Part 2: The Beginner's Guide To No-Fire and ALL-Fire Sensitivity

Determining Response Levels

There is currently no single methodology capable of exactly determining an initiator's no-fire or all-fire response. As such, determining the no-fire and all-fire levels of the device requires destructive testing, which is typically costly and time-consuming. Therefore, it is important to determine these levels in the most efficient way possible. Various test methods, such as Prohibit Analysis, have been created and applied in the past to statistically determine a test specimen's safety and reliability characteristics. Today, the most commonly used methods applicable to EEDs are: the Bruceton, Langlie and Neyer sensitivity tests. In general, all the test methods operate similarly; a probability distribution function is assumed, e.g. normal distribution, an initial stimulus is tested, the response is documented and influences the stimulus level of the following test(s) until a convergence occurs between the input stimulus and the device's ignition threshold, as shown below in Figure 3.

The results of all the tests are analyzed to determine the mean, standard deviation, reliability, and confidence level of the response level, effectively determining the no-fire and/or all-fire characteristics. While there are some similarities between the test methods, each has its advantages and disadvantages.

Sensitivity Test Methods Explained

The Probit (probability unit) method, conceptualized in 1934 by Chester Bliss and further expanded by David Finney in 1952, is a type of regression model used to analyze binomial (go/no-go, head or tails, all or nothing) response variables. It transforms the sigmoid (S-shape) input-response curve to a straight line that can then be analyzed by regression either through least squares or maximum likelihood methods. Probit analysis can be conducted by one of three techniques; using tables to estimate the probits, regression coefficient, and confidence intervals, or having a statistical package such as SPSS, SAS or R do it all for you. Although this is the simplest sensitivity test to perform and provides a straightforward method to analyze the data, it generally requires many more samples than other tests because it does not concentrate the testing where the most information can be obtained. In addition, for the method to work somewhat efficiently, it requires that both mean and standard deviation of the population be well known in advance so that the testing can be conducted in the range of stimulus levels which allow convergence.

The Bruceton (up-and-down) method, published in 1948 by Dixon and Mood, relies on simple calculations which can be done without the aid of a computer, and are based on an initial guess close to the population mean and a constant step size approximately equal to the standard deviation. It is generally more efficient than the Probit method since it concentrates the testing close to the population mean. However, the Bruceton method is very sensitive to the selected step size. If the step size is much bigger than the standard deviation, then none of the test will concentrate near the mean. On the other hand, if the step size is much smaller than the standard deviation and the initial guess is not near the true mean of the population, this method will not quickly converge to a final value, which can be costly due to extended testing.

The Langlie (one-shot) method, published in 1962 by Langlie, efficiently provides accurate values for mean and standard deviation, without requiring that an initial guess be selected close to the population standard deviation. The Langlie approach is to bound the estimated mean by selecting an upper and lower limit. However, convergence of the method requires the certainty that none of the test samples will initiate at the lower limit, while ensuring that all the test samples will initiate at the upper limit. Once the upper and lower limits are chosen, the first stimulus level is chosen halfway between the limits interval. If the test interval is inappropriately chosen, then the stress levels will tend to converge towards either the lower or the upper limit. In such a case, convergence toward the upper limit would be indicative of an incorrect stimulus selection, and little will be learned, while convergence toward the upper limit can be shown statistically acceptable by use of the likelihood ratio test method. The main problem with the Langlie method is that it concentrates the test levels too close to the mean, which results in the inefficient determination of the standard deviation of the population.

The Neyer D-Optimal method, published in 1994 by Neyer, is the most efficient of all methods requiring the smallest test sample size and only three parameters; lower and upper limits and an estimate of the standard deviation. It was designed to extract the maximum amount of statistical information from the test sample. Unlike previous methods which only require paper and pencil, the Neyer D-Optimal test requires detailed computer calculations to determine the test levels. In addition, the test method uses the results of all the previous test results to compute the next test level. The test method uses a three-step approach to establish the mean and standard deviation. First, the test algorithm "closes in" on the region of interest to within a few standard deviations of the mean. Second, the test algorithm determines the unique estimates of the parameters efficiently. Finally, the test continuously refines the estimates once convergence has been estables.

To summarize, the efficiency of the Bruceton method is strongly dependents on the choice of step size. The efficiency of the Langlie method is somewhat dependent on the spacing between the upper and lower test levels. The Neyer D-Optimal test is essentially independent of the choice of parameters.

At PacSci EMC, we use the Neyer D-Optimal sensitivity test method to determine EED's no-fire and all-fire characteristics due to its efficiency, accuracy and proven reliability.

Safety & Reliability at PacSci EMC

PacSci EMC's highest priority is the safety and reliability of our products. Having clear and accurately defined all-fire and no-fire characteristics guarantees that our customers can safely operate our products as intended. These well-defined parameters also ensure our initiators and other EED's will work reliably when required. Whether the application is in Space, Defense, Energy, or any other field, PacSci EMC guarantees that our product will work with the highest safety and reliability, on command, when commanded.

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