Merge branch 'main' into release

content/Week_2_8/WS_2_8_dirty_water.ipynb

@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Workshop 16: Dirty Water\n",
+    "# WS 2.8: Dirty Water\n",
     "\n",
     "<h1 style=\"position: absolute; display: flex; flex-grow: 0; flex-shrink: 0; flex-direction: row-reverse; top: 60px;right: 30px; margin: 0; border: 0\">\n",
     "    <style>\n",
@@ -17,7 +17,7 @@
     "<h2 style=\"height: 10px\">\n",
     "</h2>\n",
     "\n",
-    "*[CEGM1000 MUDE](http://mude.citg.tudelft.nl/): Week 2.8. Wednesday January 16, 2024.*"
+    "*[CEGM1000 MUDE](http://mude.citg.tudelft.nl/): Week 2.8. Wednesday January 15, 2024.*"
    ]
   },
   {
@@ -38,7 +38,7 @@
     "\n",
     "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.\n",
     "\n",
-    "The city has also considered the regulations in a nearby region which uses a maximum allowable probability of 1 person getting sick as p_f=0.01. The city agrees with this, however, they are very much _risk averse_ (that's a hint!), regarding spills with more significant consequences.\n",
+    "The city has also considered the regulations in a nearby region which uses a maximum allowable probability of 1 person getting sick as $p_f=0.01$. The city agrees with this, however, they are very much _risk averse_ (that's a hint!), regarding spills with more significant consequences.\n",
     "\n",
     "_*M = million, so 7,000M is 7e9, or 7 billion. All costs in this exercise are expressed in units €M._"
    ]
@@ -61,11 +61,18 @@
     "<p>\n",
     "<b>Task 1:</b>  \n",
     "\n",
-    "What is optimal strategy in terms of total cost of the system?\n",
+    "What is best strategy in terms of total cost of the system?\n",
     "</p>\n",
     "</div>"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "_Your answer here._"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -73,15 +80,43 @@
     "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
     "<p>\n",
     "<b>Task 2:</b>  \n",
-    "\n",
     "Assuming that the number of people in a future spill would also be 10 people, what is the maximum allowable spill probability based on societal risk standards?\n",
     "\n",
     "Make a plot of the societal risk limit and add a point for the case of the city factory.\n",
-    "    \n",
     "</p>\n",
     "</div>"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "C = YOUR_CODE_HERE\n",
+    "alpha = YOUR_CODE_HERE\n",
+    "\n",
+    "pf_societal = YOUR_CODE_HERE\n",
+    "print(pf_societal)\n",
+    "\n",
+    "N_values = YOUR_CODE_HERE\n",
+    "limit_line = YOUR_CODE_HERE\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(8, 6))\n",
+    "YOUR_CODE_HERE\n",
+    "YOUR_CODE_HERE\n",
+    "ax.set_title('YOUR_CODE_HERE')\n",
+    "ax.set_xlabel('YOUR_CODE_HERE')\n",
+    "ax.set_ylabel('YOUR_CODE_HERE')\n",
+    "ax.legend(fontsize=14)\n",
+    "plt.yscale('log')\n",
+    "plt.xscale('log')\n",
+    "ax.grid(True)\n",
+    "plt.show()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -100,13 +135,23 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Spill Protection System\n",
+    "_Your answer here._"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Additional Risk Analysis\n",
     "\n",
-    "The factory has two areas where the hazardous chemical is produced, and each eara has a direct route to the groundwater table. The large spill prevention system design (mentioned above) consists of the same spill containment structure that is built twice: one at each area.\n",
+    "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:\n",
     "\n",
-    "During your review, you find out that a material essential to the containment structure is made in large batches, and sometimes an entire batch turns out to be faulty. The failure probability calculation for the design of the structure was made under the assumption of independent events.\n",
+    "$$\n",
+    "p_i = P[n_{i-1} < N \\leq n_i]\n",
+    "$$\n",
     "\n",
-    "_Note for the exam: we won't ask you to identify or justify positive or negative correlations, but given information like correlation coefficient, you should be able to provide quantitative results regarding the impact on simple series and parallel systems, relative to the independent case._\n"
