Question

In a mechanical assembly operation, the first work unit required 7.83 min to complete and the learning rate for mechanical assembly is 84% in the Crawford model. Using this learning curve model, determine the unit times to produce (a) the second unit, (b) the 10th unit, and (c) the 100th unit (d) the total cumulative time to produce units 1-100

Answer 1

Answer:

(a) 6.5774 minutes

(b) 4.3879 minutes

(c) 2.459 minutes

(d) 245.902 minutes

Explanation:

The learning curve model follows the following equation:

$Y=aX^b$

where Y are the units time to produce X units, and a is the time for assembly the first unit. Additionally, b is calculated as:

$b=\frac{ln(r)}{ln(2)}$

Where r is the learning rate for mechanical assembly. So, b is equal to:

$b=\frac{ln(0.84)}{ln(2)}=-0.2515$

Then, the equation is:

$Y=7.83X^{-0.2515}$

Finally, the unit times to produce the second unit are:

$Y=7.83(2)^{-0.2515}=6.5774$

The 10th unit:

$Y=7.83(10)^{-0.2515}=4.3879$

The 100th unit:

$Y=7.83(100)^{-0.2515}=2.459$

Then, the total cumulative time T to produce 100 units in the Crawford model is calculated as:

$T=7.83\frac{(100.5)^{1-0.2515}-(0.5)^{1-0.2515})}{1-0.2515} \\T=323.5383$