Learning Curves: introduction

1. Learning Curves: introduction Learning curves are an important part of business life. This presentation is aimed at introducing them to you. Learning curves are an important part of business life. This presentation is aimed at introducing them to you.

2. Learning Curves 1 The learning curve was first observed in the aircraft industry in the USA in the 1920s where the number of direct labour hours needed to produce a unit of output were seen to decline as additional units were manufactured. The concept has been broadened to other activities as it was discovered that the cost of doing most repetitive tasks decreases as experience is gained. This general concept of a learning curve can be applied to the analysis of cost behaviour in industry pricing, new product improvements, manufacturing cost forecasting, and many other values and variables regarding efficiency versus volume. Of course, education and training are designed to improve peoples� learning curves! Learning curves are usually described by a percentage (%) value. This value is typically 1 minus the change rate of the measured value (Y) each time cumulative volume (X) doubles. For example, a "100%" learning curve would be a flat, horizontal line for all X�s. A "90%" learning curve would drop 10% each time X doubled. A �80%" learning curve would drop 20% each time X doubled, and so on. There is the story of the man in the USA whose job it has been for several years to fold pieces of cardboard into box shapes. We are led to believe that he has made 6 million boxes to date and STILL he is learning how to improve his technique!The learning curve was first observed in the aircraft industry in the USA in the 1920s where the number of direct labour hours needed to produce a unit of output were seen to decline as additional units were manufactured. The concept has been broadened to other activities as it was discovered that the cost of doing most repetitive tasks decreases as experience is gained. This general concept of a learning curve can be applied to the analysis of cost behaviour in industry pricing, new product improvements, manufacturing cost forecasting, and many other values and variables regarding efficiency versus volume. Of course, education and training are designed to improve peoples� learning curves! Learning curves are usually described by a percentage (%) value. This value is typically 1 minus the change rate of the measured value (Y) each time cumulative volume (X) doubles. For example, a "100%" learning curve would be a flat, horizontal line for all X�s. A "90%" learning curve would drop 10% each time X doubled. A �80%" learning curve would drop 20% each time X doubled, and so on. There is the story of the man in the USA whose job it has been for several years to fold pieces of cardboard into box shapes. We are led to believe that he has made 6 million boxes to date and STILL he is learning how to improve his technique!

3. Learning Curves 2 Many textbooks discuss learning curves only in terms of people. However, it is true that machinery can learn as can systems. Some people wrongly refer to the learning curve as the experience curve. The experience curve is similar to the learning curve BUT it applies to the whole organisation and not just one job or activity. Where and how can we apply learning curve ideas? New Product Production Costs Make or Buy Decisions Suppliers Progress Payments Analyze Pricing Practices of Suppliers Cost-Volume-Profit (CVP) Analysis Evaluation of Production Employees Multi-Year Procurement Analysis Production Rate Evaluation Production Improvement Cycle Times Costs versus Prices Over Time Competitive Bidding Technology Forecasting When learning curves were first noted, in the Aircraft Building industry in the early part of the 20th century, engineers typically found an 80% learning curve � for this reason, and because the arithmetic is nicer, we tend to talk in terms of an 80% curve. The learning curve for that industry now is reported to be more like 70 � 75%. Read on, though, since your rate of learning could be higher or lower than 80%.Many textbooks discuss learning curves only in terms of people. However, it is true that machinery can learn as can systems. Some people wrongly refer to the learning curve as the experience curve. The experience curve is similar to the learning curve BUT it applies to the whole organisation and not just one job or activity. Where and how can we apply learning curve ideas? New Product Production Costs Make or Buy Decisions Suppliers Progress Payments Analyze Pricing Practices of Suppliers Cost-Volume-Profit (CVP) Analysis Evaluation of Production Employees Multi-Year Procurement Analysis Production Rate Evaluation Production Improvement Cycle Times Costs versus Prices Over Time Competitive Bidding Technology Forecasting When learning curves were first noted, in the Aircraft Building industry in the early part of the 20th century, engineers typically found an 80% learning curve � for this reason, and because the arithmetic is nicer, we tend to talk in terms of an 80% curve. The learning curve for that industry now is reported to be more like 70 � 75%. Read on, though, since your rate of learning could be higher or lower than 80%.

