Learning and The Learning Curve

Introduction The 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.

Learning theory The theory of learning recognizes that repetition of the same operation results in less time or effort expended on that operation. Its underlying concept is that, for example 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.

Psychology of Learning: Based on the theory of learning it is easier to learn things that are related to what you already know. The likelihood that new information will be retained is related to how much previous learning there is that provides "hooks" on which to hang the new information.

Learning Curve A steep learning curve is often referred to indicate that something is difficult to learn. In practice, a curve of the amount learned against the number of trials (in experiments) or over time (in reality) is just the opposite: if something is difficult, the line rises slowly or shallowly. So the steep curve refers to the demands of the task rather than a description of the process.

Learning Curve Gragh

Valley of Despair The goal is to make the "valley of despair" as Shallow and as Narrow as possible. To make it narrow: you must give plenty of training, and follow it up with continuing floor support, help desk support, and other forms of just-in-time support so that people can quickly get back to the point of competence. If they stay in the valley of despair for too long, they will lose hope and hate the new software and the people who made them switch. NB: experts agree that the learning effect is the result of other factors in addition to actual worker learning. Some of the improvements can be traced to:

Preproduction factors as selection of tooling and equipment, product design, methods analyses the amount of effort expended prior to the start of the work.

Other contributing factors Other contributing factors include changes after production has begun, such as changes in: Methods Tooling Design

Management input Management input can be an important factor through improvements in: planning, scheduling, motivation control

Production Changes changes that are made once production is under way can cause a temporary increase in time per unit until workers adjust to the change. Even though they eventually lead to an increased output rate. If a number of changes are made during production, the learning curve would be more realistically described by a series of scallops instead of a smooth curve as illustrated in the figure below:

Improvements vs Learning Curve

Example: An activity is known to have an 80 percent learning curve. It has taken a worker 10 hours to produce the first unit. Determine expected completion times for these units: the 2nd, 4th, 8th and 16th

Solution Each time the cumulative output doubles, the time per unit for that amount should be approximately equal to the previous time multiplied by their learning percentage (80%) percent in this case). Thus Learning percentage * previous unit time Unit Unit Time (hours) 1 = 10 2 0.8(10) = 8 4 0.8(8) = 6.4 8 0.8(6.4) = 5.12 12 0.8(5.12) = 4.096

Explanation NB: the above example illustrates an important point and question. The point is that the time reduction per unit becomes less as the number of repetitions increases. For example, the second unit required two hours less time than the first, and the improvement from the 8th to the 16th unit was only slightly more than one hour. The question raised is: how are times computed for values such as 3, 5, 6, 7 and other units that do not fall into this pattern.

Formula Approach: The formula is based on the existence of a linear relationship between the time per unit and the number of units when these two variables are expressed in logarithms. The unit time (i.e., the number of direct labor hours required) for the nth unit can be computed using the formula: Tn = T1 *nb Where; Tn = Time for nth unit T1 = Time for first unit b = 1n learning percent / 1n 2; 1n stands for the natural logarithm

Example For example, for an 80 percent curve with T1 = 10 hours, the time for the third unit would be computed as: T3 = 10(31n.8/1n 2) = 7.02

The Learning Factor Approach Obtained from table representing learning curve coefficients. The table shows two things for some selected learning percentages. One is a unit value for the number of repetitions (unit number). This enables us to easily determine how long any unit will take to produce. The other is a cumulative value, which enables us to compute the total number of hours needed to complete any given number of repetitions. The computation for both is a relatively simple operation: multiply the table value by the time required for the first unit.

Learning Curve Coefficients

Illustration To find the time for an individual unit (e.g., the 10th unit), use the formula: Tn = T1 * unit time factor Thus, for an 85 percent curve, with T1 = 4 hours, the time for the 10th unit would be 4 *.583 = 2.33 hours. To find the time for all units up to a specified unit (e.g., the first 10 units), use the formula. ∑Tn = T1 *total time factor

Example Thus, for an 85 percent curve, with T1 = 4 hours, the total time for all 10 units (including the time for unit 1) would be 4 * 7.116 = 28.464 hours.

