Learning (Experience) Curves

Two models are available for learning curves. In the first model it is assumed that the learning coefficient is known, while in the second model it is assumed that the production time for two units is known and that the learning curve coefficient is computed based on these. In either case we can find the production times for units from 1 to a specified number and the cumulative production time for these units. In addition, for either model the learning curve can be graphed.

The Data

Consider a situation in which unit 1 took 10 hours, the learning curve coefficient is 90% and we are interested in the first 20 units. Following is a screen that contains both the data and the one line of primary output.

Unit number of base unit. This is usually 1 as in our example, but can be set to any number.

Time for base unit. This is the length of time that it takes to manufacture the unit number as specified above. In our example it is 10 hours.

Number of the last unit. This is the item number for the last unit which will be displayed and/or used for computations. In the example we are interested in unit 20 or the first 20 units.

Learning curve coefficient. This is a number between 0 and 1. It is the percentage of the first unit's time that it takes to make the second unit and also the percentage of the second unit's time that it takes to make the fourth unit. The learning curve coefficient is only entered for the first model. The second model will determine the learning curve coefficient based on the next data input item.

Time to make last unit. Not shown on this screen, but shown in the next example, the last piece of information for the second model is the time it takes to produce the last unit rather than the learning curve coefficient. Based on this piece of information, the learning curve coefficient will be determined (see example 2).

Example 1 - Computing times and cumulative times

The sample problem appears in the preceding screen. The four lines of input data indicate that the first unit (unit number 1) takes 10 minutes to manufacture, the last unit is unit number 20, and the learning coefficient is 90%. That is, the decrease in time is such that with the doubling of the unit number the time is 90% of the previous time.

The solution in the preceding screen is that the last unit (number 20) takes 6.34 minutes.

An additional table of times and cumulative times can be displayed. The output consists of three columns.

Unit number. This runs from 1 to the last unit, which in our example is 20. The two additional columns are as follows.

Time to produce a single unit (production time). This column contains the time to produce a unit. For example, it takes 10 minutes to produce unit 1 (as specified by the input), 9 minutes to produce unit 2 (as computed using the learning coefficient), 8.1 minutes to produce unit 4 (90% of 9 minutes), 7.29 minutes to produce unit 8, and so on. The interesting numbers are the ones that are not powers of 2. For example, it takes 6.34 units to produce unit 20.

Cumulative time. The last column contains the amount of time to produce all of the units up to and including that unit number. Obviously, it takes 10 minutes to produce unit 1. It takes 19 minutes to produce units 1 and 2; 35.20 minutes to produce the first four units, and 146.08 minutes to produce the first 20 units. A graph of the unit production times can be displayed.

Example 2 - Finding the learning curve coefficient

Following is the solution screen for an example of the second model. In this case, we know that unit 4 took 73 minutes and unit 37 took 68 minutes. The program has computed that based on these two times the learning curve coefficient is .9781.