OpenSpecEngineering

Predicts how the time to build one unit falls as a crew gains experience. From the first unit’s time and a learning rate, it gives the time for any later unit, the total time for the run so far, the average time per unit and the drop from the first unit. Estimators and planners use it to quote production runs and schedule labor [2], [3]. The graph below the Solution redraws the curve as you type and marks the unit you asked about.

Equations

T_n = T₁ · n^b     b = ln(r) / ln 2

T₁ is the time for the first unit, n the unit number and T_n the time for unit n. r is the learning rate as a fraction: on an 80 % curve each doubling of the count cuts the unit time to 80 % of what it was, so unit 2 takes 0.8T₁, unit 4 takes 0.64T₁. b is negative. The total for the first n units is the sum of T_i for i = 1 to n (for n above 100,000 the page uses the integral of the curve instead), and the average is that total divided by n.

The Typical Learning Rate by Industry list fills in a rate from NASA’s table [4]. Where the table gives a range, the page uses its middle.

Limits and common mistakes

• This is the unit model: T_n is the time of unit n itself. Wright’s original model [1] puts the same equation on the cumulative average time instead. Check which one your rate was fitted to.
• A lower percentage means faster learning. A 70 % curve learns faster than a 90 % curve, and 100 % means no learning.
• T₁ should be the real first unit. If you start from a later unit’s time, back T₁ out first: T₁ = T_n / n^b.
• Learning stops at machine-paced work, and long breaks in production lose some of it.

Worked example

A fabrication shop built the first of 25 welded frames in 40 hr. It needs the labor for the whole order and the time the last frame should take.

1. Enter Time for First Unit 40.
2. Choose Typical Learning Rate by Industry Repetitive welding operations — 90 %. The learning rate fills in as 90.
3. Enter Unit Number of Interest 25 and press Solve. The Solution shows: Learning exponent b = ln(rate)/ln(2): -0.152003
   Time for unit n: 24.5227 hr
   Cumulative total time for first 25 units: 708.529 hr
   Cumulative average time (first 25 units): 28.3412 hr
   Reduction vs first unit: 38.6932 %

Check by doubling. Units 2, 4, 8 and 16 take 36, 32.4, 29.2 and 26.2 hr. Unit 25 lies between 16 and 32, where the curve gives 23.6 hr, so 24.5 hr is in the right place. The order needs about 709 hr, against 1,000 hr if every frame took as long as the first.