(115d) The Geometry of Experience Curves

Abstract: A project involves change, usually a change in capacity of a process or facility hence growth. To effectively manage a project or a portfolio or any human endeavor it is helpful to know what the variables are that affect costs, capacity, price, volume and investment. It is also helpful to understand the historic cause and effects variables for the project, business or corporation. Projection of those variables into the future is often helpful if there is a sound basis for their projection. Experience Curves frequently enter into the discussion of history and future expectations but the literature abounds with disclaimers of not knowing what they teach and prove or how to extend them into the future. This article provides the basis to understand the primary cause and effect variables for experience curves.

Not only has Geometry been the essential element for Newton's and Einstein's description of gravity, time and space it also provides the basis for the quantitative description of Experience Curves in dimensions of Men, Time and Space. While Bruce Henderson never did come to understand the cause and effect relationships of Experience Curves and as reported in Michael Rothschild's Bionomics, wrote: 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 reasons for the experience curve effect are not particularly important. The important fact is that the experience curve is a universable phenomenon.

This lack of understanding leads to its non-quantativeness by Henderson and its downfall in its subsequent literature. In the literature, Experience Curves never have the reason for their shape or the slope of curves that have been drawn through their data quantitatively explained. While there is a large literature based upon an unexplained phenomenon it is of limited value to the engineer interested in specific quantitative cause and effect relationships. The original non-quantitative explanation of "cumulative experience" gained from cumulative production volume is only assumed and not proven. In the absence of a science of cause and effect for experience curves any expectation of future events is justifiably met with skepticism and disbelief. The reason why experience curves are what they are, and do what they do, as well as what the real variables are, is disclosed in this article. The three physical dimension of our world, time, and employed people define the relationship between Log(Current Price(t)) and Log(Cumulative Volume(t)) for a given product, which is the Experience Curve of the literature. Quantification of that relationship, for example, for a product that is growing essentially exponentially is developed. The reader is reminded that the capacity of a production facility, and its investment and the number of construction men one can hire at a given wage rate to build that facility is proportional to a characteristic dimension of that facility raised to a power of 1/m, where m is determined by the geometry of the production facility and is the number of dimensions primarily being used for the facility. (e.g. 1 for a long pipeline, 2 for an area controlled production rate, e.g. a plate and frame filter press, and 3 for a volumetric rate controlling facility, e.g. a tank). 1/m is the scale factor (SF) for scale vs. investment and is the slope of a log(scale) vs. log(investment) plot. The identities common to a given products economic representation of wages*men= price*volume=dollars sales=dollars cost for a supply demand balance are presented and the demand vs. supply differential equations are developed to define the slope of the experience curve thus defining its previously unexplained shape.

The belief that learning is the cause of the experience curve is replaced with a quantitative cause and effect relationship between men, price, volume, scale of production and time. The now supportable scientific cause and effect relationships defining experience curves shape as a function of time, employed persons, scale factor and the demands growth rate constant (kg) is disclosed as:

Slope(t)=(SF-1)*(1-exp(-kg*t))=(1/m-1)*(1-exp(-kg*t))

Where m= the number of dimensions being used to expand the process capacity for the product. M for a pipeline etc. is 1.0, and for an area process like a filter press is 2.0 and for a volumetric process is 3.0.