Question

1. Mass Balance Company is manufacturing a new digital scale for use by a large chemical company. The order is for 40 units. The first scale took 60 hours of direct labor. Learning rate is 90%.

1. What is the estimated time for the 40^th unit?
2. What is the estimated time for producing all 40 units?
3. What is the average time per unit for producing the first 10 units?

Answer 1

Sol.

Calculate the learning curve factor b with the help of formula that is given below:

In(P) In(2)

P is the learning percentage which is 90% or 0.9.

In(2) is the natural logarithm of 2.

In(0.90) In(2)

= -0.152

Now, use the given equation:  

T,= T' xn

n is the number of units which is 40.

T_n is the amount of time of produce unit n.

T¹ is the amount of time of produce 1 unit which is 60 hours.   

Determine the estimate time for the 40th unit as follow:

T,= T' xn

T40 = 60 x 40-1.52

T40 = 34.35 hours

The estimated time for producing all 40 units is as follow:

= 60 X 60-1.52 x 40

= 1288.04 hours

The average time per unit for producing the first 10 units is as follow:

$&=60\times1^{-0.152}$

$&=60$

$&=60\times2^{-0.152}$   

$&=54.00$

$&=60\times3^{-0.152}$

$&=50.77$

$&=60\times4^{-0.152}$

$&=48.60$

$&=60\times5^{-0.152}$

$&=46.97$

$&=60\times6^{-0.152}$

= 45.69

$&=60\times7^{-0.152}$

$&=44.63$

= 60 X 8-0.152

= 43.74

= 60 x 9-0.152

$&=42.96$

$&=60\times10^{-0.152}$

= 42.28

Add all the calculation and divide it with 10.

479.64 10

$\begin{aligned}&=\text{47.96 hours}\end{aligned}$