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E Concepts of Probability Analysis
damaged,” “temperature measurement wrong,” “heating steam fed,” and “no ice.”
This can be calculated using Eq. 7.3 defining AND connections and Eq. 7.4 defining
OR connections:
P 3 = (P 4 + P 5 ) × (P 6 + P 7 )
(E.17)
Important to note within this fault tree is that both the events “alarm damaged”
(P 4 ) and “no ice” (P 7 ) are dependent on the electricity supply. The probability of
having no electricity (P no electricity ) can therefore be considered in the calculation of
P 3 :
P 3 = P no electricity + (P 5 × P 6 ) × (1 − P no electricity )
(E.18)
Without electricity (P no electricity = 1), both the safeguards of a temperature alarm
and ice cooling system are simultaneously lost. This results in the temperature
becoming too high (P 3 ) and therefore also in the occurrence of the top event
(P Top ) since P 1 , P 2 , and P 3 are all OR connected. Without an independent backup
electricity supply provided for each of these safeguards, this system is at risk,
especially in regions that do not have a reliable electricity supply. Be sure to
carefully check the independence of safeguards. They are of no use if they all can
fail due to a single underlying issue.
Through the use of Eqs. E.16–E.18, the probability data of all the events can be
combined to obtain the probability of occurrence of the top event. As mentioned in
Sect. 7.6.2.2, quantitative probability data can be obtained from historical records or
reliability analysis.
To consider the impact of mitigative safeguards in this example, an event tree can
be used. For illustrative purposes, it is assumed here that the presence of mitigative
safeguards does lead to different consequence scenarios.
Figure E.5 shows the event tree starting from the top event (decomposition
of cyanuric chloride) and the failures and successes of the mitigative safeguards
leading to different consequences (i = 1 to i = 5).
The probability of the worst-case scenario is given by P (i = 5), which represents
the scenario in which all mitigative safeguards fail. Assuming independent events,
and using Eq. 7.5, this probability can be expressed as:
P (i = 5) = P Top × (1 − P I ) × (1 − P II ) × (1 − P III ) × (1 − P IV )
= P Top ×
I V
i=I
(1 − P i )
(E.19)
To calculate the probability of the worst-case scenario (i = 5) in Eq. E.19, the
probability of the top event as well as the probability of success of all the existing
safeguards (P I to P IV ) need to be known. This example yet again highlights the
E Concepts of Probability Analysis
damaged,” “temperature measurement wrong,” “heating steam fed,” and “no ice.”
This can be calculated using Eq. 7.3 defining AND connections and Eq. 7.4 defining
OR connections:
P 3 = (P 4 + P 5 ) × (P 6 + P 7 )
(E.17)
Important to note within this fault tree is that both the events “alarm damaged”
(P 4 ) and “no ice” (P 7 ) are dependent on the electricity supply. The probability of
having no electricity (P no electricity ) can therefore be considered in the calculation of
P 3 :
P 3 = P no electricity + (P 5 × P 6 ) × (1 − P no electricity )
(E.18)
Without electricity (P no electricity = 1), both the safeguards of a temperature alarm
and ice cooling system are simultaneously lost. This results in the temperature
becoming too high (P 3 ) and therefore also in the occurrence of the top event
(P Top ) since P 1 , P 2 , and P 3 are all OR connected. Without an independent backup
electricity supply provided for each of these safeguards, this system is at risk,
especially in regions that do not have a reliable electricity supply. Be sure to
carefully check the independence of safeguards. They are of no use if they all can
fail due to a single underlying issue.
Through the use of Eqs. E.16–E.18, the probability data of all the events can be
combined to obtain the probability of occurrence of the top event. As mentioned in
Sect. 7.6.2.2, quantitative probability data can be obtained from historical records or
reliability analysis.
To consider the impact of mitigative safeguards in this example, an event tree can
be used. For illustrative purposes, it is assumed here that the presence of mitigative
safeguards does lead to different consequence scenarios.
Figure E.5 shows the event tree starting from the top event (decomposition
of cyanuric chloride) and the failures and successes of the mitigative safeguards
leading to different consequences (i = 1 to i = 5).
The probability of the worst-case scenario is given by P (i = 5), which represents
the scenario in which all mitigative safeguards fail. Assuming independent events,
and using Eq. 7.5, this probability can be expressed as:
P (i = 5) = P Top × (1 − P I ) × (1 − P II ) × (1 − P III ) × (1 − P IV )
= P Top ×
I V
i=I
(1 − P i )
(E.19)
To calculate the probability of the worst-case scenario (i = 5) in Eq. E.19, the
probability of the top event as well as the probability of success of all the existing
safeguards (P I to P IV ) need to be known. This example yet again highlights the