4. Learning Curves 3 Here we have a table containing the number of batches of a job or product that we have carried out or made. In the second column we have recorded the TOTAL time taken for 1 batch, then 2 batches, then 4 batches and so on. We are required here to work out the CAT = Cumulative Average Time for each combination of total time and batches.Here we have a table containing the number of batches of a job or product that we have carried out or made. In the second column we have recorded the TOTAL time taken for 1 batch, then 2 batches, then 4 batches and so on. We are required here to work out the CAT = Cumulative Average Time for each combination of total time and batches.

5. Learning Curves 4 Here�s the answer to the question on the previous slide: Learning Curves 3. We can see here why we have labelled this the 80% Learning Rate table. The CAT for 2 batches is 80% of the CAT for 1 batch; the CAT for 4 batches is 80% of the time for 2 batches; the CAT for 8 batches is 80% of the time for 4 batches and so on. You might be asking now, why we have not included 3 batches or 5 or 6 or 7 � we�ll look at this later � it�s a really interesting point!Here�s the answer to the question on the previous slide: Learning Curves 3. We can see here why we have labelled this the 80% Learning Rate table. The CAT for 2 batches is 80% of the CAT for 1 batch; the CAT for 4 batches is 80% of the time for 2 batches; the CAT for 8 batches is 80% of the time for 4 batches and so on. You might be asking now, why we have not included 3 batches or 5 or 6 or 7 � we�ll look at this later � it�s a really interesting point!

6. Learning Curves 5 Just in case it�s not obvious why we are talking about learning curves and their impact, consider this slide. If we did NOT learn at all, this slide shows what the position would be, assuming that the number of batches was the same as in previous slides and we started at a total time of 50 (days, hours, minutes �. doesn�t matter). If there is no learning taking place, the CAT will be a constant 50. Compare this table with the table on slide Learning Curve 4Just in case it�s not obvious why we are talking about learning curves and their impact, consider this slide. If we did NOT learn at all, this slide shows what the position would be, assuming that the number of batches was the same as in previous slides and we started at a total time of 50 (days, hours, minutes �. doesn�t matter). If there is no learning taking place, the CAT will be a constant 50. Compare this table with the table on slide Learning Curve 4

7. Learning Curves 6 What are the implications of learning taking place as opposed to no learning taking place? The next two slides will help us with an answer here; but think about this for a minute or two and we what you can come up with.What are the implications of learning taking place as opposed to no learning taking place? The next two slides will help us with an answer here; but think about this for a minute or two and we what you can come up with.

8. Learning Curves 7: �1/hour Concentrating only on labour costs, and assuming a rate of pay of 1 per hour, this table gives us the total labour cost at the various numbers of batches produced when there is a learning rate of 80%.Concentrating only on labour costs, and assuming a rate of pay of 1 per hour, this table gives us the total labour cost at the various numbers of batches produced when there is a learning rate of 80%.

9. Learning Curves 8: �1/hour Still concentrating only on labour costs, and assuming a rate of pay of 1 per hour, this table gives us the total labour cost at the various numbers of batches produced when there is no learning � compare this with the previous slide. There�s a huge difference between them. Still concentrating only on labour costs, and assuming a rate of pay of 1 per hour, this table gives us the total labour cost at the various numbers of batches produced when there is no learning � compare this with the previous slide. There�s a huge difference between them.

10. Learning Curves 9 Just to complete the logic, let�s imagine that each batch contains 5 units � the costs per unit with 80% learning and no learning?Just to complete the logic, let�s imagine that each batch contains 5 units � the costs per unit with 80% learning and no learning?

11. Learning Curves 10 Surprised? The differences between the two columns become larger and larger �Surprised? The differences between the two columns become larger and larger �

12. Learning Curves 11 When we plot the batch number against the CAT for an 80% learning rate, this is what it looks like!When we plot the batch number against the CAT for an 80% learning rate, this is what it looks like!

