IE 3265 Production and Operation Management

LABORATORY 1

MATERIALS:

1. Brass Faucet

2. Stop Watch

3. Assembly/disassembly tools

INTRODUCTION:

The[1] concept of the learning curve was introduced to the aircraft industry in 1936 when T. P. Wright published an article in the February 1936 Journal of the Aeronautical Science. Wright described a basic theory for obtaining cost estimates based on repetitive production of airplane assemblies. Since then, learning curves (also known as progress functions) have been applied to all types of work from simple tasks to complex jobs like manufacturing a Space Shuttle.

The theory of learning is simple. It is recognized that repetition of the same operation results in less time or effort expended on that operation. For the Wright learning curve, the underlying hypothesis is that the direct labor man-hours necessary to complete a unit of production will decrease by a constant percentage each time the production quantity is doubled. If the rate of improvement is 20% between doubled quantities, then the learning percent would be 80% (100-20=80). While the learning curve emphasizes time, it can be easily extended to cost as well.

The learning percent is usually determined by statistical analysis of actual cost data for similar products. Lacking that, you may use the following guidelines from "Cost Estimator's Reference Manual- 2nd Ed.," by Rodney Stewart:

  • 75% hand assembly/25% machining = 80% learning
  • 50% hand assembly/50% machining = 85%
  • 25% hand assembly/75% machining = 90%

or

  1. Aerospace 85%
  2. Shipbuilding 80-85%
  3. Complex machine tools for new models 75-85%
  4. Repetitive electronics manufacturing 90-95%
  5. Repetitive machining or punch-press operations 90-95%
  6. repetitive electrical operations 75-85%
  7. Repetitive welding operations 90%
  8. Raw materials 93-96%
  9. Purchased Parts 85-88%

In this experiment, we will study the concept of the Learning Curve. Learning concepts are based on the IDEA that as an activity is repeated a worker trains him/herself and their personal "Assembly System" to reduce the time taken to perform an activity. This ability to improve should, ultimately, then be limited by physical rather than mental constraints. Note, this concept is suggested to apply to production systems as well. To test our ability to learn, each engineering team will develop a Learning Curve for assembly of a brass faucet for three members of the team. Each test members ability to assemble the faucet will be studied and their observed performance will be compared to the foundation of the Learning Curve theory, ie. that the time to assemble the faucet will decrease by a fixed percentage each time the number of activity replications doubles.

METHOD of STUDY:

Each tested participant (2 per group) will assemble the brass faucet at least 24 times using a different "Best Technique." Times will be recorded. An average time for the 24 repetitions should be computed. In addition, the recorded times will be used to build the learning curves for each test subject.

The data so generated is assumed to follow the relationship[Nahmias, 2005]:

y = axb

y - time to assemble the xth unit

a - time to assemble the 1st unit

b - measure of "Learning Rate"

x - unit number

This equation, the “Learning Curve” will be enumerated for each of your test subjects. The data should be plotted in both "RAW" and "LINEARIZED" graphical form to perform this linearization, consider the Log-Log relationship: log(y) = log(a) + b*log(x). Make a Best Fit line using your linearized data. Compute this best fit line with log(time) as a dependent variable and log(unit ass’bly number) as the independent variable. After conversion to "linear" data, what is the meaning of the "Learning Rate," how is the value “a” in the original equation to be found? Speculate on the long term effect of this learning effect – while your equation suggests that the time to assemble a faucet can eventually become zero does this make sense? While we won’t define it here, we will eventually find that there is a physical limit based on human capacity that would become a standard time. See the discussion on Learning Curves in [Salvendy, 1982] considering “Training Costs,” standard time and the organization.

