56069 7 0.83496 25 0.70853 256 0.50586 8 0.82172 26 0.70472 512 0.45594 9 0.80998 27 0.70106 600 0.44519 10 0.79945 28 0.69754 700 0.43496 11 0.78991 29 0.69416 800 0.42629 12 0.78120 30 0.69090 900 0.41878 13 0.77320 31 0.68775 1,000 0.41217 14 0.76580 32 0.67471 1,200 0.40097 15 0.75891 33 0.68177 1,400 0.39173 16 0.75249 34 0.67893 1,600 0.38390 17 0.74646 35 0.67617 1,800 0.37711 18 0.74080 36 0.67350 2,000 0.37114 -How long will it take to make 25 units if the first one took 8 hours and there is a 90 percent learning rate? Refer to the copy of Table G.1 above.

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit 80\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.53718 37 0.43976 2 0.90000 20 0.52425 38 0.43634 3 0.83403 21 0.51715 39 0.43304 4 0.78553 22 0.51045 40 0.42984 5 0.74755 23 0.50410 64 0.37382 6 0.71657 24 0.49808 128 0.30269 7 0.69056 25 0.49234 256 0.24405 8 0.66824 26 0.48688 512 0.19622 9 0.64876 27 0.48167 600 0.18661 10 0.63154 28 0.47668 700 0.17771 11 0.61613 29 0.47191 800 0.17034 12 0.60224 30 0.46733 900 0.16408 13 0.58960 31 0.46293 1,000 0.15867 14 0.57802 32 0.45871 1,200 0.14972 15 0.56737 33 0.46464 1,400 0.14254 16 0.55751 34 0.45072 1,600 0.13660 17 0.54834 35 0.44694 1,800 0.13155 18 0.53979 36 0.44329 2,000 0.12720 90\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.73545 37 0.67091 2 0.95000 20 0.73039 38 0.66839 3 0.91540 21 0.72559 39 0.66595 4 0.88905 22 0.72102 40 0.66357 5 0.86784 23 0.71666 64 0.62043 6 0.85013 24 0.71251 128 0.56069 7 0.83496 25 0.70853 256 0.50586 8 0.82172 26 0.70472 512 0.45594 9 0.80998 27 0.70106 600 0.44519 10 0.79945 28 0.69754 700 0.43496 11 0.78991 29 0.69416 800 0.42629 12 0.78120 30 0.69090 900 0.41878 13 0.77320 31 0.68775 1,000 0.41217 14 0.76580 32 0.67471 1,200 0.40097 15 0.75891 33 0.68177 1,400 0.39173 16 0.75249 34 0.67893 1,600 0.38390 17 0.74646 35 0.67617 1,800 0.37711 18 0.74080 36 0.67350 2,000 0.37114 -The seventh unit of a long production run was produced in 3 hours.The process has an estimated learning rate of 90 percent.At what level of output will the cumulative production time exceed 40 hours? Refer to the copy of Table G.1 above.

The fifth unit took 10 hours to produce and the learning rate is expected to be 85 percent.How long will it take to produce the tenth unit?

