A Markov Model of the Learning Curve

Larsen, Harry (2026): A Markov Model of the Learning Curve. Published in: Journal of Cost Analysis & Parametrics , Vol. 13, No. 1 (18 March 2026): pp. 104-113.

Abstract

A learning curve is the labor hours per unit of production in the production sequence. Before its cost realization, it is typically forecast using the power function, hours(unit) = a unitb, with a and b derived from historical data via regressions. After the first unit’s cost is realized, future costs can be projected from the sequence of actualized units. This paper transforms the power function into a Markov model and applies a Kalman Filter to estimate the expected value, slope, and variance of a learning curve projection. To exemplify the solution, the parameters of the Kalman Filter are estimated from a set of twenty 1000-unit learning curves derived from The Theory of Complex Work. For those responsible for predicting future values of an ongoing production program, this procedure provides optimal estimates of unit labor hours and their variances.

• Item Type: MPRA Paper
• Language: English
• Keywords: Markov, Kalman Filter, Learning Curve, Excel, Solver
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; L - Industrial Organization > L6 - Industry Studies: Manufacturing; L - Industrial Organization > L6 - Industry Studies: Manufacturing > L60 - General; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M2 - Business Economics; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M2 - Business Economics > M21 - Business Economics

References

*Larsen, Harry, 2022. "Theory of Complex Work," MPRA Paper 113369, University Library of Munich, Germany. https://ideas.repec.org/p/pra/mprapa/113369.html Larsen, Harry, “The Theory of Complex Work” Journal of Cost Analysis and Parametrics, Volume 10, Issue 2, November 2022, 90-103 https://www.iceaaonline.com/wp-content/uploads/2022/11/JCAPv10i3.pdf ** The “Source Book of World War II Basic Data Airframe Industry Progress Curves” unit direct labor hours are available in Excel format at: harrylarsen.yolasite.com