In addition, most processes are subject to an effect called the “Forgetting Factor.” When considering this effect, basically we find that the operator or process, in general, will have a loss of efficiency if time elapses between batches of product. That is to say, if you make 100 faucets then go away for a few months, you would not, necessarily, be as efficient in making the 101st faucet as you made the 100th. In fact your time for this may be about the time it took to make the 50th faucet (a 50% forgetting factor) or the 90th faucet (a 10% forgetting factor). In Figure 1, [Chase and Aquilano, 1992] this effect is graphically displayed and the cumulative effect on production and time to complete the various batches is illustrated. In A and B, the time for each successive batch declines – much more in A than B since we “retrace” our steps in B by the 50% forgetting factor effect. In Graph C, the effect illustrated is a full forgetting or 100% forgetting factor. Here, the workers (likely different people for each batch – or even different production centers or factories) must each follow the same learning curve to the same point and we gain nothing between batches. When you are working with the forgetting factor, the following equation is used [Chase & Aquilano, 1992]:

Comparing the equations for the Learning Effect and the Forgetting Factor (FF), care should be taken. While looking at the Learning equation, y is a time per unit while in the forgetting equation Y is a production rate which is the reciprocal of the time to make a unit. To work with this relationship, we could compute first piece production rates for the next batch from production times in a first batch using the FF equation, while last piece product rates can be estimated as calculated using the Learning Effect equation as modified by the forgetting factor effect. This method can be moved forward over time as the starting and stopping production methods are followed.

Figure 1: Effect of Forgetting Factors on production rates

A final point must be made concerning Forgetting Factor efforts. It has often been observed that the learning rates for subsequent batches made will be improved over the previous batches thus we progress faster (typically by a few percent) over each subsequent batch – the decay is quicker. Thus when batch production times for additional batches are computed we could (should) increase the learning rate. If, for example we found that the Learning rate was 90% in our initial study (as calculated from our data) then the rate might be 88% for a second batch regardless of the Forgetting Factor, while a third might be 85% a fourth 83%, etc. until the system reaches an asymptotic value.

A last point of interest would be the cumulative time to compute a batch of any given size. This can be found using the following equations [Salvendy, 1982]:

This equation would only work under the following conditions:

  1. No breaks in production are made
  2. If production breaks do occur, the forgetting factor is 0%
  3. Note: we compute b as a negative value (from our expected slopes thus we should use plus signs rather than minus signs when we see: 1-b (should compute 1+b)

DISCUSSION and Calculations:

While discussing your experimental results consider the following issues related to the Learning curve:

  1. Discuss the results of your studies. Is learning progressing at the same rate for each subject? Did each person’s starting point agree? What would be expected to happen to the results of your experiment if each subject continues to assemble faucets? Will the learning curve change over time? How did your calculations agree with the data extracted from the NASA website (the suggested learning rate percentages). State and comment on each individual (best fit) values computed for “a” and “b.”
  1. What would the expected time be for assembling the 100th faucet? 1000th faucet? 10,000th faucet? Do you feel that our experimental times would be valid as a good estimator over this range of production? What is the meaning of and value for the "asymptotic" value for each curve -- that is, why and when would the curve flatten out?
  1. We have been introduced to the concept of a "Forgetting Factor.” Comment on how this effect would impact the production rates we would predict using our Learning Curve. Would Group Technology (large lots and family of similar parts) or Job shop production (small batch size) be most affected by this factor? Why?
  1. If faucets are made in lots of 500 and our forgetting factor is 25%, how long would it take to make the1501th faucet for each of your tested team members? Note that in the Forgetting factor equations the "Y" is a rate not a time value. Plot the history over the 3 lots + 1 production set.
  1. Determine an average time expected for the production of a 2nd batch (501 to 1000) without forgetting factor? How long would you expect each assembler to take to produce the total of 1000 faucets with and without the 25% forgetting factor?
  1. How would the Learning Curve and any forgetting factor be used in the Scheduling and Control of a production facility?
  1. What other conclusions can be developed as a result of this study?

NOTE: Each team member is responsible for the mathematics developed here!!

Reference List

  1. S. Nahmais, Production and Operations Analysis, 5th Ed., McGraw-Hill/Irwin, 2001.
  2. Chase & Aquilano, Production & Operations Management, 6th Ed., Irwin, 1992.
  3. G. Salvendy,editor, Handbook of Industrial Engineering, Wiley-Interscience, 1982.

Website Reference:

1. NASA Webpage, 20Jan2002.

[1] NASA Webpage, 20Jan2002