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 

Two Approaches

The above log-log relationship can be expressed mathematically as follows.

The cumulative average time (or cost) for each of 'n' units up to the 'n'th unit, when plotted against the number of units on log-log paper, produces a straight line.

This may be referred to as the "Log Linear - Cumulative Average Approach" (The LL-CA Model). This relationship is useful in forecasting or comparing similar operations but with significantly different numbers of units involved. It is also useful in analyzing large amounts of data as, for example, the records of a large number of units produced from a precasting yard. This is because the cumulative average curve has considerable power to smooth out the unit data. It can also be deceptive because this power increases as the quantity increases (Thomas 1986). It is, therefore, less useful for examining the expectations for individual units or the latest unit such as would be needed in tracking actual progress on a construction site.

This has led to a variation of the first relationship which states as follows.

The time (or cost) of the 'n'th unit, when plotted against the number of units on log-log paper, produces a straight line.

This may similarly be referred to as the "Log Linear - Unit Approach" (The LL-U Model) (Drewin 1982; DSMC 1989). The mathematics of both models are developed and compared in Appendix 2. Table 2 shows calculations of the time to the nth unit and the time of the nth unit over a range from one to fifty units for ratios ranging from 70% to 95% as determined by each approach. The Cumulative Average figures are shown on white background, while the corresponding Cumulative Unit figures are shaded. As might be expected, the results of the two approaches are similar but not identical. The differences in results obtained from the two approaches vary from about 7% for a repetition of only five units at a 95% productivity ratio to over 100% for 50 units at a ratio of 70%.

Table 2: Comparison of Cum. Av. and Cum. Unit Productivity from 70% to 90%

In practice, one would select one approach or the other depending on the objective, and use the corresponding set of ratios. It does mean, however, that

When comparing the learning ratios on different jobs or of different crews on similar work, the method of calculation must be the same and it must be specified.

Original Theory

Illustration of Learning Curve Application

Home | Issacons | PM Glossary | Papers & Books | Max's Musings
Guest Articles | Contact Info | Top of Page