Optimal Mating of Precision Components in Manufacturing
In the January 2021 issue of Operations Research Letters, Prof. Weber presents a new method for robustly matching random parts with the smallest possible error. The method is useful for selective assembly systems typically employed in high-precision assembly such as in the watch and automotive industries, where the input tolerances often exceed the allowable output tolerances. For example, when assembling a simple electrical oscillator, its resonance frequency depends on the characteristics of the capacitor and inductivity in the circuit, both of which may be subject to uncontrollable variations. To still achieve a low-tolerance resonance frequency, it is possible to group the constituent parts into multiple bins, each with smaller variations, to then match the parts among corresponding high-precision matching classes. Prof. Weber’s results provide a solution for how to bin the assembly parts optimally, minimizing the maximum absolute deviation from a given criterion (such as the resonance frequency of the electrical oscillator in our example).
Abstract: This paper examines the binning of two types of parts with random characteristics, so that a componentwise monotonic evaluation criterion exhibits a minimum deviation to a given target value over all possible realizations. The optimal matching classes are balanced, in the sense that the maximum error needs to be the same over all matching classes. This condition allows for a complete solution of the minimum-error matching-class design problem in closed form.
Weber, T.A. “Minimum-Error Classes for Matching Parts,” Operations Research Letters, Vol. 49, No. 1 (January 2021), pp. 106—112. [Download]