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Technical Paper

The Theory of Cost Risk in Design

In a recent paper (Hoult & Meador, [1]) a novel method of estimating the costs of parts, and assemblies of parts, was presented. This paper proposed that the metric for increments of cost was the function log (dimension/tolerance). Although such log functions have a history,given in [1], starting with Boltzman and Shannon, it is curious that it arises in cost models. In particular, the thermodynamic basis of information theory, given by Shannon [2], seems quite implausible in the present context. In [1], we called the cost theory “Complexity Theory”, mainly to distinguish it from information theory. A major purpose of the present paper is to present a rigorous argument of how the log function arises in the present context. It happens that the agrument hinges on two key issues: properties of the machine making or assembling the part, and a certain limit process. Neither involves thermodynamic reasoning.