NFPA-EconomicImpactFire-case3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NFPA-CBA Example 3 : Government office (GOV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notebook initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import packages\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "This Notebook presents an example application of the prototype methodology for cost-benefit analysis. This case study considers a governmental office building area of 6000 m2 (6 floors of 1000 m2 each), inspired by the case study in (Yung et al., 1997). The cost-benefit of the following fire protection systems is investigated: (i) advanced automatic detection system, and (ii) extra staircase.  \n",
    "\n",
    "The case study is envisioned as an early-stage cost-benefit evaluation based on statistical data and expert judgement (supplemented with parameter studies). This allows to assess whether the information provided by detailed fire development and evacuation models can reasonably influence the decision-making. If a simplified assessment based on expert judgement clearly indicates that an investment is, or is not, cost-effective, then further detailed analyses do not add value.\n",
    "\n",
    "The reference design has only basic fire detection. The cost-benefit of three design alternatives are investigated: (a) presence of advanced detection system; (b) presence of an additional staircase; (c) presence of both an advanced detection system and an additional staircase.  \n",
    "\n",
    "The benefit evaluation is done considering the event tree diagram visualized below. Three scenarios are identified: (I) No detection system warning; (II) Detection system warning, no occupant suppression; (III) Detection system warning and suppression by occupants. The fire frequency considers reported fires, and thus already includes occupant detection and early stage suppression."
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![sketch.jpg](attachment:8d571929-6805-41e2-ba8d-a4a69ed3e7bc.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. Input\n",
    "User input in this area.\n",
    "Note: All monetary values in 2022 USD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.1 Building characteristics\n",
    "Six story government office building (6000m2 total floor area). Concrete moment frame.  \n",
    "Cost evaluation of structure and the cost of fire protection measures considering (RSMeans 2022), see background document.  \n",
    "\n",
    "The additional staircase is considered not to increase the total construction cost, as the total floor area is constant.  \n",
    "The additional staircase however results in a loss of usable floorspace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "S_area = 6000 # [m2] Total floor area\n",
    "Construction_Cost = 3903 # [USD/m2] Construction cost; 3908 (RSMeans, 2022)\n",
    "DemolAndDisp_cost = 0.03*Construction_Cost # [USD/m2] Demolition and disposal cost; assessessed as 3% of construction cost, informed by case 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.2 Discount rate and obsolescence rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = 0.03 # [1/year] continuous discount rate; 3% based on (Fischer, 2014)\n",
    "o = 0    # [1/year] obsolescence rate; 0% - building obsolescence neglected"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.3 Cost of fire protection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I.3.a Investment cost fire protection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "## detection system\n",
    "c_det_unit_full=10.33+9.47 # [USD/m2] System installation cost; 10.33 for detectors, 9.47 for fire alarm command sensor and voice alarm (RSMeans, 2022)\n",
    "c_det_unit=c_det_unit_full-4 # [USD/m2] Additional cost over reference (minus 4 USD/m2 based on case 1 and case 2)\n",
    "c_det = c_det_unit*S_area  # [USD] Total system installation cost\n",
    "\n",
    "## staircase\n",
    "c_sc = 0 # [USD] Installation cost staircase; 0 as cost included in total building cost (total footprint of the building considered constant)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I.3.b Maintenance cost fire protection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "## detection system\n",
    "m_det= 0.05 * c_det_unit_full * S_area # [USD per year] annual maintenance cost; 5% of detection system installation cost assumed - maintenance cost assumed to include replacement of parts for system lifetime extension\n",
    "\n",
    "## additional staircase\n",
    "A_sc=6*6 # [m2] staircase total footprint; 6 m2 floor space used per floor for additional staircase = 6*6 m2\n",
    "rent=430 # [USD/m2 per year] rental cost per m2; 430 USD/(year*m2) adopted as test value\n",
    "m_sc=rent*A_sc # [USD per year] annual cost associated with loss of floorspace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.4 Benefit of fire protection\n",
    "Benefit evaluation as reduction in cost of fire losses, assessed through the event tree listed in the Introduction.\n",
    "<br> See background document for discussion."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I.4.a Fire frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "## fire frequency\n",
    "lambda_fi= 0.002 # [1/year] fire frequency for office (ignition frequency + unsuccessful immediate suppression by occupants); 0.002 based on (Manes and Rush, 2019) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I.4.b Fire barrier reliability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "## automatic detection and fire alarm reliability\n",