13. Learning Curves 12 When we plot the batch number against the CAT for an 90% learning rate, this is what it looks like!When we plot the batch number against the CAT for an 90% learning rate, this is what it looks like!

14. Learning Curves 13 When we plot the batch number against the CAT for an 60% learning rate, this is what it looks like!When we plot the batch number against the CAT for an 60% learning rate, this is what it looks like!

15. Learning Curves 14: overlays When we put the previous three graphs together, we can see the differences between the 60, 80 and 90% learning rates. When we put the previous three graphs together, we can see the differences between the 60, 80 and 90% learning rates.

16. Learning Curves 15: formulae We mentioned before that we have prepared our tables for 1 batch, 2 batches, 4 � 8 � 16 � batches. Why did we do this? We did this because MATHEMATICALLY the CAT reduces at the rate of 80% (or 60% or 90% or whatever) only at the DOUBLING POINTS. That is, we can only use the learning curve tables to predict the CAT at 1 then 2 then 4 then 8 � then 128 � batches or units. We cannot directly predict the CAT for 3 units or 5 or 6 or 7 of 11 or any number of units other than a doubling point number of units � Unless we introduce and use some ALGEBRA � aaaaaaaaaahhhhhh!We mentioned before that we have prepared our tables for 1 batch, 2 batches, 4 � 8 � 16 � batches. Why did we do this? We did this because MATHEMATICALLY the CAT reduces at the rate of 80% (or 60% or 90% or whatever) only at the DOUBLING POINTS. That is, we can only use the learning curve tables to predict the CAT at 1 then 2 then 4 then 8 � then 128 � batches or units. We cannot directly predict the CAT for 3 units or 5 or 6 or 7 of 11 or any number of units other than a doubling point number of units � Unless we introduce and use some ALGEBRA � aaaaaaaaaahhhhhh!

17. Learning Curves 16: formulae You need a calculator that can calculate things to the power of and that has natural logarithms. Natural logarithms are shown as ln on your calculator. Work through this and the following screens carefully to learn how to use these functions.You need a calculator that can calculate things to the power of and that has natural logarithms. Natural logarithms are shown as ln on your calculator. Work through this and the following screens carefully to learn how to use these functions.

18. Learning Curves 17: formulae Step by step: slowly, slowly catchee monkey! Note, if the learning rate is 80%, then b always = ln0.8/ln2. If the learning rate is x%, then b = lnx/ln2Step by step: slowly, slowly catchee monkey! Note, if the learning rate is 80%, then b always = ln0.8/ln2. If the learning rate is x%, then b = lnx/ln2

19. Learning Curves 18: formulae Make sure you can work your calculator correctly and can AGREE with what you see on this slide.Make sure you can work your calculator correctly and can AGREE with what you see on this slide.

20. Learning Curves 19: exercise Let�s see if you�ve followed all of that. Here�s one for you to do �Let�s see if you�ve followed all of that. Here�s one for you to do �

21. Learning Curves 19b: solution � the answer is � the answer is

22. Learning Curves 20: exercise Another one for you, with a different learning rate now � Another one for you, with a different learning rate now �

23. Learning Curves 20b: solution � and the answer is.� and the answer is.

24. Learning Curves 21 If you were in my group now you�d be about to start a series of fascinating activities, at the end of which you would know your own learning rate!If you were in my group now you�d be about to start a series of fascinating activities, at the end of which you would know your own learning rate!

25. Learning Curves 22 If you were in my group now you�d be about to start a series of fascinating activities, at the end of which you would know your own learning rate!If you were in my group now you�d be about to start a series of fascinating activities, at the end of which you would know your own learning rate!

