Extreme value theory and the St. Petersburg paradox in the failure statistics of wires

TL;DR

This paper reinterprets the failure statistics of wires, traditionally explained by extreme value theory, using the St. Petersburg paradox, and discusses the influence of rate-dependent effects on fracture stress.

Contribution

It demonstrates that wire failure data can be more accurately explained by extreme value statistics rather than the St. Petersburg paradox, clarifying the underlying probabilistic mechanisms.

Findings

Extreme value statistics better explain wire failure data.

Rate-dependent effects influence fracture stress.

Reinterpretation of previous results in probabilistic failure models.

Abstract

The fracture stress of materials typically depends on the sample size and is traditionally explained in terms of extreme value statistics. A recent work reported results on the carrying capacity of long polyamide and polyester wires and interpret the results in terms of a probabilistic argument known as the St. Petersburg paradox. Here, we show that the same results can be better explained in terms of extreme value statistics. We also discuss the relevance of rate dependent effects.