Learning curve Theory and applications Abderrahmane Sokri Ph
Learning curve: Theory and applications Abderrahmane Sokri, Ph. D. Defence R&D Canada Centre for Operational Research and Analysis Department of National Defence, Ottawa, Canada ICEAA Canada Workshop Ottawa, 22 -23 February 2016.
Outline Learning curve concept Traditional model Extensions Applications in defence cost estimating A methodological limitation Directions for future research 1
Learning curve The learning curve (LC) is a mathematical tool that describes workers’ performance in repetitive activities (Jaber, 2011) Due to cumulative experience and increasing familiarity with tasks, workers are likely to do tasks faster and at less cost LC was empirically developed by Wright (1936) in the aeronautical industry It is also known in the literature as the experience curve, the improvement curve, or the progress curve 2
Illustration - The learning curve for naval production 3
Traditional model (Wright model) 4
Traditional model 5
Extensions Many factors may affect the learning process. These factors include: (1) prior experience, (2) the influence of machinery, (3) the steady state of workers’ performance, and (4) the production rate. Several extensions of Wright’s model were suggested to adapt the traditional model to specific applications (Anzanello and Fogliatto, 2011) 6
Stanford-B model 7
Dejong’s model 8
The plateau model 9
The augmented learning curve model 10
Application in defence cost estimating Learning curve has been used by many defence analysts to: analyze the cost of military systems Arena et al. (2008) used it to examine the trends in U. S. military aircraft costs present the cost projections and the production plans Kaluzny (2011) applied it to project cost estimates for aircraft production conduct cost risk analysis Sokri and Ghanmi (Forthcoming) used it to examine the labour cost in the military shipbuilding sector More references can be found in (Badiru, 2012) 11
A methodological limitation In the two-factor learning curve, Cumulative quantity and production rate may be positively correlated This may be observed when production runs are relatively short This statistical problem can affect the accuracy and robustness of the estimates derived Due to correlation, Arena et al. , (2008), for example, reduced the number of systems to be analyzed from 52 to 24 12
Directions for future research Further efforts (to those discussed in slide 10) are ongoing to address other aspects of the learning curve model. Examples of such challenges include: estimation of a learn-forget curve model (e. g. , when production breaks occur) determination of the steady state where knowledge level and unit cost remain constant over time 13
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Jaber, M. Y. (2011) Learning curves: Theory, models, and applications. CRC Press, Taylor & Francis group Wright, T. P. (1936). Factors Affecting the Cost of Airplanes. Journal of the Aeronautical Sciences (Institute of the Aeronautical Sciences), Vol. 3, No. 4, pp. 122 -128. (Teplitz, 1991) Anzanello, M. J. and Fogliatto, F. S. (2011). Learning curve models and applications: Literature review and research directions. International Journal of Industrial Ergonomics, Vol. 41, 573 -583 Yelle, L. E. (1979). The learning curve: historical review and comprehensive survey. Decision Science, 10(2), 302– 328 Badiru, A. B. (1992). Computational Survey of Univariate and Multivariate Learning Curve Models. IEEE Transactions On Engineering Management, Vol. 39, No. 2 Matthew S. Goldberg, M. S. and Touw, A. (2003). Statistical Methods for Learning Curves and Cost Analysis. The CNA Corporation, Virginia, USA Younossi, O. , Arena, M. V. , Brancato, K. , Graser, J. C. , Goldsmith, B. W. , Lorell, M. A. , Timson, F. , and Sollinger, J. M. (2007). F-22 A Multiyear Procurement Program: An Assessment of Cost Savings, RAND Corporation Report MG-664 -OSD, CA, USA Arena, M. V. , Younossi, O. , Brancato, K. , Blickstein, I. , and Grammich, C. A. (2008). Why Has the Cost of Fixed-Wing Aircraft Risen? A Macroscopic Examination of the Trends in U. S. Military Aircraft Costs over the Past Several Decades, RAND Corporation Report MG-696 -NAVY/AF, CA, USA Kaluzny, B. (2011). The Unit Recurring Flyaway Cost of a Canadian Joint Strike Fighter. DRDC CORA TM 2011– 200, Ottawa, Canada Sokri, A. and Ghanmi, A. (Forthcoming). Cost risk analysis and learning curve in the military shipbuilding sector. International Journal of Data Analysis Techniques and Strategies Badiru, A. B. ( 2012). Half-Life Learning Curves in the Defense Acquisition Life Cycle. Defense ARJ, July 2012, Vol. 19 No. 3 : 283– 308 14
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