26. Learning Curves 23 If you were in my group now you�d be about to start a series of fascinating activities, at the end of which you would know your own learning rate! When I first started doing these activities with my students, I had a three year old daughter and I used some of her toys as my activities. Something that takes no more than a minute per trial or test to do is ideal: prevents boredom, is easily repeated � must be clearly understandable and easy to set up. Since my daughter grew older and we disposed of her toys, I replaced the activities I used. I tend to get the students to repeat each activity at least 10 times and no more than 15 times (of course, this is up to you and them!). Any less than 10 and the data may not be reliable any more than 15 and the calculations and graph drawing can become tedious if you�re not using a spreadsheet. For example, I now use such activities as copying out simple sentences, finding numbers in a grid, completing jigsaws. See the accompanying Word file for examples of what I do! If you were in my group now you�d be about to start a series of fascinating activities, at the end of which you would know your own learning rate! When I first started doing these activities with my students, I had a three year old daughter and I used some of her toys as my activities. Something that takes no more than a minute per trial or test to do is ideal: prevents boredom, is easily repeated � must be clearly understandable and easy to set up. Since my daughter grew older and we disposed of her toys, I replaced the activities I used. I tend to get the students to repeat each activity at least 10 times and no more than 15 times (of course, this is up to you and them!). Any less than 10 and the data may not be reliable any more than 15 and the calculations and graph drawing can become tedious if you�re not using a spreadsheet. For example, I now use such activities as copying out simple sentences, finding numbers in a grid, completing jigsaws. See the accompanying Word file for examples of what I do!

27. Learning Curves 24: results You�d do it 10 times and record your results here: extend the form if your students are carrying out more than 10 trials. Be as accurate as possible and tell your guinea pigs that they shouldn�t necessarily bust a gut to do each task, but as efficiently and effectively as possible. Tip for the teacher: if you are going to set an assignment for your students to do out of class or out of your eye and ear shot, you can check whether their results are genuine by applying the following test. What follows is based on my own experience of doing this kind of thing for more than 10 years; and you won�t find this tip in any textbook that I�ve seen! With only ONE exception, any guinea pig doing any activity will normally return the following profile: assumed results. Trial 1 75 Trial 2 50 Trial 3 48 Trial 4 51 Trial 5 46 Trial 6 45 Trial 7 43 Trial 8 48 Trial 9 44 Trial 10 43 That is, initially ALL guinea pigs improve, then they improve again then they might improve again OR regress and so on, as you see in this table. I have only had one guinea pig who didn�t follow this pattern. You�d do it 10 times and record your results here: extend the form if your students are carrying out more than 10 trials. Be as accurate as possible and tell your guinea pigs that they shouldn�t necessarily bust a gut to do each task, but as efficiently and effectively as possible. Tip for the teacher: if you are going to set an assignment for your students to do out of class or out of your eye and ear shot, you can check whether their results are genuine by applying the following test. What follows is based on my own experience of doing this kind of thing for more than 10 years; and you won�t find this tip in any textbook that I�ve seen! With only ONE exception, any guinea pig doing any activity will normally return the following profile: assumed results. Trial 1 75 Trial 2 50 Trial 3 48 Trial 4 51 Trial 5 46 Trial 6 45 Trial 7 43 Trial 8 48 Trial 9 44 Trial 10 43 That is, initially ALL guinea pigs improve, then they improve again then they might improve again OR regress and so on, as you see in this table. I have only had one guinea pig who didn�t follow this pattern.

28. Learning Curves 25 These are the kind of things you can do � see the accompanying Word fileThese are the kind of things you can do � see the accompanying Word file

29. Learning Curves: follow up 1 This slide assumes you have had one lecture/lesson with slides 1 � 25 and are now reviewing your work later. Change last week for yesterday � Monday � whatever is appropriate.This slide assumes you have had one lecture/lesson with slides 1 � 25 and are now reviewing your work later. Change last week for yesterday � Monday � whatever is appropriate.

