Question

What is the estimate of the cumulative average hours per unit required to produce the first 5 units of a production run that has a(n) 78% learning curve, if the first unit takes 61 hours? (HINT: skip unit)

Answer 1

Time required to produce n units = K₁ * n^b

here

K₁ = direct labor hours for the first unit

n = cumulative numbers of unit produced

b = (log r) / (log 2)

= log 0.78 / log 2

= - 0.107905 / 0.30102 = -0.35845

r = learning rate = 0.78

Time required to produce first unit = 61 hours

Time required to produce second unit = 61 * 2^{(log0.78 / log2)}

                                                       = 61 * 2 ^-(0.35845)

                                                                         = 61 * 0.780002

                                                       = 47.58 hours

Time required to produce third unit = 61 * 3^-(0.35845)

                                                                    = 61 * 0.67449

                                                   = 41.14 hours

Time required to produce fourth unit = 61 * 4^-(0.35845)

                                                                     = 61 * 0.60840

                                                    = 37.11 hours

Time required to produce fifth unit = 61 * 5^-(0.35845)

                                                = 61 * 0.56164

                                                = 34.26 hours

Cumulative average time to produce first five units = Time required to produce (first unit + second unit + third unit + fourth unit + fifth unit)

Cumulative average time to produce first five units = 61 hours + 47.58 hours + 41.14 hours + 37.11 hours + 34.26 hours

Cumulative average time to produce first five units = 221.09 hours