the-geometry-of-experience-curves-aiche5-cut

Defines what an experience curve really is and why.

A: For an Economy, like say the U.S. where we have variables Employed Men, Price,Volume,Wages,Investment,Scale of Operation, Production Process Mean Dimensions of Radius R with Number of space dimensions being used = m, Dollars, A Gross National Product, Specific Products and the change in time of these variables then:

For a change in Production of a Product with time the Behavior of Men is to Minimize their time/Per unit of Volume of the product, i.e. that ratio (dMen/dRadius with time)=0.

Using reduced values, or indexed values of these variables based on a given year for GNP, Price, Volume, etc. and the Fact that Dollars=Price*Volume=Wages*Men, and Volume=Radius^m gives a Slope for the Experienc Curve=(1/m-1)*(1-Exp(-k*t)) wherE k=growth rate constant for the product and t=time (usually years) .

Because “All Men involved minimize their time per unit of space dimension, with time”.  Thus this Law of Nature is claimed as Garnett’s Minimization Law

(more)

Inherent in the foregoing is also the fact that Investment=Scale^(1/m).

In the world of Supply and Demand the money that one group of people are willing to spend for something is equal to the amount of Money another group of  people are willing to provide (sell) that something.  The something can be anything, either goods (a product) or services.  Money is identical to the time of Employed men times their Wage rate as that is exactly what one can buy with money.  The production of that something in a physical facility has dimensons, like the Radius of a spherical tank brewing beer, and the quantity of beer or its Volume is proportional to the Radius raised to the power of the number of dimensions.  In this case V=R^(N)=R^(3), since the number of dimensions is 3.  In general, the economy is evolving, that is, it is a function of Time.  The rate of change with time for the variable, say Employed is dE/dT, and Radius  is dR/dT.  The behavior of people when it comes time to change supply and demand is defined as Garnett’s Minimization Law:

.

“People minimize their time per unit of dimension, namely d((dE/dt) / (dR/dT))/dT  = zero = 0 .

.

The result is that the Log(Money)=(1/N)*Log(Volume).  Also,

Log(Price)=(1/N-1)*Log(Volume)

and other relationships that can be worked out from Money=Price*Volume=Wages*Employed=Wealth+Costs,

.

and the fact that demand is frequently exponential with time.

The price of the flu is death of a fraction (shown below) of those infected.  The volume is those that have been infected.  The experience curve of the h1n1 flu follows:

recent-us-deaths

Which has slope of 2.

The number of dimensions m, normally being used is: Slope=1/m-1, hence in this case 1/m=2+1=3.

However, we are not infecting the virus it is the other way around.  Hence from the viruses point of view the number of dimensions is 1/m not m, and therefore=3.  It is a volumetric production rate.  Presumably the graph of deaths vs. invections will continue until the number of uninfected people is beginning to diminish, somewhere over half of the population.

The death rate per thousand infected people (the “fraction”) has been rising but recently has been diminishingas shown in:

recent-us-deaths1

Presentation made on August 24, 2009, in Montreal, Canada.

dig-presentation-v3

Power Point presentation “with recorded voice”.  Research as Investment

spare1a1-research-as-investment-power-point1

spare1a2-research-as-investment-power-point1

spare1a3-research-as-investment-power-point1

spare1a4-research-as-investment-power-point1

spare2a-research-as-investment-power-point1

spare2b1-research-as-investment-power-point1

spare2b2-research-as-investment-power-point1

spare2c-research-as-investment-power-point1

spare2d1research-as-investment-power-point

spare2d2research-as-investment-power-point

spare2e-research-as-investment-power-point

Once you accept that the investment for a tank or reactor or container scales up with the 1/3rd power of volume then the scale up with pressure naturally follows.

If the rate of reaction of a chemical reaction is proportional to pressure (P) then raising pressure will lower the volume required at the same time that it will raise the thickness of the walls to contain that higher pressure.  It follows that Investment will be:

Investment=k*(1/P)^(1/3)*P

Investment =k*P^(2/3)

If the reaction is proportional to the pressure squared (2 species->one species)

Investment=k*(P)^(1-2/3)=k*(P)^(1/3)

For a 3rd order pressure dependency on the reaction rate the Investment is independent of pressure, i.e.

Investment=k*P^(1-3/3)=k

For orders higher than 3 other things like heat transfer to/from the reactants (i.e. area or order 2),  or limiting conversion to limit temperature rise, or use of diluents to control temperature rise,  may become dominant, limiting the pressure effect between P^0 to P^(1/3).

By my memory the investment for polyethylene plants scale as the 1/4th power of Pressure.

The foregoing is applicable for a fixed production rate.  However if one is in the position of building a plant where the justification of the capital is a key element then one likes to consider investment per annual pound.  Larger plants tend to give lower investments/annual lb.  Since production rate is proportional to P raised to the power of 1,2, or 3 preceding the investment per annual lb will be proportional to Pressure raised to the power of -1/3, -5/6, -6/3=-2.  That being the case plants tend to be at the highest pressure and largest scale.

Is the Learning Curve the cause for the Experience Curve?

Bruce Henderson in his “Perspective on Experience” alluded to learning being responsible for the experience Curve being the way that it is. However, he never did quantify the relationship between price and cumulative volume much less their relationship to learning. Henderson’s lack of understanding of the cause and effect relationships is exemplified by the many assertions of not knowing why the curves were as they were. Michael Rothschild in his Bionomics: Economy as Ecosystem asserts Henderson as writing:

“The experience curve phenomenon is as real as gravity. . . . [Its] effect can be observed and measured in any business, any industry, any cost element, anywhere. . . . The reason for the experience curve effect are not particularly important. The important fact is that the experience curve is a universally observable phenomenon.”

Clearly Henderson did not know and did not want to know the reasons behind experience curves as long as his experience curve phenomenon continued to be acknowledged.

See link for more:

rats_motivation

Why do scale up rules of thumb work and why is the historic six tenths power six tenths?

The cause and effect relationship is shown in this link (publication)

scale

Experience curves show the scale factor or number of dimensions “m” of the production facility, the growth rate constant constant, and contain cycles with time.  The full equation for the experience curves depends upon the scale of the production facility at a given time, the number of men currently working on it and the expansion effort currently underway.  Using men(t) as a variable, which is proportional to money via wages, and an exponential demand from the population gives the following differential equation and its’ solution.  The periodicity is shown to be a fundamental part of the solution.

the-full-experience-curve

I was talking to Gregory S. Patince recently about Research being an Investment, or not.  My view of course is that it can be if managed to be an investment.  Just how that is so is included in the following documents.  The criteria of what is required is defined.

research-as-investment-power-point1

research-as-investment-manuscript

These documents are part of the continuing dialog about what Experience Curves are and how they can be extended beyond historic data.