Sensitivity testing templates
This webpage contains templates in Microsoft Excel for impact and friction sensitivity testing. The Excel files contain no macros or Visual Basic for Applications (VBA) code - all computations and algorithms are implemented using standard Excel functions and formulas.
Impact sensitivity
When using the template, the data should be entered in the rows 17-37 in the notation of Dixon and Mood (1948), with "x" denoting "go" and "o" denoting "no-go". Note that it is possible to enter fewer than 50 trials, even though the template allows for 50. The step size of the up-and-down test design can be changed in cell H12, and the lowest log height in cell B17.
Upon entering the data, cell Z5 indicates whether the maximum likelihood estimate of a probit model on a log scale exists. If it does, cells U8 and U9 give the estimated model parameters. Cells Z8 and Z9 do the same, but with a different parametrisation, see Christensen et al. (2024) for details.
The estimate for H50 (i.e. the height at which there is a 50% probability of an explosion occurring) is given in cell U12, along with a confidence interval in cells AD12 and AD13. Note that a confidence interval for mu (i.e. log H50) is also given in cells AD8 and AD9. The confidence level of the interval can be adjusted in cell H13 (the default is 95%).
Friction sensitivity
When using the template, the data should be entered in the rows 17-37 in the notation of Dixon and Mood (1948), with "x" denoting "go" and "o" denoting "no-go". Note that it is possible to enter fewer than 50 trials, even though the template allows for 50. The loads are entered in column C. In column B, it is also possible to specify the weights used and their positions on the BAM friction machine load arm.
Upon entering the data, cell Z5 indicates whether the maximum likelihood estimate of a probit model on a log scale exists. If it does, cells U8 and U9 give the estimated model parameters. Cells Z8 and Z9 do the same, but with a different parametrisation, see Christensen et al. (2024) for details.
The estimate for F50 (i.e. the force for which there is a 50% probability of an explosion occurring) is given in cell U12, along with a confidence interval in cells AD12 and AD13. Note that a confidence interval for mu (i.e. log F50) is also given in cells AD8 and AD9. The confidence level of the interval can be adjusted in cell H11 (the default is 95%).
References
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W. J. Dixon and A. M. Mood. A method for obtaining and analyzing sensitivity data. Journal of the American Statistical Association 43:109—126, 1948.
- D. Christensen, G. P. Novik and E. Unneberg. Estimating sensitivity with the Bruceton method: Setting the record straight. Propellants, Explosives, Pyrotechnics 49, 2024. DOI: 10.1002/prep.202400022