risk_reduction.tex

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Let $R$ be the set of identified risks, with each risk denoted as $r_i$ ($i$ ranges from 1 to $|R|$). For each risk $r_i$, let $C_{ij}$ be the cost of implementing control measure $j$ for risk $r_i$ ($j$ ranges from 1 to $|C_i|$, where $|C_i|$ is the number of control measures associated with risk $r_i$). Let $OCC_i$ represent the likelihood of occurrence for risk $r_i$, and let $SEV_i$ represent the severity of risk $r_i$. Define $RR_{ij}$ as the risk reduction achieved by control measure $j$ for risk $r_i$.

Define the indicator function $I_{ij}$ as follows:

\[
I_{ij} =
\begin{cases}
    1 & \text{if control measure $j$ is necessary for risk $r_i$} \\
    0 & \text{if control measure $j$ is redundant for risk $r_i$}
\end{cases}
\]

The indicator function is based upon hierarchy of controls. Higher level controls supercede combinations of lower level controls.

1. Calculate Risk Reduction ($RR_{ij}$) for each control measure, considering the indicator function:

\[
RR_{ij} = I_{ij} \cdot (OCC_i \cdot SEV_i - (OCC_i' \cdot SEV_i'))
\]

2. Calculate the Total Cost for Risk $r_i$ while considering the indicator function:

\[
TC_i = \sum_{j=1}^{|C_i|} (I_{ij} \cdot C_{ij})
\]

3. Calculate the Total Risk Reduction for Risk $r_i$ considering the indicator function:

\[
TRR_i = \sum_{j=1}^{|C_i|} (I_{ij} \cdot RR_{ij})
\]

4. Calculate the Cost-Effectiveness Ratio for Risk $r_i$:

\[
CE_i = \frac{TC_i}{TRR_i}
\]

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