SME
Construction Engineering · Problem type
Learning curve
Use this for “A crew took 120 hours to build the first of many identical forms. On an 85% learning curve, how long does the 10th one take?”
Chart
T(10) ≈ 69.94
This is an example. Type your own values to start a new problem.
b
=
log(
r (%)
)
log
2
Tₙ (h)
=
T₁ (h)
×
n
Formulas
b
=
log(
r
÷ 100)
log 2
−0.2345
=
log(85 ÷ 100)
log 2
Tₙ
=
T₁
×
n
b
69.94
=
120 ×
10
−0.2345
Assumptions
•
The unit (Wright) model: each doubling of the count multiplies the unit time by r.
•
Repeated identical units, built by one crew.
•
r is near 80–90% for repetitive construction work.
Step-by-step
WE KNOW
T₁ = 120 h, r = 85%, n = 10
FIND
learning exponent (b), time for unit n (Tₙ)
Step 1 · Find learning exponent (b)
Use b = log(r ÷ 100) ÷ log 2
Each
doubling
multiplies
the
time
by
r
100,
and
doubling
n
multiplies
nᵇ
by
2ᵇ,
so
2ᵇ
=
r
100
.
b
=
log(85 ÷ 100)
log 2
b
=
log(0.85)
log 2
b
=
−
0.07058
0.301
b
=
−0.23447
Step 2 · Find time for unit n (Tₙ)
Use Tₙ = T₁ × nᵇ
The
unit
time
falls
as
the
power
b
of
the
unit
number,
starting
from
the
first
unit’s
time.
Tₙ
=
120 ×
10
−0.23447
Doubling
check:
unit
8
takes
120
×
0.85
3
=
73.69
h
Tₙ = 69.94 h
Check
Put the numbers back in. Both sides should match.
−0.23447
=
log(85 ÷ 100)
log 2
✓
69.94
=
120 ×
10
−0.23447
✓
Topic check
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