# PROBIT and TIL Analysis

Below are descriptions of PROBIT and TIL analysis. These are ways to evaluate the sensitivity of energetic materials to Friction, Impact, and ESD impetuses. To read more about how to compare whether or not two samples have different sensitivities based on test results please see our discussion on statistical evaluation under the Resources tab.

## PROBIT

Probability of Initiation (PROBIT) Analysis is a statistical method that relates reaction frequency to a statistical probability of initiation; enabling quantitative or numerical evaluation of an energetic material’s sensitivity. With this information, a material’s sensitivity can be directly measured against potential in-process energy levels. This enables the user to design and control processes that maintain adequate safety factors to help protect personnel, equipment, and facilities.

Other methods typically compare the sensitivity of an energetic material relative to a reference substance (e.g. dry PETN or RDX). Such qualitative comparisons cannot predict the behavior of the material to stimulus energies encountered in processing operations, handling operations, or maintenance activities.

PROBIT Analysis is an invaluable tool that provides simple and direct analysis of a material’s sensitivity. Further, PROBIT analysis may be used in conjunction with an analysis of the In-Process Potential (IPP) to evaluate the probability of initiation and margins of safety due to potential stimulus conditions from (1) processing operations, (2) normal handling operations, and (3) inadvertent dropping of tools or equipment.

The product of the PROBIT analysis is a curve and corresponding mathematical equation that defines the probability of initiation (x-axis) as a function of calculated stimulus energy (y-axis), as shown below for Modified Bureau of Mines Impact data (shown as circles):

Sample PROBIT Curve for Impact Data

The curve represents the 95% confidence interval (95% confident that the curve represents the maximum probability of initiation as a function of stimulus energy) while the straight line represents the 50% line (50% of the test data is above the line and 50% is below the line). The test data appears as small circles on the plot.

## TIL Analysis

The Threshold Initiation Level (TIL) represents the minimum amount of energy required to initiate a sample. The TIL is first determined through standardized impact, friction, and/or ESD testing. Because testing is typically limited to discrete energy levels, the TIL resulting from laboratory testing is usually an approximate value. PROBIT analysis further refines the TIL to a calculated statistical value. Statistically, the TIL represents the energy level which has a 3.4% probability of initiation for the given test material.

When calculating the TIL through testing, the tests are performed at a series of input energy levels. The test begins at a predetermined, low stimulus level. If the test produces two consecutive “no-go” reactions, the test is continued at the next higher standard level. If the event results in a “go” reaction, the test is continued at the next lower standard level. After the first “go” reaction occurs, the test continues at each subsequently lower energy level until 20 “no-go” responses are observed at an energy level and at least one “go” response was observed at the next higher standard input level (out of 20 trials if necessary). An example test series is shown below.

Once the TIL for a substance has been determined, a PROBIT analysis of the material can be conducted. At least 10 trials are performed at each of four different energy levels above the TIL (a 20 trial PROBIT is preferred for higher accuracy). The data received from these trials are statistically analyzed. The resulting PROBIT curve represents the probability of initiation as a function of the input stimulus. The results are used to calculate margins of safety and the probability of initiation of the material for a given stimulus. The curve obtained from the PROBIT is a more accurate representation of the reactivity of the material than obtainable from the TIL alone, and can be extrapolated to regions of low reaction probability.

## TIL and PROBIT Example

The following example is a hypothetical test series for determining a TIL and collecting PROBIT data. The steps detailed below explain how this hypothetical case proceeded.
Sample PROBIT/TIL Test Series Sheet

The first objective is to establish a TIL:

1. Select a level at which no reaction is anticipated and perform two trials (in this case, energy level 600 was selected).
2. Since no reactions were observed in two trials, the next higher energy level (700) was selected.
3. Since no reactions were observed in two trials, testing continued at the next higher energy level (800).
4. Since a reaction was observed at energy level 800, testing resumed at the next lower energy level (700) and continued with trial #3 since trials #1 and 2 were performed in step 2.
5. Since a reaction was observed at energy level 700 before 20 trials were completed, testing resumed at energy level 600 and 20 trials were completed without a reaction.

In Step 5, sufficient additional trials were obtained at energy level 600 to combine with the trials in step 1 to get 20 trials with no reaction, establishing the TIL value at energy level 600.

The second objective is to establish the PROBIT data by completing 10 trials at a minimum of four energy levels above the TIL value.

1. Complete testing of 10 trials at one energy level higher than the TIL, in this case, start with trial # 7 at energy level 700.
2. Complete testing of 10 trials at energy level 800 (two levels above the TIL).
3. Complete testing of 10 trials at energy level 900 (three levels above the TIL).
4. Complete testing of 10 trials at energy level 1000 (four levels above the TIL).

This completes the testing required for the basic PROBIT Series. A 20 trial PROBIT would increase the confidence in the test data and may slightly change the calculated statistical data. For this type of series, 20 trials at each energy level would be conducted.

It should be noted that a TIL level as established by 20 no-go’s at a given energy input level will not necessarily be the same as a TIL calculated by a PROBIT analysis. The TIL calculated by the PROBIT analysis is the 3.4% probability point on the PROBIT line that is fit to all test data in the series. The TIL value from the 20 no-go test series is one of the test points used to establish the PROBIT line, and thus is not a precise measure of the 3.4% probability point, but is merely the lowest energy level tested that gives a 20 no-go trial series. The accuracy of each type of test is directly related to the number of tests and the range of values over which the data are taken.

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### DOT/DOD Resource

##### Troy Gardner, PE, CSP
###### Chemical Engineer
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