# Learning Curve

HISTORY

Introduced to the aircraft industry in 1936 by T. P. Wright in his article Journal of the Aeronautical Science He found that per unit production time reduced at an unvarying rate Since then, learning curves (also known as progress functions) have been applied to all types of work

INTRODUCTION

A graphical representation of the changing rate of learning (in the average person) for a given activity or tool The underlying hypothesis is that the direct labor man-hours necessary to complete a unit of production will decrease by a constant percentage each time the production quantity is doubled

EXAMPLE

FUNDAMENTAL PROPERTIES

As the number of completed tasks increases: time taken to complete a task decreases time savings from one task to another decreases amount of improvement decreases

ASSUMPTIONs

That the task is repetitive That only manual labour is involved and there is no automation of processes. That staff are fully motivated and there are no constraints. That no labour turnovers occurred for a long time That the products and processes are standardised, no midway modification. There must be continuous production- no stoppage That repetitive process will increase production

FACTS ABOUT LEARNING CURVE…

• Learning applies to people, machinery, systems • Learning Curve is similar to Experience curve but

former applies more to whole organisation.

• Learning Curve is based on empirical evidences. • 80% learning curve usually assumed

WHERE CAN WE APPLY learning curve?

• • • • • • • • • • • •

New Product Production Costs Make or Buy Decisions Suppliers Progress Payments Analyze Pricing Practices of Suppliers Cost-Volume-Profit (CVP) Analysis Evaluation of Production Employees Multi-Year Procurement Analysis Production Rate Evaluation Production Improvement Cycle Times Costs versus Prices Over Time Competitive Bidding Technology Forecasting

ARITHMETIC APPROACH

Empirical evidence shows that doubling of repetition results in constant percentage decrease in time per repetition. Unit 1ST 2ND 4TH 8TH 16TH 32ND Man hours 1000 800 640 512 410 328

1000 X .80 800 X .80 640 X .80 512 X .80 410 X .80

LIMITATIONS OF BASIC APPROACH

It’s very difficult to calculate or predict the Man Hrs for anything other than that at the DOUBLING POINT: 1, 2, 4, 8, 16 … 128 …

Now it gets mathematical! 1. Use of Formula 2. Use Of Table of Coefficients

LEARNING THEORY

Two variations:

Cumulative Average Theory Unit Theory

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CUMULATIVE AVERAGE THEORY

“If there is learning in the production process, the cumulative average cost of some doubled unit equals the cumulative average cost of the undoubled unit times the slope of the learning curve” Described by T. P. Wright in 1936 based on examination of WW I aircraft production costs

CUMULATIVE AVERAGE LEARNING THEORY

Defined by the equation YN = AN b where YN = the average cost of N units A = the theoretical cost of unit 1 N = the cumulative number of units produced b = a constant representing the slope

UNIT THEORY

“If there is learning in the production process, the cost of some doubled unit equals the cost of the undoubled unit times the slope of the learning curve” Credited to J. R. Crawford in 1947 led a study of WWII airframe production commissioned by USAF to validate learning curve theory

CONCEPT OF UNIT THEORY

As the quantity of units produced doubles, the cost to produce a unit is decreased by a constant percentage 80% Unit Learning Curve $120.00 $100.00 $80.00 $60.00 $40.00 $0.50 $20.00 $0.00 0 2 4 6 8 10 12 14 16 $0.00 0 0.5 1 1.5 100 80 66.92 54.98 44.638 $2.50 $2.00 $1.50 $1.00

UNIT THEORY

Defined by the equation Yx = Axb ,where Yx = the cost of unit x (dependent variable) A = the theoretical cost of unit 1 (a.k.a. T1) x = the unit...

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