This function calculates the overall probability of a risk event 'R' occurring
based on the probabilities of multiple root causes and their associated conditional probabilities.
Usage
risk_prob(cause_probs, risks_given_causes, risks_given_not_causes)
Arguments
- cause_probs
A vector of probabilities for each root cause 'C_i'.
- risks_given_causes
A vector of conditional probabilities of the risk event 'R' given each cause 'C_i'.
- risks_given_not_causes
A vector of conditional probabilities of the risk event 'R' given not each cause 'C_i'.
Value
The function returns a numeric value for the probability of risk event 'R'.
Details
Each cause contributes a marginal probability
\(P(R \mid C_i) P(C_i) + P(R \mid \bar{C}_i) P(\bar{C}_i)\) via the law of
total probability. Independent causes are combined with a noisy-OR — the
probability that the risk event is triggered by at least one cause — so the
result always lies in \([0, 1]\) and reduces to the single-cause marginal
when there is one cause.
References
Damnjanovic, Ivan, and Kenneth Reinschmidt. Data analytics for engineering and
construction project risk management. No. 172534. Cham, Switzerland: Springer, 2020.
Examples
cause_probs <- c(0.3, 0.2)
risks_given_causes <- c(0.8, 0.6)
risks_given_not_causes <- c(0.2, 0.4)
risk_prob_value <- risk_prob(cause_probs, risks_given_causes, risks_given_not_causes)
print(risk_prob_value)
#> [1] 0.6528
