To calculate the expected time for the 200th, 400th, and 800th units using the learning curve, you can use the following formula:
T_n = T_1 \times (n)^{\log(0.75) / \log(2)}T
n
=T
1
×(n)
log(0.75)/log(2)
Where:
T_nT
n
is the expected time for the nth unit.
T_1T
1
is the initial time (0.20 hours per unit).
nn is the unit number.
Let's calculate:
For the 200th unit:
T_{200} = 0.20 \times (200)^{\log(0.75) / \log(2)}T
200
=0.20×(200)
log(0.75)/log(2)
T_{200} ≈ 0.20 \times (200)^{-0.415} ≈ 0.20 \times 0.653 ≈ 0.1306 \text{ hours}T
200
≈0.20×(200)
−0.415
≈0.20×0.653≈0.1306 hours
For the 400th unit:
T
400
=0.20×(400)
log(0.75)/log(2)
T_{400} ≈ 0.20 \times (400)^{-0.415} ≈ 0.20 \times 0.413 ≈ 0.0827 \text{ hours}T
400
≈0.20×(400)
−0.415
≈0.20×0.413≈0.0827 hours
For the 800th unit:
T_{800} = 0.20 \times (800)^{\log(0.75) / \log(2)}T
800
=0.20×(800)
log(0.75)/log(2)
T_{800} ≈ 0.20 \times (800)^{-0.415} ≈ 0.20 \times 0.206 ≈ 0.0413 \text{ hours}T
800
≈0.20×(800)
−0.415
≈0.20×0.206≈0.0413 hours
So, the expected times for the 200th, 400th, and 800th units are approximately:
0.13 hours for the 200th unit.
0.08 hours for the 400th unit.
0.04 hours for the 800th unit.