    "p_det = 0.90 # [-] probability of succesful detection and alarm; 0.90 based on PD7974-7:2019\n",
    "\n",
    "## fire suppression by occupants following automatic detection\n",
    "p_occ = 0.5 # [-] probability of succesful fire suppression by occupants; 0.5 based on (Albrecht and Hosser, 2010)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### I.4.c Fire-induced losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "## valuation of risk to life\n",
    "VSL = 5.657*10**6 # [2022 USD] Value of Statistical Life (VSL); 5.657*10**6 based on (ISO 2394:2015) \n",
    "xi_in = (0.047 * VSL) # [2022 USD] valuation of average injury risk; 0.047*VSL based on (Zhuang et al., 2017)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "## [fatalities/fire]\n",
    "Nf_civilian = 0.9/1000 # [fatality/fire] probability of civilian fatalities; 0.9 fatalities per 1000  fires based on (NFPA 2022)\n",
    "Nf_firefighter_onground = 6.9/1e5 # [fatality/fire] probability of firefighter fireground fatality; 2.8/1e5 based on (NFPA, 2022)\n",
    "Nf_firefighter_response = 6.3/1e5 # [fatality/fire] probability of firefighter response fatality; 2.5/1e5 based on (NFPA, 2022)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "## [injuries/fire]\n",
    "Ni_civilian = 1.4/100 # [injury/fire] civilian injuries; 1.3 injuries per 100 reported fires based on (NFPA, 2022)\n",
    "Ni_firefighter_onground = 16.2/1000 # [injury/fire] firefighter fireground injuries; 16.2 injuries per 1000 reported fires based on (NFPA, 2022)\n",
    "Ni_firefighter_response = 3.7/1000  # [injury/fire] firefighter response injuries; 3.7 injuries per 1000 reported fires based on (NFPA, 2022)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## property loss\n",
    "S_loss_0 = 97.34 # [m2] average damage area reference situation; 97.34 based on (Manes and Rush, 2019)\n",
    "S_loss_sup = 5 # [m2] average damage area in case of succesful occupant suppression following automatic alarm; 5 m2 as exploratory assessment\n",
    "\n",
    "eps_loss_content = 2.0 # [-] property loss multiplication factor; eps_loss = ((building loss + content loss) / building loss); 2.0 based on (FEMA, 2015)\n",
    "eps_loss_indirect = 1.25 # [-] total property loss multiplication factor accounting for indirect costs; 1.25 based on (Ramachandran and Hall, 2002)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "### loss reduction factors additional staircase\n",
    "# note : the effect of the staircase can be taken into account through, for example, evacuation modelling; here an early-stage assessment is made considering loss reduction factors\n",
    "\n",
    "## reduction factors for civilian fatalities and injuries (enabling exploratory investigation); single parameter applied for simplicity\n",
    "reduxSC_civ=0.3 # in case of additional staircase \n",
    "reduxDET_civ=0.4 # in case of early warning\n",
    "reduxSup_civ=0.5 # injuries only - very low (effectively zero) fatality rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II. Design fire risk evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.1 Calculation of fire scenario parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Unit replacement cost\n",
    "Replace_cost = Construction_Cost + DemolAndDisp_cost # [USD/m2] replacement cost as sum of demolition, disposal and reconstruction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.2 Scenario consequence evalluation\n",
    "Evaluation of consequences for identified scenarios (event tree- Scenarios I, II and III);  \n",
    "The consequence severity depends on the design alternative (presence of additional staircase yes/no)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### II.2.a Scenario I \"No detection system warning\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Fatalities and injuries\n",
    "# Fatalities\n",
    "Nf_I = Nf_civilian + Nf_firefighter_onground + Nf_firefighter_response # [fatality/fire] total fatality rate\n",
    "Nf_Isc = Nf_civilian*(1-reduxSC_civ) + Nf_firefighter_onground + Nf_firefighter_response # [fatality/fire] total fatality rate with additional staircase\n",
    "# Injuries\n",
    "Nin_I = Ni_civilian + Ni_firefighter_onground + Nf_firefighter_response # [injury/fire] total injury rate\n",
    "Nin_Isc = Ni_civilian*(1-reduxSC_civ) + Ni_firefighter_onground + Nf_firefighter_response # [injury/fire] total injury rate with additional staircase\n",
    "\n",
    "### Valuation of fatalities and injuries\n",
    "Df_I=Nf_I*VSL # [USD/fire] valuation expected life loss\n",
    "Df_Isc=Nf_Isc*VSL # [USD/fire] valuation expected life loss with additional staircase\n",
    "Din_I = Nin_I*xi_in # [USD/fire] valuation expected injuries\n",
    "Din_Isc = Nin_Isc*xi_in # [USD/fire] valuation expected injuries with additional staircase\n",
    "\n",
    "### Material loss\n",
    "xi_d_I = S_loss_0 * Replace_cost * eps_loss_content * eps_loss_indirect # [USD] property loss\n",
    "\n",
    "### Total loss valuation\n",
    "D_I=Df_I+Din_I+xi_d_I # [USD] expected value fire-induced loss, scenario I \"no detection system warning\"\n",
    "D_Isc=Df_Isc+Din_Isc+xi_d_I # [USD] expected value fire-induced loss, scenario I \"no detection system warning\" with additional staircase"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### II.2.b Scenario II \"Detection system warning, no occupant suppression\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Fatalities and injuries\n",