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit 80\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.53718 37 0.43976 2 0.90000 20 0.52425 38 0.43634 3 0.83403 21 0.51715 39 0.43304 4 0.78553 22 0.51045 40 0.42984 5 0.74755 23 0.50410 64 0.37382 6 0.71657 24 0.49808 128 0.30269 7 0.69056 25 0.49234 256 0.24405 8 0.66824 26 0.48688 512 0.19622 9 0.64876 27 0.48167 600 0.18661 10 0.63154 28 0.47668 700 0.17771 11 0.61613 29 0.47191 800 0.17034 12 0.60224 30 0.46733 900 0.16408 13 0.58960 31 0.46293 1,000 0.15867 14 0.57802 32 0.45871 1,200 0.14972 15 0.56737 33 0.46464 1,400 0.14254 16 0.55751 34 0.45072 1,600 0.13660 17 0.54834 35 0.44694 1,800 0.13155 18 0.53979 36 0.44329 2,000 0.12720 90\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.73545 37 0.67091 2 0.95000 20 0.73039 38 0.66839 3 0.91540 21 0.72559 39 0.66595 4 0.88905 22 0.72102 40 0.66357 5 0.86784 23 0.71666 64 0.62043 6 0.85013 24 0.71251 128 0.56069 7 0.83496 25 0.70853 256 0.50586 8 0.82172 26 0.70472 512 0.45594 9 0.80998 27 0.70106 600 0.44519 10 0.79945 28 0.69754 700 0.43496 11 0.78991 29 0.69416 800 0.42629 12 0.78120 30 0.69090 900 0.41878 13 0.77320 31 0.68775 1,000 0.41217 14 0.76580 32 0.67471 1,200 0.40097 15 0.75891 33 0.68177 1,400 0.39173 16 0.75249 34 0.67893 1,600 0.38390 17 0.74646 35 0.67617 1,800 0.37711 18 0.74080 36 0.67350 2,000 0.37114 -How long will it take to make 25 units if the third one took 6.5 hours and there is a 90 percent learning rate? Refer to the copy of Table G.1 above.

Which of the following statements about learning curves is generally TRUE?

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit 80\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.53718 37 0.43976 2 0.90000 20 0.52425 38 0.43634 3 0.83403 21 0.51715 39 0.43304 4 0.78553 22 0.51045 40 0.42984 5 0.74755 23 0.50410 64 0.37382 6 0.71657 24 0.49808 128 0.30269 7 0.69056 25 0.49234 256 0.24405 8 0.66824 26 0.48688 512 0.19622 9 0.64876 27 0.48167 600 0.18661 10 0.63154 28 0.47668 700 0.17771 11 0.61613 29 0.47191 800 0.17034 12 0.60224 30 0.46733 900 0.16408 13 0.58960 31 0.46293 1,000 0.15867 14 0.57802 32 0.45871 1,200 0.14972 15 0.56737 33 0.46464 1,400 0.14254 16 0.55751 34 0.45072 1,600 0.13660 17 0.54834 35 0.44694 1,800 0.13155 18 0.53979 36 0.44329 2,000 0.12720 90\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.73545 37 0.67091 2 0.95000 20 0.73039 38 0.66839 3 0.91540 21 0.72559 39 0.66595 4 0.88905 22 0.72102 40 0.66357 5 0.86784 23 0.71666 64 0.62043 6 0.85013 24 0.71251 128 0.56069 7 0.83496 25 0.70853 256 0.50586 8 0.82172 26 0.70472 512 0.45594 9 0.80998 27 0.70106 600 0.44519 10 0.79945 28 0.69754 700 0.43496 11 0.78991 29 0.69416 800 0.42629 12 0.78120 30 0.69090 900 0.41878 13 0.77320 31 0.68775 1,000 0.41217 14 0.76580 32 0.67471 1,200 0.40097 15 0.75891 33 0.68177 1,400 0.39173 16 0.75249 34 0.67893 1,600 0.38390 17 0.74646 35 0.67617 1,800 0.37711 18 0.74080 36 0.67350 2,000 0.37114 -It took 100 hours to produce the first unit and the learning rate is 80 percent.How much time will it take to produce units 16 through 20? Refer to the copy of Table G.1 above.

