Regulatory testing for safety: The mathematics of broad-based results

Timothy Paul Hutchinson, R. W. G. Anderson, D. J. Searson


Testing of the safety of manufactured products is typically conducted under a specified set of conditions. For example, when projecting an instrumented headform at the front of a car to assess the pedestrian safety of that model of car, the speed of the headform is specified. But surely, if they were asked, the public and policymakers would say that the result at one speed is a rather artificial measure, and they instead wish to know the average level of safety across real-world impact scenarios. One possible solution is to directly test across the range of conditions and combinations of conditions. However, manufacturers typically want to economise by conducting fewer tests. This article considers how to determine a product's saftey for a range of conditions, while also being economical with the testing. What is proposed has three steps. The first is to generalise the quantity observed in test conditions to what would be observed under different conditions. This is likely to involve a theory and a formula. For example, in a headform impact test the quantity observed might be HIC (the Head Injury Criterion), the condition that varies might be impact speed, and a formula might be available for the dependence of HIC on speed. The second is to convert the test quantity to something that is meaningfully averaged. This might be the dollar cost associated with a particular level of HIC, or perhaps the probability of death. The third is to obtain the average, by integration over the condition that varies from crash to crash (such as impact speed). In principle, this procedure is quite general and applicable to many other forms of testing. Good information is required for the three steps, but this is inherent in aiming for a broad-based result, rather than due to the method.

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impact testing; head injury; cushioning; test generalisation

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