From 7fb3ef06614b0dbf9e5347d36d5f96a961965712 Mon Sep 17 00:00:00 2001
From: Isabel Slingerland <I.C.Slingerland-1@student.tudelft.nl>
Date: Thu, 9 Jan 2025 19:38:33 +0100
Subject: [PATCH] fixed some typos

---
 book/pd/risk-analysis/definition.md            | 1 +
 book/pd/risk-analysis/steps.md                 | 6 +++---
 book/pd/risk-evaluation/decision.md            | 8 +++++---
 book/pd/risk-evaluation/econ-optimization.md   | 4 ++--
 book/pd/risk-evaluation/example-dike-height.md | 4 ++--
 book/pd/risk-evaluation/safety-standards.md    | 6 +++---
 6 files changed, 16 insertions(+), 13 deletions(-)

diff --git a/book/pd/risk-analysis/definition.md b/book/pd/risk-analysis/definition.md
index 44318d2b..84adca85 100644
--- a/book/pd/risk-analysis/definition.md
+++ b/book/pd/risk-analysis/definition.md
@@ -90,6 +90,7 @@ Substantial research has also focused on factors that determine the perception o
 :::{list-table} Formal definitions of risk used in social sciences {cite:p}`vlek1996`
 :header-rows: 1
 :name: risk_definitions
+:widths: 10 90
 
 * - No.
   - Definition
diff --git a/book/pd/risk-analysis/steps.md b/book/pd/risk-analysis/steps.md
index 75545349..e654c70a 100644
--- a/book/pd/risk-analysis/steps.md
+++ b/book/pd/risk-analysis/steps.md
@@ -53,7 +53,7 @@ The probabilities and consequences of the undesired events identified in step 2
 
 In simple cases the probability can be computed directly, but generally the undesired event must broken down into multiple steps or processes to facilitate the computation of probability, which are then recombined using integration or the total probability theorem. Such an approach results in systems of systems, each of which is composed of individual *components* (or elements), each of which is typically evaluated using the limit state concepts defined above. Often this the probability of a limit state being exceeded is referred to as the probability of failure, which of course reflects the component, not necessarily the system. Techniques for computing the probability of failure are covered in the {ref}`rel_comp` and {ref}`rel_sys` Chapters.
 
-Whereas the most critical aspect of the previous step is identifying the most important failure modes, in the quantitative analysis it is critical to precisely define the quantity of interest, as ambiguity can lead to misunderstandings and incorrect assessment of risk. Often such ambiguities have a direct relationship with the conditional terms used inthe probability computations, which imply specific statements about dependence (or independence). Consider the previous example of river level exceeding the dike height $P(h_w>h_{dike})$: the probability can be significantly different if a design lifetime of one year or fifty years is considered. In addition, the time of year may also play a role as different types of floods may occur. If the seasonal probability of flooding is binary and mutually exclusive with wet and dry season each lasting 6 months of the year, the following expression holds (all values computed an a *per year* basis):
+Whereas the most critical aspect of the previous step is identifying the most important failure modes, in the quantitative analysis it is critical to precisely define the quantity of interest, as ambiguity can lead to misunderstandings and incorrect assessment of risk. Often such ambiguities have a direct relationship with the conditional terms used in the probability computations, which imply specific statements about dependence (or independence). Consider the previous example of river level exceeding the dike height $P(h_w>h_{dike})$: the probability can be significantly different if a design lifetime of one year or fifty years is considered. In addition, the time of year may also play a role as different types of floods may occur. If the seasonal probability of flooding is binary and mutually exclusive with wet and dry season each lasting 6 months of the year, the following expression holds (all values computed an a *per year* basis):
 
 $$
 P(h_w>h_{dike}) = 0.5 \cdot P(h_w>h_{dike}|\mathrm{wet}) + 0.5 \cdot P(h_w>h_{dike}|\mathrm{dry})
@@ -63,7 +63,7 @@ Thus, if the risk analysis were only focusing on floods during the wet season, t
 