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit 80\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.53718 37 0.43976 2 0.90000 20 0.52425 38 0.43634 3 0.83403 21 0.51715 39 0.43304 4 0.78553 22 0.51045 40 0.42984 5 0.74755 23 0.50410 64 0.37382 6 0.71657 24 0.49808 128 0.30269 7 0.69056 25 0.49234 256 0.24405 8 0.66824 26 0.48688 512 0.19622 9 0.64876 27 0.48167 600 0.18661 10 0.63154 28 0.47668 700 0.17771 11 0.61613 29 0.47191 800 0.17034 12 0.60224 30 0.46733 900 0.16408 13 0.58960 31 0.46293 1,000 0.15867 14 0.57802 32 0.45871 1,200 0.14972 15 0.56737 33 0.46464 1,400 0.14254 16 0.55751 34 0.45072 1,600 0.13660 17 0.54834 35 0.44694 1,800 0.13155 18 0.53979 36 0.44329 2,000 0.12720 90\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.73545 37 0.67091 2 0.95000 20 0.73039 38 0.66839 3 0.91540 21 0.72559 39 0.66595 4 0.88905 22 0.72102 40 0.66357 5 0.86784 23 0.71666 64 0.62043 6 0.85013 24 0.71251 128 0.56069 7 0.83496 25 0.70853 256 0.50586 8 0.82172 26 0.70472 512 0.45594 9 0.80998 27 0.70106 600 0.44519 10 0.79945 28 0.69754 700 0.43496 11 0.78991 29 0.69416 800 0.42629 12 0.78120 30 0.69090 900 0.41878 13 0.77320 31 0.68775 1,000 0.41217 14 0.76580 32 0.67471 1,200 0.40097 15 0.75891 33 0.68177 1,400 0.39173 16 0.75249 34 0.67893 1,600 0.38390 17 0.74646 35 0.67617 1,800 0.37711 18 0.74080 36 0.67350 2,000 0.37114 -The fourth unit took 10 hours to produce and the learning rate is expected to be 80 percent.How long will it take to produce the tenth unit? Refer to the copy of Table G.1 above.

Under learning curve theory,with a learning rate of 70 percent

The mathematical model that is used to generate a learning curve is ________.

The first unit produced in 15 hours has an estimated learning rate of 90 percent.At what level of output will the average production time per unit fall below 11 hours?

Which statement regarding the effect of automating some of the direct labor in a process is best?

The simpler the product,the more pronounced the learning rate.

The production schedule for a new product follows Month No Units 1 15 2 20 3 40 4 35 The first unit took 100 hours to complete, and the rate of learning is 80 percent. Each employee works 40 hours per month. Refer to the copy of Table G.1 below. Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit 80\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.53718 37 0.43976 2 0.90000 20 0.52425 38 0.43634 3 0.83403 21 0.51715 39 0.43304 4 0.78553 22 0.51045 40 0.42984 5 0.74755 23 0.50410 64 0.37382 6 0.71657 24 0.49808 128 0.30269 7 0.69056 25 0.49234 256 0.24405 8 0.66824 26 0.48688 512 0.19622 9 0.64876 27 0.48167 600 0.18661 10 0.63154 28 0.47668 700 0.17771 11 0.61613 29 0.47191 800 0.17034 12 0.60224 30 0.46733 900 0.16408 13 0.58960 31 0.46293 1,000 0.15867 14 0.57802 32 0.45871 1,200 0.14972 15 0.56737 33 0.46464 1,400 0.14254 16 0.55751 34 0.45072 1,600 0.13660 17 0.54834 35 0.44694 1,800 0.13155 18 0.53979 36 0.44329 2,000 0.12720 90\% Learning Rate ( n= cumulative production) n n n 1 1.00000 19 0.73545 37 0.67091 2 0.95000 20 0.73039 38 0.66839 3 0.91540 21 0.72559 39 0.66595 4 0.88905 22 0.72102 40 0.66357 5 0.86784 23 0.71666 64 0.62043 6 0.85013 24 0.71251 128 0.56069 7 0.83496 25 0.70853 256 0.50586 8 0.82172 26 0.70472 512 0.45594 9 0.80998 27 0.70106 600 0.44519 10 0.79945 28 0.69754 700 0.43496 11 0.78991 29 0.69416 800 0.42629 12 0.78120 30 0.69090 900 0.41878 13 0.77320 31 0.68775 1,000 0.41217 14 0.76580 32 0.67471 1,200 0.40097 15 0.75891 33 0.68177 1,400 0.39173 16 0.75249 34 0.67893 1,600 0.38390 17 0.74646 35 0.67617 1,800 0.37711 18 0.74080 36 0.67350 2,000 0.37114 -Using the information in Case G.1,what is the minimum number of employees needed in month 3?