Experience Curves » analysis

Learning from Cumulative Volume?

Don — Sun, 28 Feb 2010 04:39:33 +0000

If the result of repeated activities by mankind always results in learning, what is it that causes mankind to adopt a new learned procedure? Why does it always work no matter what the activity is? And why does it affect cost of manufacture differently for different products?

The post “The Geometry of Experience Curves” in this blog shows that the answer is: “That Men minimize their Time per unit of dimension”. Thus providing the incentive (less time spent by men) and the reason (geometry difference) for each product being different.

Garnett’s Minimization Law of Human Behavior

Don — Tue, 25 Aug 2009 04:16:19 +0000

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.

WCCE8 Presentation: Research as Investment

Don — Sun, 26 Jul 2009 06:05:09 +0000

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

dig-presentation-v3

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

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Scale up of Investment with Pressure

Don — Fri, 17 Jul 2009 01:17:20 +0000

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.

Rats Motivation

Don — Thu, 16 Jul 2009 07:20:15 +0000

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

Scale-up Investment vs. Scale

Don — Thu, 16 Jul 2009 07:03:10 +0000

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

The Full Experience Curve

Don — Sat, 25 Apr 2009 19:54:05 +0000

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

Research as Investment

Don — Mon, 13 Apr 2009 06:38:07 +0000

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.

Why firms should be cautious in using experience curves as a strategic guide in their operations?

Don — Sat, 17 Jan 2009 04:50:22 +0000

The equation for the slope of an experience curve is (1/m-1)*(1-exp(-kg*t)) or
(SF-1)*(1-exp(-kg*t)), where: t is time typically years, kg is the exponential growth rate

constant, SF is scale factor from the slope of an xy plot of scale of the facility vs investment

in constant dollars, m is the number of dimensions of the production facility eg. 1 for linear

like a pipe line, 2 for an area facility like a plate and frame filter press, and 3 for a volumetric

facility like a tank. For a mature product slope becomes (1/m-1) or (SF-1).

If an experience curve is being extrapolated into the future any change in “m, SF, kg, or constant dollars” will cause deviation from historic performance but in accordance with the preceding equations. Since an extrapolated experience curve is basically a price-volume-time forcast based on historic performance of price-volume-time the firm should be confident it understands the historic cause and effect relationships. The foregoing equations come from fundamental considerations of Scale of Operations vs. Investment hence costs, scale factor, time, and the national deflator. The derivation of these equations is presented in experiencecurves.com.

Power Point version “Geometry of Experience Curves”

Don — Thu, 01 Jan 2009 01:16:13 +0000

geometry81

Defines what an experience curve really is.