Stop using limiting stimuli as a measure of sensitivities of energetic materials

TL;DR

The paper argues that the UN-style limiting-stimulus approach to explosive sensitivity is ill-defined and hides uncertainty because the stimulus depends on arbitrary test parameters. It advocates quantile-based sensitivity measures and evaluates three alternatives—up-and-down with parametric estimation, biased coin design (BCD), and Robbins–Monro–Joseph (RMJ)—through simulations and a PETN data example. Across analyses, BCD and RMJ provide better point estimates and credible confidence intervals, with Fieller-based up-and-down performing well under near-normal conditions. This work offers a practical path to robust, interpretable sensitivity assessment with explicit uncertainty quantification, improving safety decisions and cross-lab comparability.

Abstract

Accurately estimating the sensitivity of explosive materials is a potentially life-saving task which requires standardised protocols across nations. One of the most widely applied procedures worldwide is the so-called '1-In-6' test from the United Nations (UN) Manual of Tests in Criteria, which estimates a 'limiting stimulus' for a material. In this paper we demonstrate that, despite their popularity, limiting stimuli are not a well-defined notion of sensitivity and do not provide reliable information about a material's susceptibility to ignition. In particular, they do not permit construction of confidence intervals to quantify estimation uncertainty. We show that continued reliance on limiting stimuli through the 1-In-6 test has caused needless confusion in energetic materials research, both in theoretical studies and practical safety applications. To remedy this problem, we consider three well-founded alternative approaches to sensitivity testing to replace limiting stimulus estimation. We compare their performance in an extensive simulation study and apply the best-performing approach to real data, estimating the friction sensitivity of pentaerythritol tetranitrate (PETN).

Figures (10)

• Figure 1: Kernel density estimates $\log W$ for $n=30, 100$ and $d=0.1, 0.2$, based on $S=100{,}000$ datasets. The solid curve shows the exact distribution of the logarithm of a $\chi^2_1$ random variable.
• Figure 2: Limiting frictional stimuli (log scale) based on $S=100,000$ simulations using two different interpretations of the loads available for test F1 from the UN manual. The dashed vertical line gives the manual's threshold for sensitive versus insensitive material.
• Figure 3: Limiting frictional stimuli (log scale) based on $S=100,000$ simulations using two different interpretations of the loads available for test F1 from the UN manual, using type II tests rather than type I. The dashed vertical line gives the manual's threshold for sensitive versus insensitive material.
• Figure 4: Mean squared errors (MSEs) from the simulation study after $n=30$ trials.
• Figure 5: Average width of confidence intervals from the simulation study after $n=30$ trials.