The Role of Design Complexity in Technology Improvement

Abstract

We study a simple model for the evolution of the cost (or more generally the performance) of a technology or production process. The technology can be decomposed into n components, each of which interacts with a cluster of d − 1 other, dependent components. Innovation occurs through a series of trial-and-error events, each of which consists of randomly changing the cost of each component in a cluster, and accepting the changes only if the total cost of the entire cluster is lowered. We show that the relationship between the cost of the whole technology and the number of innovation attempts is asymptotically a power law, matching the functional form often observed for empirical data. The exponent α of the power law depends on the intrinsic difficulty of finding better components, and on what we term the design complexity: The more complex the design, the slower the rate of improvement. Letting d as defined above be the connectivity, in the special case in which the connectivity is constant, the design complexity is simply the connectivity. When the connectivity varies, bottlenecks can arise in which a few components limit progress. In this case the design complexity is more complicated, depending on the details of the design. The number of bottlenecks also determines whether progress is steady, or whether there are periods of stasis punctuated by occasional large changes. Our model connects the engineering properties of a design to historical studies of technology improvement.experience curve | learning curve | progress function | performance curve | design structure matrix | evolution of technology T he relation between a technology's cost c and the cumulative amount produced y is often empirically observed to be a power law of the formwhere the exponent α characterizes the rate of improvement. This rate is commonly termed the progress ratio 2 −α , which is the factor by which costs decrease with each doubling of cumulative production. A typical reported value [9] is 0.8 (corresponding to α ≈ .32), which implies that the cost of the 200th item is 80% that of the 100th item. Power laws have been observed, or at least assumed to hold, for a wide variety of technologies [2,18,9], although other functional forms have also been suggested and in some cases provide plausible fits to the data 1 . We give examples of historical performance curves for several different technologies in Figure 1. The relationship between cost and cumulative production goes under several different names, including the "experience curve", the "learning curve" or the "progress function". The terms are used interchangeably by some, while others assign distinct meanings [9,29]. We use the general term performance curve to denote a plot of any performance measure (such as cost) against any experience measure (such as cumulative production), regardless of the context. Performance curve studies first appeared in the 19th century [10,6], but their application to manufacturing and technology originates from the 1936 study by Wright on aircraft produc...

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