 ### Consequences
 
-After failure has been defined, consequences of the events are quantified. First, physical effects associated with an undesired event are considered, sucha s heat and/or smoke from a fire, or inflow of water due to dike breach. Depending on the exposure of people or objects to the physical effects, damages, life loss or other impacts may occur. As an example, a specific consequence, $D$, of dike failure during a flood is considered as a sequence of three discrete events:
+After failure has been defined, consequences of the events are quantified. First, physical effects associated with an undesired event are considered, such as heat and/or smoke from a fire, or inflow of water due to dike breach. Depending on the exposure of people or objects to the physical effects, damages, life loss or other impacts may occur. As an example, a specific consequence, $D$, of dike failure during a flood is considered as a sequence of three discrete events:
 
 - The probability that a dike fails, $P(E_{1})$
 - The conditional probability that water flows into the polder given a dike breach $P(E_{2}|E_{1})$
@@ -136,7 +136,7 @@ In the risk evaluation phase a decision is made whether the risk is acceptable o
 
 **Cost Benefit Analysis**: costs and benefits of risk reduction measures are considered.  When a large number of design choices are possible, an **economic optimization** can be applied to select an optimal system design, based on the costs and benefits of risk reduction.
 
-**Safety Standards**: risk is compared with predetermined safety standards to directly determin acceptability. Such standards are typically imposed by government organizations or standards of practice and often focus on loss of life as the primary risk metric.
+**Safety Standards**: risk is compared with predetermined safety standards to directly determine acceptability. Such standards are typically imposed by government organizations or standards of practice and often focus on loss of life as the primary risk metric.
 
 Given the nature of the key question "how safe is safe enough?", several political, psychological and social processes play a role in the evaluation of risk---in other words: risk evaluation is not purely a technical process, but involves many subjective elements and decisions. One difficulty facing regulators is that preferences and risk attitudes within society may diverge and that costs and benefits may not be distributed evenly, and that a single, collective decision has to be based on strongly divergent individual preferences. In practice, this implies that the establishment of collective decision making procedures is inevitably a political process. This ambiguity can also be found in the numerous interpretations of “the” precautionary principle, which is interpreted by some as a decision making criterion that requires proof of harmlessness (a scientific impossibility), whereas it is seen by others as a decision making procedure that puts emphasis on dialogue and stakeholder involvement, (e.g. {cite:t}`jongejan2008`).
 
diff --git a/book/pd/risk-evaluation/decision.md b/book/pd/risk-evaluation/decision.md
index 271ce97a..77bd7fe5 100644
--- a/book/pd/risk-evaluation/decision.md
+++ b/book/pd/risk-evaluation/decision.md
@@ -37,7 +37,7 @@ Decision tree.
 
 Based on the possible results a choice is made for an action. To be able to assess the different results, a numerical value is assigned to each outcome, $\omega$, which can be used to establish the benefit of each outcome. This number can be a monetary value, a number on an arbitrary scale or utility--as long as the decision maker(s) can establish a consistent ranking of the outcomes with it. In the last two cases the benefit has no absolute value, but only gives the relative value of the different outcomes.
 
-Utility, $u$, is a concept used to rank the possible outcomes according to the preferences of the decision maker, with possible values $0\leq u \leq 1$ . A utility function can be used to characterize the relative utility of various outcomes. The elaborations below are based on the monetary values as a measure for the outcomes and assume a risk neutral decision maker. This is a decision maker who is indifferent between choices with equal expected outcomes, even if one choice is riskier than the other. For example, a risk neutral decision maker would have the same preference for a € 400 pay out, or a 50/50 bet with a coin toss with outcomes of € 0 (head) or € 800 (tail). Utility and risk aversion are further discussed in ater sections.
+Utility, $u$, is a concept used to rank the possible outcomes according to the preferences of the decision maker, with possible values $0\leq u \leq 1$ . A utility function can be used to characterize the relative utility of various outcomes. The elaborations below are based on the monetary values as a measure for the outcomes and assume a risk neutral decision maker. This is a decision maker who is indifferent between choices with equal expected outcomes, even if one choice is riskier than the other. For example, a risk neutral decision maker would have the same preference for a € 400 pay out, or a 50/50 bet with a coin toss with outcomes of € 0 (head) or € 800 (tail). Utility and risk aversion are further discussed in later sections.
 