EXAMPLE 3 An assembly operation has a 90% learning curve. The line has just began work on a new item; the initial unit required 28 hours. Estimate the time that will be needed to complete: A) The first 5 units B) Units 20 through 25

Solutions A) use the total time factor in the 90% column of learning curve coefficients. Table value: 4.339. estimated time for 5 units: 28(4.339) = 121.49 hours. B) the total time for units 20 through 25 can be determined by subtraction: Total time for 25 units: 28(17.713)= 495.96 Total time for 19 units: 28(13.974)=391.27 Total time for 20 through 25 104.69

Example 4 A manager wants to determine the appropriate learning rate for a new type of work his firm will undertake. He has obtained completion times for the initial six repetitions of a job of this type. What learning rate is appropriate? Unit completion time (hrs) 1 15.9 2 12.0 3 10.1 4 9.1 5 8.4 6 7.5

Solution According to the theory, the time per unit decreases at a constant rate each time the output doubles (e.g unit 1 to 2, 2 to 4 and 3 to 6). The ratios of these observed times will give us an approximate rate. Thus, Unit 2 = 12.0 Unit 4 = 9.1 Unit 6 = 7.5 Unit 1 15.9 Unit 2 12.0 Unit 3 10.1 =.755 =.758 =.743 Nb. The rate is a smoothed approximation hence a rate of 75 percent seems reasonable in this case

Applications of learning curves Learning curve theory has found useful applications in a number of areas, including: manpower planning and scheduling negotiated purchasing pricing new products budgeting, purchasing, and inventory planning capacity planning

knowledge of output projections in learning situation can help manager make better decisions about how many workers they will need than they could determine from decisions based on initial output rates. Of course, managers recognize that improvements will occur, what the learning curve contributes is a method for quantifying expected future improvements.

Negotiated purchasing Negotiated purchasing often involves contracting for specialized items that may have a high degree of complexity. The direct labour cost per unit of such items can be expected to decrease as the size of the order increase. Hence, negotiators first settle on the number of units and then negotiate price on that basis.

pricing new products Managers must establish prices for their new products and services, often on the basis of production of a few units. Generalizing from the cost of the first few units would result in a much higher price than can be expected after a greater number of units have been produced. The manager needs to use the learning curve to avoid underpricing or over pricing.

budgeting, purchasing, and inventory planning The learning curve projections help managers to plan costs and labour, purchasing and inventory needs. For example, initial cost per unit will be high and output will be fairly low, so purchasing and inventory decisions can reflect this. As productivity increases, purchasing and inventory actions must allow for increased usage of raw materials and purchased parts to keep pace with output. Because of learning effects, the usage rate will increase over time. Hence, failure to refer to a learning curve would lead to overestimates of labor needs and underestimates of the rate of material usage.

Modeling the Learning Curve Learning curves are all about ongoing improvement. Managers and researchers noticed, in field after field, from aerospace to mining to manufacturing to writing, that stable processes improve year after year rather than remain the same. Learning curves describe these patterns of long-term improvement. Learning curves help answer the following questions.

Critical questions How fast can you improve to a specific productivity level? What are the limitations to improvement? Are aggressive goals achievable? Explain how changes in a process, once it is underway can cause scallops in learning curve. What factors might cause a learning curve to tip toward the end of a job?

Summary The learning curve was adapted from the historical observation that individuals who perform repetitive (types of production systems; job, batch and flow production and their implications on learning) tasks exhibit an improvement in performance as the task is repeated a number of times.

Summary Contd.... With proper instruction and repetition, workers learn to perform their jobs more efficiently and effectively and consequently, e.g., the direct labor hours per unit of a product are reduced. This learning effect could have resulted from better work methods, tools, product design, or supervision, as well as from an individual’s learning the task.

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