Apr 24

Wright’s Law

No, I confess I had not heard of it either. It turns out that there are a number of ‘laws’ that purport to predict the evolution of technologies. In the semiconductor business we are only too familiar with Moore’s law, the prediction made by Gordon Moore that the number of transistors on a chip would double every one to two years. Originally made back in the mid 60’s, this law has truly stood the test of time. The exact number of years over which the doubling has taken place has varied a little but otherwise this has proved to a remarkable predictor of the evolution of the IC industry. Mind you maybe it is not too surprising as Moore’s law is really a roadmap for economic survivability. If you miss, the next doubling and your competition don’t you suffer in the market place. There have been a few examples of companies who have survived after missing a node, notably Toshiba when they missed (I believe I have the right node) the 64kb DRAM node and everybody assumed they were dropping out of the DRAM business. But they had not dropped out at all and by the 1Mb generation, they were the market leader.

Back to Wright and his law. But first one does need to make the point that Gordon Moore did not include ‘price’ in his original ‘law’. He did, however, state that “the cost per component is nearly inversely proportional to the number of components”. Thus, if the number of components doubles every one or two years, the cost per component should drop exponentially with time. Again in hindsight this has proved remarkably descriptive of historical price trends. However, with the advent of double patterning and more, current trends suggest a rather greater increase in the cost of manufacturing per chip. Indeed, some predictions are being made that the price per transistor will essentially flatten out. Personally I find it hard to believe that this is a sustainable economic model for the industry.

Wright came up with his law to predict the cost of airplanes in the 1930’s. His premise was that the key factor determining cost per component is cumulative production, i.e. the total number of airplanes (transistors) manufactured (Theodore P. Wright, ‘Factors affecting the costs of airplanes’ 1936) Wright’s law was found to be marginally more effective predictor than Moore’s law over a number of different technologies (62 to be precise) over a 40+ time frame. Both these laws performed better than the four others studied by the authors of a Santa Fe Institute paper (Statistical Basis for Predicting Technological Progress, by Bela Nagy, J. Doyne Farmer, Quan M. Bui, and Jessika E. Trancik) considered. However, it is worth noting that for the case where production rises exponentially with time (as the semiconductor industry) Moore’s and Wright ‘s laws are to all intents and purposes identical.

Christie Marrian, ReRAM-Forum.com moderator

*For a summary of the Sante Fe Institute paper, see spectrum.ieee.org/tech-talk/at-work/test-and-measurement/wrights-law-edges-out-moores-law-in-predicting-technology-development. The other ‘laws’ are:
Goddard’s law (1982) cost decreases as the scale of production increases
Nordhaus (2009): combines time and cumulative production
Sinclair et al (2000): costs fall with scale of and cumulative production
plus a variant on Wright’s law

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