 ## Decision rules
 
@@ -182,13 +182,15 @@ The previous analysis has shown that the probability of flooding of the excavati
 Without drainage, the risk, defined as the expected value of the loss, is
 
 $$
-\textrm{risk, without drainage = }0.12 \cdot \euro{} 5,000,000 = \euro{} 600,000
+\textrm{risk, without drainage = }0.12 \cdot \text{€ } 5,000,000 = \text{€ } 600,000
 $$
+
 With drainage the risk is:
 
 $$
-\textrm{risk, with drainage = }0.04 · \euro{} 5,000,000 = \euro{} 200,000
+\textrm{risk, with drainage = }0.04 · \text{€ } 5,000,000 = \text{€ } 200,000
 $$
+
 Costs and probabilities can also be shown in the decision tree (see Figure {numref}`example-river-excavation-3`). The expected values of the costs can be calculated for the different actions by adding the present values of the cost of actions and risk:
 - $\textit a_{1}$ : expected value (additional) costs = risk =€ 600,000
 - $\textit a_{2}$ : expected value (additional) costs 
diff --git a/book/pd/risk-evaluation/econ-optimization.md b/book/pd/risk-evaluation/econ-optimization.md
index 7d9e8ee0..4f194fa0 100644
--- a/book/pd/risk-evaluation/econ-optimization.md
+++ b/book/pd/risk-evaluation/econ-optimization.md
@@ -14,7 +14,7 @@ $$
     C_{tot} = I + R
 $$
 
-The annual risk, or expected economic dagmage is found by:
+The annual risk, or expected economic damage is found by:
 
 $$
     E(D) = P_f D
@@ -23,7 +23,7 @@ $$
 where:
 
 - $E(D)$ the expected value of the risk [€/year]
-- $P_f$ the failure probablity of the system per year [1/year]
+- $P_f$ the failure probability of the system per year [1/year]
 - $D$ the damage in case of failure [€]
 
 In this approach it is thus assumed that all damages are expressed in monetary terms. Additional criteria for separately considering the loss of human life are included in the next section. 
diff --git a/book/pd/risk-evaluation/example-dike-height.md b/book/pd/risk-evaluation/example-dike-height.md
index e246b1c5..80e10407 100644
--- a/book/pd/risk-evaluation/example-dike-height.md
+++ b/book/pd/risk-evaluation/example-dike-height.md
@@ -1,7 +1,7 @@
 (ex-dike-height)=
 # Economic Optimization Example
 
-Economic optimization is illustrated through the determination of an optimial dike height to protect against flooding.
+Economic optimization is illustrated through the determination of an optimal dike height to protect against flooding.
 
 Before the major floods of 1953, dikes in the Netherlands were not designed for a specified safety level but mainly strengthened based on practical experience. One of the main questions after the disaster was the optimal dike height and the “acceptable” probability of flooding. Van Dantzig was a professor in mathematics and a member of the first Delta  committee. He developed an econometric approach to determine the  optimal  probability of flooding (or protection level) and the corresponding dike height {cite:p}`vandantzig1956`.
 
@@ -15,7 +15,7 @@ $$ (prob_dist_water_levels)
 
 In which:
 - $h$ the water level [m]
-- $A,B$ constants of the exponential ditribution [m]
+- $A,B$ constants of the exponential distribution [m]
 
 Neglecting wave run-up, the probability of failure of the dikes - leading to flooding -  can be approximated by the probability of exceedance of the dike height $h_d$, i.e.
 
diff --git a/book/pd/risk-evaluation/safety-standards.md b/book/pd/risk-evaluation/safety-standards.md
index 4739cb51..855be9b0 100644
--- a/book/pd/risk-evaluation/safety-standards.md
+++ b/book/pd/risk-evaluation/safety-standards.md
@@ -270,12 +270,12 @@ A risk aversion index $k$ has been introduced to account for risk aversion. For
 
 ````{admonition} Expected value and standard deviation for two systems
 
-We consider two sytems
+We consider two systems
 
-1. This sytem has a high failure probability of 0.01 per year and 1 fatality
+1. This system has a high failure probability of 0.01 per year and 1 fatality
 2. The second system has a smaller failure probability of 0.0001 per year but a higher number of 100 fatalities.
 
-For both systems a binomical distribution of the number of fatalities is applied meaning that the number of fatalities in case of failure is exactly known. The expected value and standard deviation of the number of fatalities are found as follows:
+For both systems a binomial distribution of the number of fatalities is applied meaning that the number of fatalities in case of failure is exactly known. The expected value and standard deviation of the number of fatalities are found as follows:
 
 $$
   E(N) = P_fN \;\;\;\; \sigma^2(N) = P_f(1-P_f)N
-- 
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