PROBIT Calculator

Probability of death
Our probability of death calculator, based on the Probit formula, allows you to obtain accurate estimates in a matter of seconds, thus avoiding the effort and possibility of errors associated with manual calculations. These results can be useful for decision making in workshops such as What if or HAZOP analysis that allow you to explore different scenarios and quickly assess the possible risks of death. These tools give you the flexibility and agility to make informed safety decisions quickly and efficiently.

Probit Equation
The probit is a function for calculating the probability of death due to exposure to toxic substances, overpressures and exposure to radiant heat. The probit equations are based on experimental dose-response data and take the following form.

Where:

    • Pr = Probit
    • C = represents the magnitude of the hazard
    • t = time of explosion
    • a, b, and n = constants

The product (Cⁿ. t) is often referred to as the dose factor. According to the Probit equations, all combinations of concentration (C) and time (t) that result in dose factors also result in equal values for the Probit (Pr) thus yielding equal expected mortality rates for the exposed population.

In the case of the probit function for toxicity C is the concentration of the toxic vapor in the inhaled air measured in ppm or mg/m³ , the exposure time t is in minutes, and the constants a, b and n are taken from the book “Reference Manual Beve Risk Assessment version 3.2, National Institute of Public Health and the Environment (RIVM) Centre for External Safety, 2009”.

Substance a
(C in mg/m³)
a
 (C in ppmv)
b n
Acrolein -4,1 -3,22 1 1
Acrylonitrile -8,6 -7,52 1 1,3
Ammonia -15,6 -16,21 1 2
Arsine -11,2 -8,78 1,61 1,24
Bromine -12,4 -8,54 1 2
Carbon monoxide -7,4 -7,21 1 1
Chlorine -6,35 -4,81 0,5 2,75
Ethylene oxide -6,8 -6,16 1 1
Ethyleneimine -11,6 -10,36 1,77 1,13
Hydrogen chloride -37,3 -35,62 3,69 1
Hydrogen cyanide -9,8 -9,43 1 2,4
Hydrogen fluoride -8,4 -8,62 1 1,5
Hydrogen sulphide -11,5 -10,76 1 1,9
Methyl bromide -7,3 -5,75 1 1,1
Methylisocyanate -1,2 -0,57 1 0,7
Methylmercaptan -17,8 -16,33 2,05 0,98
Nitrogen dioxide -18,6 -16,06 1 3,7
Phosgene -10,6 -7,69 2 1
Phosphine -6,8 -6,03 1 2
Sulur dioxide -19,2 -16,76 1 2,4
Tetraethyl Lead -9,8 -4,53 1 2

Table 1 . Probit constants for toxic substances

Note : The constant a of the Reference Manual Bevi Risk Assessment is similar to the values shown in the “Yellow book Methods for the calculation of Physical Effects, Third Edition, 2005” and the book “Less’ loss prevention in the Process Industries, Third edition, Sam Mannan, 2005”.
In the case of the probit function for radiation C is the thermal radiation given W/m², the exposure time t is in seconds and the constants a, b and n are taken from “Purple book CPR 18E – Guidelines for quantitative risk assessment, 2005” from equation 5.4, shown in the calculator as TNO model.

For the CCPs model we took the constants from the book “Guidelines for Chemical Process Quantitative Risk Analysis, Second Edition, 2000, CCPS” in equation 2.37, shown in the calculator as CCPS model.

Calculation of probability of death
Based on the probit equation, the probability of death calculation can be performed, which is based on the following integral to be calculated between minus infinity and the value generated from the probit equation denoted by Pr.

The probability of death equation was taken from the book “Chemical process safety – fundamentals with applications, second edition, Daniel a. Crowl / Joseph F. Louvar, 2002”

 

How to use

To use the toxicity calculator, the substance generating the toxicity, the amount of ppm and the exposure time in minutes must be chosen.
Although the constants per product were indicated in the table for mg/m³, the conversion was made internally in the calculator to ppm.
For the calculation of probability by radiation, the thermal radiation in kW/m², the time in seconds and the type of model must be indicated.

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PROBIT Calculator