+    "For $i=1:N_s$, where $N_s$ is the number of scenarios; specific values of the consequence, $n_i$, of each scenario $i$ are provided in the Python code cell below, along with the associated probability. Note that the intervals of $N$ are used to simplify the analysis, rather than provide a specific value for every possible number of people getting sick.\n",
+    "\n"
    ]
   },
   {
@@ -117,8 +162,67 @@
     "<p>\n",
     "<b>Task 4:</b>  \n",
     "\n",
-    "Given the new information, advise the city whether the current estimate of failure probability is over- or under-conservative. Explain why.\n",
+    "Create the FN curve for the factory and compare it with the societal risk limit you determined above.\n",
+    "</p>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#facb8e; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\"> <p>\n",
+    "<b>Hint:</b> you may find it useful to use <code>np.cumsum</code> as well as Matplotlib's <code>step</code> function (in particular, consider whether to use <code>pre</code>, <code>post</code> or <code>mid</code> for keyword argument <code>where</code>).\n",
+    "</p></div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "n_and_p = np.array([[1,   0.099],\n",
+    "                    [2,   7e-4],\n",
+    "                    [5,   2e-4],\n",
+    "                    [10,  9e-5],\n",
+    "                    [20,  5e-6],\n",
+    "                    [60,  3e-6],\n",
+    "                    [80,  6e-7],\n",
+    "                    [100,  4e-7],\n",
+    "                    [150, 8e-8]])\n",
+    "\n",
+    "N_plot = n_and_p[:, 0]\n",
     "\n",
+    "p_cumulative = YOUR_CODE_HERE\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(8, 6))\n",
+    "YOUR_CODE_HERE\n",
+    "YOUR_CODE_HERE\n",
+    "YOUR_CODE_HERE\n",
+    "ax.set_title('YOUR_CODE_HERE')\n",
+    "ax.set_xlabel('YOUR_CODE_HERE')\n",
+    "ax.set_ylabel('YOUR_CODE_HERE')\n",
+    "ax.legend(fontsize=14)\n",
+    "plt.yscale('log')\n",
+    "plt.xscale('log')\n",
+    "# plt.xlim(YOUR_CODE_HERE, YOUR_CODE_HERE)\n",
+    "# plt.ylim(YOUR_CODE_HERE, YOUR_CODE_HERE\n",
+    "ax.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
+    "<p>\n",
+    "<b>Task 5:</b>  \n",
+    "\n",
+    "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.\n",
+    "\n",
+    "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>\n",
     "</p>\n",
     "</div>"
    ]
@@ -127,18 +231,51 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "<div style=\"background-color:#C8FFFF; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
+    "<div style=\"background-color:#facb8e; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\"> <p>\n",
+    "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.\n",
+    "</p></div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "n_and_p_modified = n_and_p.copy()\n",
+    "n_and_p_modified[YOUR_CODE_HERE, YOUR_CODE_HERE] = YOUR_CODE_HERE\n",
+    "\n",
+    "DUPLICATE_ANALYSIS_FROM_ABOVE_WITH_MODIFIED_VALUES"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:#AABAB2; color: black; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px; width: 95%\">\n",
     "<p>\n",
-    "<b>Thirsty for more?</b>   \n",
+    "<b>Task 6:</b>  \n",
+    "\n",
+    "Calculate the expected number of people getting sick per year for the factory under the current conditions.\n",
+    "\n",
+    "<em>Note that we don't do anything with this calculation in this assignment, but it is often a useful way to quantify the risk of a system, or, for example, comparing two or more types of systemts; various factories, in this case.</em>\n",
     "\n",
-    "We added <a href=\"https://mude.citg.tudelft.nl/book/pd/reliability-component/contamination.html\" target=\"_blank\">a new interactive page</a> to the book that illustrates component reliability analysis for another part of this contaminant transport case study.\n",
     "</p>\n",
     "</div>"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "YOUR_CODE_HERE"
+   ]
+  },
   {
    "cell_type": "markdown",
-   "id": "b8af792e",
+   "id": "c2f76fae",
    "metadata": {},
    "source": [
     "**End of notebook.**\n",
@@ -168,7 +305,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "mude-base",
    "language": "python",
    "name": "python3"
   },
@@ -182,7 +319,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.4"
+   "version": "3.12.3"
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   "widgets": {
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