An improved statistical analysis of 80 sensitivity datasets

Dennis Christensen1, Antoine van der Heijden2, Geir Petter Novik1

1 Norwegian Defence Research Establishment (FFI), Kjeller, Norway
2 Netherlands Organisation for Applied Scientific Research (TNO), Den Haag, Netherlands

Abstract. This paper addresses the statistical estimation of sensitivities of energetic materials to friction, impact, and shock. The NATO Standardisation Agreements (STANAGs) for sensitivity testing still rely on a pen-and-paper approximation of maximum likelihood estimation from 1948. Although useful for its time, this approximation is today unnecessary as maximum likelihood estimation is easily implemented in virtually any general-purpose programming language and spreadsheet software. In this paper we show how the use of the approximation manifests in practice by analysing 80 datasets for impact and friction sensitivity of multiple energetic materials. For a substantial minority of the datasets, the use of the approximation is not valid, as a certain simplification of the likelihood function cannot be applied. Despite the STANAGs' requirement to discard such datasets, we find that the maximum likelihood estimates exist and provide perfectly valid results for all of them. For the remaining datasets, where the use of the approximation is valid, we find that it performs poorly when constructing confidence intervals. For extreme quantiles, we obtain a relative error as high as 20%. In conclusion, our paper serves as further evidence that the 1948 approximation should be abolished and replaced with direct maximum likelihood estimation.

Keywords: sensitivity testing;statistics;Bruceton method


ID: 36, Contact: Dennis Christensen, dennis.christensen@ffi.no NTREM 2025