Question

CHAPTER 6: LEARNING CURVE (MONDAY)

1. The unit improvement factor for a 60 percent learning curve at 25 units is 0.0933. The first and second timings of a person doing a job are 5 minutes and 3 minutes respectively. What is the learning-adjusted time estimate for unit number 25?

2. You have just timed a person doing a job a few times. The first time it took the person 25 minutes, the second time it took 20 minutes, and the third time it took 17.55 minutes. What learning curve unit improvement factor should you use?

3. You have determined that a 75 percent learning curve is appropriate for a task. If the initial timing of the person performing that job was 50 minutes, and if you need the job performed 500 times, how many minutes of work will be required?

4. With an 80 percent unit improvement factor learning curve and an initial time of 100 minutes to do a job, at what number of repetitions will the job take less than 50 minutes?

5. The 50th repetition of a job is timed at 100 minutes. If the learning curve for this job is 90 percent, what is the estimated time for the 100th repetition of this job?

# i want to know how to calculate the solution

Answer 1

Learning Curve:

1.

Learning curve rate = 60% = 0.6

Unit improvement factor at 25 units = 0.0933

Time required for 1^st unit = 5 minutes

The unit time for the nth unit can be calculated using learning curve formula as follows:

T_n = T₁ x C

T₁ = time required for first unit

T_n = time required for nth unit

C = unit improvement factor

T₂₅ = T₁ x C = 5 x 0.0933 = 0.4665 minute

Learning-adjusted time estimate for unit number 25 = 0.4665 minute

2.

T₁ = time required for first unit = 25 minutes

T₂ = time required for 2^nd unit = 20 minutes

T₃ = time required for 3^rd unit = 17.55 minutes

T_n = time required for nth unit

Learning rate from 1^st to 2^nd unit = Time required for 2^nd unit/time required for 1^st unit = L₂/ L₁

T₂/ T₁ = 20/25 = 0.80

Learning curve improvement of 80% is appropriate for given process.

To confirming 80% learning curve, determine the time required for third unit.

The unit improvement factor for 3^rd unit of 80% curve = 0.7021

The unit time for the nth unit can be calculated using learning curve formula as follows:

T_n = T₁ x C

T₃ = 25 x 0.7021 = 17.5525 minutes

Since, the calculated time and given time for the third unit is sam, the learning curve rate of 80% is correct.

3.

T₁ = time required for first unit = 50 minutes

Learning curve rate = 75%

Total time required to perform the job n times = Tn = cumulative improvement factor x T₁

cumulative improvement factor for 500 units (75% rate) = 63.68

Total time required to perform the job 500 times = 63.68 x 50 = 3184 minutes

4.

Learning curve rate = 80%

T₁ = 100 minutes

T_n = 50 minutes

T_n = T₁ x C

50 = 100 x C

C = 50/100 = 0.5

For the Job number that take less than 50 minutes, the unit improvement factor should be less than 0.5

From the learning curve table, for rate of 80%, the 9^th unit results in unit improvement factor 0.4930.

9^th unit will require less than 50 minutes for 80% learning curve rate.

5.

Learning curve rate = 90%

T₅₀ = 100 minutes

T₁₀₀ = estimated time of 100^th repetition

C₅₀ = unit improvement factor for 50^th unit = 0.5518

C₁₀₀ = unit improvement factor for 100^th unit = 0.4966

T₅₀ = T₁ x C₅₀

T₁₀₀ = T₁ x C₁₀₀

T₅₀/C₅₀ = T₁₀₀/C₁₀₀

T₁₀₀ = (T₅₀/C₅₀) x C₁₀₀ = (100/0.5518) x 0.4966

T₁₀₀ = 89.99

Estimated time for the 100^th repetition of this job = 89.99 minutes