E
Concepts of Probability Analysis
E.1
Probability
In the context of process risk assessment introduced in Chap. 7, probabilities are
calculated for system failures and are usually expressed in the form of (1) frequency,
as the number of events or incidents divided by the exposure period (normally per
year) (Eq. E.1); (2) relative frequency, given as a number between 0 and 1, with
0 indicating impossibility and 1 indicating certainty (Eq. E.2); or (3) a conditional
probability that an event occurs, given the occurrence of a precursor event (Bayes’
theorem) (Eq. E.3):
F (A) =
n A
t
(E.1)
• F (A): frequency of occurrence of event A per unit of time
• n A : number of outcomes of event A
• t: time period
P (A) = lim
n→∞
n A
n
(E.2)
• P (A): probability of event A (relative frequency)
• n A : number of events A (e.g., number of failures)
• n: number of all events (e.g., total number of operations)
P (A|B) = P (B|A) × P (A)/P (B)
(E.3)
• P (A|B): the probability of event A given the occurrence of event B
• P (B|A): the probability of event B given the occurrence of event A
• P (A): the probability of event A
• P (B): the probability of event B
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
K. Hungerbühler et al., Chemical Products and Processes,
https://doi.org/10.1007/978-3-030-62422-4
287