Question

6. If it took 80 hours to produce the first unit of a product, and the learning rate is 80%, how long will it take to produce units 26 through 125? A. 1158.54 hours B. 1998.94 hours C. 1779.07 hours D. 2064.36 hours E Impossible to answer in the time allowed.

Answer 1

D. 2064.36 hrs

Explanation:

The learning curve is usually given by

Y = aX^b

Where

Y = cumulative average time per unit or batch.

a = time taken to produce the first unit; 80 hours here

X = Cumulative units of production

Learning Rate = 0.8

b = the learning coefficient, which is calculated as: log(learning rate) ÷ log 2 =

= (log(.80)/log2)

= -0.32193

Given Y₂₆ = a(26)^{(log(.80)/log2)} = 28.03 hrs

Similarly, Y₁₂₅ = 80(125)^{(log(.80)/log2)} = 16.91 hrs

Therefore, total time taken to produce from unit 26 through units 125 = ΣY_i

Where i = 26 to 125

We can create a data table for that using the formulaes above

Learning rate Number of Units Produced a Y X b 80% 80 13.5246 250 -0.3219 26 27 28 Learning Rate 80% 28.03 27.69 27.37

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 27.06 26.76 26.48 26.21 25.96 25.71 25.47 25.24 25.02 24.80 24.60 24.40 24.20 24.02 23.84 23.66 23.49 23.32 23.16 23.01 22.85 22.71 22.56 22.42 22.28 22.15 22.02 21.89 21.77 21.65 21.53 21.41 21.30

95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 18.47 18.41 18.34 18.28 18.22 18.16 18.11 18.05 17.99 17.94 17.88 17.83 17.77 17.72 17.67 17.62 17.56 17.51 17.46 17.41 17.37 17.32 17.27 17.22 17.18 17.13 17.08 17.04 16.99 16.95 16.91 2064.36 125 Total