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A city with population 10,000 uses an aquifer for its water supply, as illustrated in the figure. The city owns a factory in the region that manufactures hazardous chemicals, and recently a chemical spill occurred that resulted in 10 residents getting sick and total damages of €7,000M*. The city is going to enforce stricter regulations on the factory, and _you have been hired to advise the city council on the maximum allowable probability of a spill occurring (per year)_. You will make a recommendation based on the more stringent criteria between economic and societal risk limits.
Experts have been consulted and it appears under the current plan the probability of a spill is 1/100 per year. The city council is considering two strategies to upgrade the spill prevention system. A small upgrade would cost €25M and can reduce spill probability by a factor 10; a large upgrade with investment costs of €50M would reduce the probability by factor 100.
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It turns out that since the spill occurred an evaluation was completed by a third party company, where they identified the following scenarios, along with estimated a probability of each event occurring. The city would like you to see if it would conflict with your safety recommendations. The results of the risk analysis are provided as the probability associated with a specific number of people getting sick; that is:
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As you may have noticed, the risk in the system does not satisfy your recommendation. Play with the values of $n$ and $p$ to see how you can satisfy the safety standard. Then, select a few "modifications" to the $n$ and/or $p$ values and describe how you might be able to make that change in reality. Keep in mind that making interventions to the system is expensive, so to be realistic you should try to do this by making the <em>smallest</em> change possible; in other words, find the smallest change in $n$ or $p$ separately; don't change many values all at once.
Report your findings as if they were a recommendation to the city. For example: <em>if one were to reduce $p$ of <code>something</code> from <code>value</code> to <code>value</code> by implementing <code>your plan here</code>, the FN curve would shift <code>specify direction</code>, and the safety standard would be satisfied.</em>
Yes, this is an overly simplistic exercise exercise, but it is a good way to think about how to apply the concepts of risk analysis to real-world problems, and to make sure you understand the mathematics of how they are constructed. Also note that each "point" comes from a scenario; in real risk applications it can be quite involved to decide on and carry out the computations required for each scenario.
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