Physics of Failure (and socks)

Author: Christopher Gray

Some years ago, I spent an intensive period of my career quite obsessed with the topic of Physics of Failure. I was fascinated by the idea that the correct categorisation of a failure mechanism combined with some relatively simple mathematics can be used to predict with reasonable accuracy the time at which a failure will occur. The potential value of such a crystal ball is obvious, but can this really be true? Or is it just “voodoo” (as one of my clients once remarked!).

I too have been faced with moments of skepticism, where my faith in the methodology was shaken by a disappointing result from one or the other analysis. But then one day, whilst organising my sock drawer I realised with despair that almost all of my socks were worn out and needed replacing. It was in this moment that some fundamental truths about failure physics became clear to me. My contemplation can be summarised as follows:

I tend to buy my black work socks in batches, replacing all the old ones with new ones at the same time (an excellent strategy to avoid a situation where I end up with fifty shades of grey!).

I subject my socks to quite a uniform duty cycle. Through a process of random selection each morning, I select a pair, put them on, and then apply many cycles of frictional loading as I walk around in them. Over the course of several months, each sock is likely to see a similar number of load cycles.

The socks are apparently produced through a well controlled process, so their quality and load capacity are very homogenous.

These conditions conspire to ensure that a Physics of Failure approach can be very effectively applied to lifetime projections for any individual sock in my drawer. If I were to carefully record the number of times I wear each sock and document the time at which they reach a point of failure, then I would quite quickly be able to predict the failures of the remaining socks in any particular batch. Assuming the next batch is manufactured in exactly the same way as the last, then I would be able to apply my learnings to the new socks from day one. This would enable me to optimise my supply chain, proactively plan the purchase of new batches and ensure close to 100% availability of wearable socks.

With my faith in material science and physics reaffirmed, I reflected upon the times where the methodology sometimes seemed to have let me down. The problem was that the fortuitous conditions relating to my socks had not always been present in my failure prognosis projects. Uncertainty in the time at which equipment was initially installed, variations in the specification of equipment, inaccuracy in the quantification of the history of applied loads, variations in the quality of the material, transportation or installation, incorrect definition of the critical failure mechanism or complex interactions between multiple failure mechanisms. All of these factors threaten the accuracy of a remaining life prognosis.

As I stared into my sock drawer, I could see that order can indeed be extracted from chaos. In cases where the potential value of failure prognosis is high, the effort required to understand, manage and account for the uncertainties listed above can be justified. We can then move towards accurate prediction of remaining useful life and the implementation of predictive maintenance processes to reduce downtime and costs. Now, where are those darned socks…?