Question 7S.4: Use learning curve theory to predict the number of repetitio......

a. The table approach can be used for the learning percentages that are listed across the top of the table, such as the 90 percent curve in this example. The table approach is based on Formula 7S–2:

Setting T_{n} equal to the specified time of 6 minutes and solving for the unit table factor yields

6 min = 10 min × Unit table factor

Solving,

Unit table factor = 6 min ÷ 10 min = .600

From Table 7S.1 , under 90% in the Unit Time column, we find .599 at 29 units. Hence, approximately 29 units will be required to achieve the specified time.

b. Using the log formula,

(1) Compute the ratio of specified time to first unit time: 6 min ÷ 10 min = .600.
(2) Compute the ratio of ln learning percentage to ln 2: ln .90 ÷ ln 2 = -0.1053605 ÷ 0.6931472 = -0.1520.
(3) Find n such that n^{-.1520}\ =\ .600:\ ^{-.1520}\sqrt{.600}\ =\ 28.809. Round to 29. Hence, 29 units (repetitions) will be needed to achieve a time of 6 minutes.

The learning percentage can be estimated from data on repetition times. The procedure for doing this is illustrated in Solved Problem 2.