30. Learning Curves: follow up 2 Insert the relevant results � in my last session, I had guinea pigs with a 70% rate, a 100% rate � Insert the relevant results � in my last session, I had guinea pigs with a 70% rate, a 100% rate �

31. Learning Curves: follow up 3 Be honest about the scientific basis of what we are doing: it is usually fun; they results are indicative; but unless you have taken a great deal of time and trouble, their scientific base could easily be torn apart. Be honest about the scientific basis of what we are doing: it is usually fun; they results are indicative; but unless you have taken a great deal of time and trouble, their scientific base could easily be torn apart.

32. Learning Curves: follow up 4 These refer to the examples you�ll find in the Word file. These refer to the examples you�ll find in the Word file.

33. Learning Curves: follow up 5 I was working with some University lecturers here, so change the wording to suit your own situation. I was working with some University lecturers here, so change the wording to suit your own situation.

34. Learning Curves: follow up 6 Get the students to question what they have found. For example, it is PERFECTLY NORMAL for a guinea pig to return a 100% learning curve. This looks terrible, suggesting they are incapable of learning. However, the bead threading exercise is a good example of why this might not be a bad thing. I used my daughter�s necklace making set (plastic beads and string!) as the basis of an experiment. Simply thread fifteen beads onto the string � everyone who tried this experiment behaved normally except one smart, articulate young lady. I was intrigued as to why her learning curve was around 102% � her hobby was embroidery and needlecraft. I concluded that she was already proficient at this activity, hence she was already on the level part of her learning curve (the steady state). Similarly, a 64% learning curve doesn�t necessarily say that you�ve unearthed a genius!: that�s the best result I�ve ever had, by the way. Get the students to question what they have found. For example, it is PERFECTLY NORMAL for a guinea pig to return a 100% learning curve. This looks terrible, suggesting they are incapable of learning. However, the bead threading exercise is a good example of why this might not be a bad thing. I used my daughter�s necklace making set (plastic beads and string!) as the basis of an experiment. Simply thread fifteen beads onto the string � everyone who tried this experiment behaved normally except one smart, articulate young lady. I was intrigued as to why her learning curve was around 102% � her hobby was embroidery and needlecraft. I concluded that she was already proficient at this activity, hence she was already on the level part of her learning curve (the steady state). Similarly, a 64% learning curve doesn�t necessarily say that you�ve unearthed a genius!: that�s the best result I�ve ever had, by the way.

35. Learning Curves: follow up 7

36. Learning Curves: follow up 8

37. Learning Curves: follow up 9 In this case, I got a group of students to carry out their activities on Monday and AGAIN on Thursday of the same week. I wanted to test their learning, their retention � the students carried out the SAME activity under the same conditions on the two days. The graph here is exceptional since it gives us a discontinuity, other students� results weren�t so dramatic. If you have the time, try something like this too. In this case, I got a group of students to carry out their activities on Monday and AGAIN on Thursday of the same week. I wanted to test their learning, their retention � the students carried out the SAME activity under the same conditions on the two days. The graph here is exceptional since it gives us a discontinuity, other students� results weren�t so dramatic. If you have the time, try something like this too.

38. Learning Curves: conclusion Learning curves may not be the hottest topic on the syllabus; but they are a real life issue of enormous importance in real life. Moreover, learning curve analysis is an accounting, business and economics related topic and what you have seen here can usefully provide you with a couple of lectures/lessons of valuable work that will encourage students (and teacher!) to use a wide range of skills including communications, mathematics and data analysis and representation. Please write to me with your comments, questions and concerns. I genuinely do want to here what you think, what you did � did it work, did it fail � brickbats and bouquets equally well received! Best wishes whatever you do. Duncan Williamson April 2001 Learning curves may not be the hottest topic on the syllabus; but they are a real life issue of enormous importance in real life. Moreover, learning curve analysis is an accounting, business and economics related topic and what you have seen here can usefully provide you with a couple of lectures/lessons of valuable work that will encourage students (and teacher!) to use a wide range of skills including communications, mathematics and data analysis and representation. Please write to me with your comments, questions and concerns. I genuinely do want to here what you think, what you did � did it work, did it fail � brickbats and bouquets equally well received! Best wishes whatever you do. Duncan Williamson April 2001