Question

1. If the learning curve for a process is 100 percent, the labor requirements in the company drop sharply. TRUE OR FALSE

2. If it took 1000 hours to produce the first unit of a product, and the learning curve is 70%, how long will it take to produce units 26 through 50?

Answer: ___________ hours (use whole number)

3. Under 80% learning rate, the improvement rate is _______ %

Answer 1

1. If learning curve of the process is 100 percent, then the time required to produce nth unit remains same as of the first unit. This means there is no improvement or no learning.

Y = aX^b

Y = cumulative time required to produce x units

a = time required to produce 1st unit

b = slope of the function or improvement rate

b = log (learning rate) / log 2 = log (1) / log (2) = 0/0.301= 0

now the equation is Y = aX^0 = a

As there is no learning, the time required to produce 1st unit is the time taken to produce nth unit. So, to produce any amount of units, we need that many times of number of labor required to produce 1st unit. Hence the labor requirement in the company increases sharply.

Answer is False.

2. a = 1000 hours, learning rate = 70%,

Y = aX^b

b = log (0.7)/log(2) = -0.51457

Y = 1000*26^(-0.51457) = 187 hours

Similarly the time can be calculated for units till 50.

units	time required for nth unit	cumulative till nth unit
26	187.0239	187.0239
27	183.427	370.4509
28	180.0263	550.4771
29	176.8047	727.2819
30	173.7472	901.029
31	170.8402	1071.869
32	168.0718	1239.941
33	165.4315	1405.373
34	162.9097	1568.282
35	160.4977	1728.78
36	158.188	1886.968
37	155.9734	2042.941
38	153.8476	2196.789
39	151.8049	2348.594
40	149.8401	2498.434
41	147.9482	2646.382
42	146.125	2792.507
43	144.3664	2936.874
44	142.6687	3079.542
45	141.0284	3220.571
46	139.4424	3360.013
47	137.9077	3497.921
48	136.4218	3634.342
49	134.982	3769.324
50	133.586	3902.91

So, to produce units 26 through 50, it would require 3903 hours

3. Under 80% learning rate, the improvement rate is b = log(0.8)/log(2) = -0.32193 or -32%