1 / 16

Learning Curve Theory and Applications in Defence Cost Estimating

Explore the concept of learning curves, traditional models, extensions, and applications in defence cost estimating. Dive into the historical development of the learning curve concept, its relevance in improving workers' performance, and the various models and factors influencing learning processes. Discover methodological limitations and future research directions in optimizing learning curve models for accurate cost estimation in defence. Reference key studies and applications in military systems cost analysis.

brosen
Download Presentation

Learning Curve Theory and Applications in Defence Cost Estimating

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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.

  2. Outline • Learning curve concept • Traditional model • Extensions • Applications in defence cost estimating • A methodological limitation • Directions for future research

  3. 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

  4. Illustration - The learning curve for naval production

  5. Traditional model (Wright model) • The first formal representation of LC was given by the Wright log-linear model • The marginal cost (or time) required to produce the nth unit is given by: (1) where and b are parameters to be estimated • represents the cost (or time) of the first unit • is the learning (or improvement) index.

  6. Traditional model • The model assumes that as the quantity of units produced doubles, the cost (or time) it takes to produce an individual unit decreases at a uniform rate. This rate can be expressed as: (2) • This rate is known as “the learning rate” Lower values of u denote high learning and fast adaptation • A learning rate of 80%, for example, implies that unit 2n costs only 80% as much as unit n (Teplitz, 1991)

  7. 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)

  8. Stanford-B model • This model adds an experience factor representing the number of units of prior-experience. (3) • If , the model reduces to Wright’s model • It was the result of a study conducted by Stanford Research Institute (SRI) for the US Department of Defense (DoD) • The model was applied to the assemblage of the Boeing 707 (Yelle, 1979; Badiru, 1992).

  9. Dejong’s model • Dejong’smodel incorporates the influence of machinery in the learning process. (4) • Where M ( is the incompressibility factor that indicates the fraction of the work executed by machines (Yelle, 1979). • When , Dejong’s model becomes the Wright Model • When 𝑀=1, no learning takes place (Anzanello and Fogliatto, 2011)

  10. The plateau model • The plateau model is used for learning curve with saturation phase (steady state) • It includes a constant that describes the steady state of workers’ performance (5) • The steady state is reached when learning is completed

  11. The augmented learning curve model • This two-factor learning curve model incorporates the rate of production in the current period,It can be expressed as: (6) whereis the lot i average cost, the lot midpoint, and c the production (orprocurement) index • The lot midpoint is the unit whose marginal cost is equal to the lot average cost (Goldberg and Touw, 2003). • The production ratecan, for example,reduce the average unit cost by spreading fixed costs over more units (Goldberg and Touw, 2003; Younossiet al., 2007)

  12. 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 labourcost in the military shipbuilding sector • More references can be found in (Badiru, 2012)

  13. 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

  14. 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

  15. References • 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-22A 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

More Related