Question

A job has a 90% learning curve. If the first unit took 10 hours to complete, the fifth unit should take roughly how many hours?

Answer 1

Total hours required to produce 5 units is given by the learning equation

Y = a(X^b)

Where,

Y = cumulative average total time required to produce X units

a = Time taken by the first unit = 10 hours

X = Total number of units produced = 5

b = Log of learning rate / log 2 = log 0.9 / log 2 = -0.04575/.301 = -0.15199

So, Y = 10 x (5 ^ -0.15199)

= 10 x 0.78299

= 7.8299 hours

So, total time required

= Average time x number of units

= 7.8299 hours x 5

= 39.15 hours

Total hours required to produce 4 units is given by the learning equation

Y = a(X^b)

Where,

Y = cumulative average total time required to produce X units

a = Time taken by the first unit = 10 hours

X = Total number of units produced = 4

b = Log of learning rate / log 2 = log 0.9 / log 2 = -0.04575/.301 = -0.15199

So, Y = 10 x (4 ^ -0.15199)

= 10 x 0.81001

= 8.10 hours

So, total time required

= Average time x number of units

= 8.10 hours x 4

= 32.40 hours

So, Time required to produce the 5^th unit

= Time required to produce 5 units in total – Time required to produce 4 units in total

= 39.15 hours - 32.40 hours

= 6.75 hours