diff --git a/book/pd/risk-evaluation/decision.md b/book/pd/risk-evaluation/decision.md index 77bd7fe57f1c85adb4a4426360ac9a41f7cc8abb..3ac23e99aa97912cddc36a1bc7dac554c78a267f 100644 --- a/book/pd/risk-evaluation/decision.md +++ b/book/pd/risk-evaluation/decision.md @@ -9,7 +9,7 @@ Decision analysis, or decision-making under uncertain conditions is part of ever ## Introduction -Making a decision is in fact choosing from alternatives. The decision theory is based on the classic “Homo Economicus†model assumes that the decision-maker: +Making a decision is in fact choosing from alternatives. The decision theory is based on the classic “Homo Economicus†model. It assumes that the decision-maker: - has complete information about the decision situation; - knows all the alternatives; diff --git a/book/pd/risk-evaluation/safety-standards.md b/book/pd/risk-evaluation/safety-standards.md index 6cec0aff575d2a160177aeab28c6058f91070164..4d8c8e3dcaaabaefffe31c13aab76d248c0ed644 100644 --- a/book/pd/risk-evaluation/safety-standards.md +++ b/book/pd/risk-evaluation/safety-standards.md @@ -206,7 +206,7 @@ Accident statistics reveal that the extent to which participation in the activit :name: accident_statistics * - Prob. of death(per year) - - Exmaple/application + - Example/application - $\beta$ - Voluntariness - Benefit @@ -339,7 +339,7 @@ $$ C = \left( \frac{\beta \cdot 100}{k \sqrt{N_a}} \right)^2 = \left( \frac{0.1 \cdot 1000}{3 \sqrt{100}} \right)^2 = 0.11 $$ -The limit line for societal risk becomes $1 - F_N(n) \leq 0.11/n^2$. Both the individual and societal risk criteria are plotted in below. As a third criterion the economic optimization can be added. The optimal or acceptable probability of failure depends on the damage and investment costs. A relationship with the graph below can be established by assuming that the number of fatalities is related to the economic damages. A dike ring with many inhabitants and potential fatalities will generally also represent a large economic value. For the sake of the example we assume that every fatality corresponds to an economic damage of €$5 \cdot 10^7$ (note: this is not equal to the value of a human life). To calculate the economic optimum for the example we assume arbitrary values of $r=0.025$ and €$5 \cdot 10^6$ $B=0.33$. {numref}`combined_risk_criteria` below shows the combination for the three criteria. +The limit line for societal risk becomes $1 - F_N(n) \leq 0.11/n^2$. Both the individual and societal risk criteria are plotted below. As a third criterion the economic optimization can be added. The optimal or acceptable probability of failure depends on the damage and investment costs. A relationship with the graph below can be established by assuming that the number of fatalities is related to the economic damages. A dike ring with many inhabitants and potential fatalities will generally also represent a large economic value. For the sake of the example we assume that every fatality corresponds to an economic damage of €$5 \cdot 10^7$ (note: this is not equal to the value of a human life). To calculate the economic optimum for the example we assume arbitrary values of $r=0.025$ and €$5 \cdot 10^6$ $B=0.33$. {numref}`combined_risk_criteria` below shows the combination for the three criteria. For a given number of fatalities in a dike ring the acceptable failure probability according to the three criteria can be derived. The individual risk criterion is independent on the number of fatalities. The economic criterion shows a linear relation between the failure probability and damage or number of fatalities. The societal criterion is risk averse so shows a decreasing quadratic relationship between acceptable failure probability and consequences.