Abstract | Introduction | Resource Loading | S-curves | What can be Learned?
Productivity Improvement | Learning vs. Experience | Original Theory | Two Approaches
Illustration | Issues | Conclusions | References | Appendix 1 | Appendix 2 

Illustration of Learning Curve Application

For purposes of illustration, consider the following hypothetical case. The construction of floors on a 25 storey concrete high-rise building are being tracked. From the second floor up, all floors are virtually the same, so that the second floor is the first of a uniform series of 24. The roof and mechanical penthouse are not included in the observations. Construction data is collected as follows.[5]

Time sheets are carefully marked up with job allocations, and hours are abstracted for forming and pouring concrete on each standard floor. The man-hours for the first in the series is noted as 1175 man-hours. The second, third and fourth in the series take 855, 905, and 735 respectively. This data is plotted on log-log paper using the LL-U Model as shown by line (a) in Figure 11. At this stage the data suggests a line whose slope is -.152 (approx. 90% learning ratio) and that future floors would be expected to take the times shown in Column 1b of Table 3.

Table 3: High-rise repetitive construction: hypothetical case

However, suppose actual records for the next two floors, five and six, produce results of 700 and 690 respectively. The addition of the latest data suggests a new line whose slope is -.234 (approx. 85%) as shown by line (b) in Figure 11, and the new times taken to complete are as shown in Table 3, Column 2b. The new result shows a reduction in total hours of approximately 2200 hours (12%, or the equivalent of some four extra floors).

Figure 11: High-rise repetitive construction:
four floors projected (green), and six floors projected (turquoise)

Typically, practical reality follows neither of the two models. When record keeping is continued until all floors are completed, the results could be as shown in Table 3, Column 3. These results are shown plotted in Figure 12. Many projects experience a decrease in productivity at the end of a run of work, (Barrie, Paulson 1978) and in the example the "tail end" departs significantly from either of the two earlier projections. The total man-hours shown in Table 3, Column 3 is 15% higher than the second projected total in column 2b.

Figure 12: High-rise repetitive construction:
cumulative unit projections and observed (LL-U model)

The same data, plotted according to the LL-CA Model, are shown in Figure 13. It will be seen that this model substantially conceals the significant changes in trends associated with the "tail end" effect. Thus, the LL-U Model, although not consistent with the original theory, is a more useful tool in many practical applications and for project management observation and control.

Figure 13: High-rise repetitive construction:
cumulative average projections and observed (LL-CA model)

When the figures shown in Table 3, Column 3 are plotted at normal scales, they display a shape sometimes referred to as the "Bath Tub" effect as shown in Figure 14. In fact, this is simply a reflection of some of the considerations associated with each of the three stages of the S-curve discussed in an earlier section.

Figure 14: High-rise repetitive construction: showing the "bath tub" effect

This suggests that the application of "Learning Curve Theory" on a construction site should be limited to the first 25% or so of the total production under consideration, which is to say approximately 30-35% of the allotted time. In the high-rise construction example, the target for reaching optimum performance must be the 6th or 7th floor.

Two Approaches

Issues Regarding Total Time and Stage 1 Time

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