On Woolhouse's Cotton-Spinning Problem

TL;DR

This paper revisits Woolhouse's 1864 cotton-spinning problem, using process modeling and model checking to accurately estimate the piecer's expected walking distance, correcting previous overestimations.

Contribution

It introduces a formal modeling approach and quantitative analysis to refine Woolhouse's original problem, providing more accurate estimates.

Findings

Woolhouse's original model overestimated walking distance

Process modeling enables precise analysis of the problem

Quantitative model checking corrects previous estimates

Abstract

In 1864 W.S.B. Woolhouse formulated the Cotton-Spinning problem. This problem boils down to the following. A piecer works at a spinning mule and walks back and forth to repair broken threads. The question is how far the piecer is expected to walk when the threads break at random. This problem can neatly be solved using process modelling and quantitative model checking, showing that Woolhouse's model led to an overestimation of the walking distance.