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This paper contains both theorems and correlations based on the idea that there is a uniform metric for measuring the complexity of mechanical parts. The metric proposed is the logarithm of dimension divided by tolerance. The theorems prove that, on the average, for a given manufacturing process, the time to fabricate is simply proportional to this metric. We show corrleations for manual turning (machine lathe process), manual milling (machine milling process), and the lay-up of composite stringers. In each case the accuracy of the time estimate is as good as that of traditional cost estimation methods, but the effort is much less. The coefficient for composite lay-up compares well to that obtained from basic physiological data (Fitts Law).

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.