The first unit took 10 hours and the fourth unit 8.1 hours. What is the improvement rate?
A) 99%
B) 95%
C) 90%
D) 15%
E) 10%

Question

Quizplus · Accepted Answer

The improvement rate can be calculated using the formula for learning curve or improvement rate: $R = \left(\frac{T_n}{T_1}\right)^{\frac{1}{n-1}}$, where $T_n$ is the time taken for the nth unit, $T_1$ is the time taken for the first unit, and $n$ is the unit number. Here, $T_1 = 10$ hours, $T_4 = 8.1$ hours, and $n = 4$. Substituting these values, we get $R = \left(\frac{8.1}{10}\right)^{\frac{1}{4-1}} = \left(0.81\right)^{\frac{1}{3}}$. Solving this gives an R value of approximately 0.9, which corresponds to a 90% learning curve. However, the improvement rate is the percentage reduction, so we calculate it as $1 - R = 1 - 0.9 = 0.1$ or 10%.

The First Unit Took 10 Hours and the Fourth Unit