Cumulative Average-Time Learning Model

In the cumulative average-time learning model, cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units produced doubles. Consider Rayburn Corporation, a radar systems manufacturer. Rayburn has an 80% learning curve. This means that when Rayburn doubles the quantity of units produced, from X to 2X, the cumulative average time per unit for 2X units is 80% of the cumulative average time per unit for X units. In other words, the average time per unit drops by 20% (100%−80%). Exhibit 10-11 shows the calculations for the cumulative average-time learning model for Rayburn Corporation. Note that as the number of units produced doubles from 1 to 2 in column A, the cumulative average time per unit declines from 100 hours to 80% of 100 hours (0.80×100 hours=80 hours) in column B. As the number of units doubles from 2 to 4, the cumulative average time per unit declines to 80% of 80 hours=64 hours, and so on. To obtain the cumulative total time in column D, multiply the cumulative average time per unit by the cumulative number of units produced. For example, to produce 4 cumulative units would require 256 labor-hours (4 units×64 cumulative average labor‐hours per unit).

Exhibit 10-11

Cumulative Average-Time Learning Model for Rayburn Corporation

Spreadsheet screenshot shows the cumulative average-time learning model for Rayburn Corporation at 80% learning curve.

Details of the spreadsheet are as follows: 

Cumulative number of units (X): 1 

(A) Cumulative average time per unit–Labor-hours: 100.00 

(B) Cumulative total time–Labor hours: 100.00 

(C) Individual unit time for 1st unit–Labor-hours: 100.00

Cumulative number of units (X): 2 

(A) Cumulative average time per unit–Labor-hours: 80.00 (product of 100 and 0.8) 

(B) Cumulative total time–Labor hours: 160.00 

(C) Individual unit time for 2nd unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 60.00

Cumulative number of units (X): 3

(A) Cumulative average time per unit–Labor-hours: 70.21

(B) Cumulative total time–Labor hours: 210.63

(C) Individual unit time for 3rd unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 50.63

Cumulative number of units (X): 4

(A) Cumulative average time per unit–Labor-hours: 64.00 (product of 80 and 0.8)

(B) Cumulative total time–Labor hours: 256.00

(C) Individual unit time for 4th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 45.37

Cumulative number of units (X): 5

(A) Cumulative average time per unit–Labor-hours: 59.56

(B) Cumulative total time–Labor hours: 297.82

(C) Individual unit time for 5th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 41.82

Cumulative number of units (X): 6

(A) Cumulative average time per unit–Labor-hours: 56.17

(B) Cumulative total time–Labor hours: 337.01 

(C) Individual unit time for 6th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 39.19

Cumulative number of units (X): 7

(A) Cumulative average time per unit–Labor-hours: 53.45

(B) Cumulative total time–Labor hours: 374.14 

(C) Individual unit time for 7th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 37.13

Cumulative number of units (X): 8

(A) Cumulative average time per unit–Labor-hours: 51.20 (product of 64 and 0.8)

(B) Cumulative total time–Labor hours: 409.60

(C) Individual unit time for 8th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 35.46

Cumulative number of units (X): 9

(A) Cumulative average time per unit–Labor-hours: 49.29

(B) Cumulative total time–Labor hours: 443.65

(C) Individual unit time for 9th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 34.05

Cumulative number of units (X): 10

Cumulative average time per unit–Labor-hours: 47.65

(A) Cumulative total time–Labor hours: 476.51

(B) Individual unit time for 10th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 32.86

Cumulative number of units (X): 11

(A) Cumulative average time per unit–Labor-hours: 46.21

(B) Cumulative total time–Labor hours: 508.32

(C) Individual unit time for 11th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 31.81

Cumulative number of units (X): 12

(A) Cumulative average time per unit–Labor-hours: 44.93

(B) Cumulative total time–Labor hours: 539.22 

(C) Individual unit time for 12th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 30.89

Cumulative number of units (X): 13

(A) Cumulative average time per unit–Labor-hours: 43.79

(B) Cumulative total time–Labor hours: 569.29

(C) Individual unit time for 13th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 30.07

Cumulative number of units (X): 14

(A) Cumulative average time per unit–Labor-hours: 42.76

(B) Cumulative total time–Labor hours: 598.63

(C) Individual unit time for 14th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 29.34

Cumulative number of units (X): 15

(A) Cumulative average time per unit–Labor-hours: 41.82

(B) Cumulative total time–Labor hours: 627.30

(C) Individual unit time for 15th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 28.67

Cumulative number of units (X): 16

(A) Cumulative average time per unit–Labor-hours: 40.96 (product of 51.20 and 0.08)

(B) Cumulative total time–Labor hours: 655.36

(C) Individual unit time for 16th unit–Labor-hours (calculated by subtracting the cumulative total time with the previous): 28.06

Note: The mathematical relationship underlying the cumulative average-time learning model is as follows:

y equals a times X superscript b 

where y equals Cumulative average time (labor-hours) per unit

X equals Cumulative number of units produced

a equals Time (labor-hours) required to produce the first unit

b equals Factor used to calculate cumulative average time to produce units

The value of b is calculated as

The quotient of log natural (learning-curve % in decimal form) and log natural (2)

For an 80% learning curve, b equals log natural 0.8 divided by log natural (2) which equals negative 0.2231 divided by 0.6931 which equal negative 0.3219,

For example, when X equals 3, a equals 100, b equals negative 0.3219,

y equals 100 times 3 raised to (0.3219) which equals 70.21 labor-hours

The cumulative total time when X equals 3 is 70.21 times 3 which equals 210.63 labor-hours.

Numbers in table may not be exact because of rounding.