Learning curve tables ..

Learning curves help us to understand and track the learning benefits that comes from different repetitive processes. For example if it takes 100 hours for a shipyard to build a ship, due to the learning process, the time taken to build the second ship will be less than 100 hours. Similarly as we build more ships, the time taken to build the ships, reduces.

In studies done at the US aircraft building industry in the latter half of the twentieth century, it was observed that the time it takes to complete progressive units reduces by a fixed percentage for every doubling of units. i.e. for example if it takes 100 hrs, to build the first unit,  it took 90 hours to build the second unit, it was observed that to build the fourth aircraft it took app 81 hours and the eighth aircraft it took app 72 hours and so on. 

In the case of the shipyard, it was observed that for every doubling of the number of ships built, the time it took to build the ships reduced by a fixed percentage.  In this case it was 10 % reduction of time for every doubling of the number of ships built. We call this 90% learning curve, even though actually it is only 10 % learning !! Similarly 80% learning curve implies there is 20 % reduction in time it took for every doubling of quantity built (and not 80% reduction in time). 

The formula is this : ( can be used for different learning ratio 'r' and 'n', the no of units)

t_n = t_1 x (n) to the power (r)

where t_n = time to complete the n th unit, 

t_1 = time to complete the first unit 

   r = natural log (learning ratio)/ natural log (2),

where learning ratio is for eg. 0.9 for 90% learning, 0.8 for 80%  learning and so on ..

The table given above gives the learning ratio, unit time and cumulative time for 90%, 85%, 80%, 75% and 70% learning for upto 30 units .. For more than 30 units, the values could be substituted in the equation and computations completed.

Does it imply that as the cumulative numbers increases, the time required to manufacture the units approach zero ?? Not at all.

The time required to manufacture each additional unit is negative exponentially distributed. (as given in the curve). As the cumulative numbers increase, the time needed to manufacture each additional unit approaches a theoritical minimum, which is the standard time required for the production of the unit.  The magnitude of the incremental time taken for manufacturing each additional unit decreases as we manufacture more units.

When we say there is a steep learning curve, it just implies that after the first few units, the learning is very fast. A flat learning curve implies that the learning on the job is very slow and takes lot of time.

This helps companies to competitively bid for complex products, as the cost it takes to manufacture multiple units of complex parts decreases as the volume increases (a steep curve indicates costs to manufacture future components will be much less than the time to manufacture earlier components while a less steep curve indicates the drop in time to be less..)

george ..