    "# Fatalities\n",
    "Nf_II = Nf_civilian*(1-reduxDET_civ) + Nf_firefighter_onground + Nf_firefighter_response # [fatality/fire] total fatality rate\n",
    "Nf_IIsc = Nf_civilian*(1-reduxSC_civ)*(1-reduxDET_civ) + Nf_firefighter_onground + Nf_firefighter_response # [fatality/fire] total fatality rate with additional staircase\n",
    "# Injuries\n",
    "Nin_II = Ni_civilian*(1-reduxDET_civ) + Ni_firefighter_onground + Nf_firefighter_response # [injury/fire] total injury rate\n",
    "Nin_IIsc = Ni_civilian*(1-reduxSC_civ)*(1-reduxDET_civ) + Ni_firefighter_onground + Nf_firefighter_response # [injury/fire] total injury rate with additional staircase\n",
    "\n",
    "### Valuation of fatalities and injuries\n",
    "Df_II=Nf_II*VSL # [USD/fire] valuation expected life loss\n",
    "Df_IIsc=Nf_IIsc*VSL # [USD/fire] valuation expected life loss with additional staircase\n",
    "Din_II = Nin_II*xi_in # [USD/fire] valuation expected injuries\n",
    "Din_IIsc = Nin_IIsc*xi_in # [USD/fire] valuation expected injuries with additional staircase\n",
    "\n",
    "### Material loss\n",
    "xi_d_II = S_loss_0 * Replace_cost * eps_loss_content * eps_loss_indirect # [USD] property loss\n",
    "\n",
    "### Total loss valuation\n",
    "D_II=Df_II+Din_II+xi_d_II # [USD] expected value fire-induced loss, scenario I \"no detection system warning\"\n",
    "D_IIsc=Df_IIsc+Din_IIsc+xi_d_II # [USD] expected value fire-induced loss, scenario I \"no detection system warning\" with additional staircase"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### II.2.c Scenario III \"Detection system warning and succesful suppression by occupants\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Fatalities and injuries\n",
    "# Fatalities\n",
    "Nf_III = Nf_firefighter_response # [fatality/fire] total fatality rate\n",
    "Nf_IIIsc = Nf_firefighter_response # [fatality/fire] total fatality rate with additional staircase\n",
    "# Injuries\n",
    "Nin_III = Ni_civilian*(1-reduxSup_civ)  + Nf_firefighter_response # [injury/fire] total injury rate\n",
    "Nin_IIIsc = Ni_civilian*(1-reduxSup_civ) + Nf_firefighter_response # [injury/fire] total injury rate with additional staircase\n",
    "\n",
    "### Valuation of fatalities and injuries\n",
    "Df_III=Nf_III*VSL # [USD/fire] valuation expected life loss\n",
    "Df_IIIsc=Nf_IIIsc*VSL # [USD/fire] valuation expected life loss with additional staircase\n",
    "Din_III = Nin_III*xi_in # [USD/fire] valuation expected injuries\n",
    "Din_IIIsc = Nin_IIIsc*xi_in # [USD/fire] valuation expected injuries with additional staircase\n",
    "\n",
    "### Material loss\n",
    "xi_d_III = S_loss_sup * Replace_cost * eps_loss_content * eps_loss_indirect # [USD] property loss\n",
    "\n",
    "### Total loss valuation\n",
    "D_III=Df_III+Din_III+xi_d_III # [USD] expected value fire-induced loss, scenario I \"no detection system warning\"\n",
    "D_IIIsc=Df_IIIsc+Din_IIIsc+xi_d_III # [USD] expected value fire-induced loss, scenario I \"no detection system warning\" with additional staircase"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III. PNV calculation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Total safety system cost *C+A*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### III.1.a Investment cost, *C<sub>I</sub>*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "C_I_det=c_det # PNV investment cost for sprinkler system\n",
    "C_I_sc=c_sc # PNV investment cost for compartmentation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### III.1.b PNV maintenance cost, *C<sub>M</sub>*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "C_M_det=m_det/g # PNV of maintenace cost for sprinkler system\n",
    "C_M_sc=m_sc/g # PNV of maintenace cost for compartmentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### III.1.c Obsolescence cost, *C<sub>A</sub>*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "C_A_det=C_I_det*o/g # PNV of obsolescence cost sprinkler system\n",
    "C_A_sc=C_I_sc*o/g # PNV of obsolescence cost compartmentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### III.1.d Total safety system cost *C+A*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "net_C_a = C_I_det+ C_M_det + C_A_det # Detection system only (Design a)\n",
    "net_C_b = C_I_sc + C_M_sc + C_A_sc # Extra staircase only (Design b)\n",
    "net_C_c = net_C_a + net_C_b # Both detection system and extra staircase (Design c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### III.2 Net Benefit B-D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### III.2.a Fire induced losses reference design, *B* (no sprinkler system and no compartmentation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Expected loss reference design\n",
    "Dref  =  D_I\n",
    "\n",
    "# Present net value of reference design\n",
    "B = Dref * lambda_fi/g # [USD] PNV fire-induced losses reference design"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### III.2.b Fire-induced losses trial designs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Expected losses with design a, b and c\n",
    "# Design a (detection system only)\n",
    "Da = (1-p_det) * D_I + p_det * ((1-p_occ) * D_II + p_occ * D_III)\n",
    "\n",
    "# Design b (extra staircase only)\n",
    "Db  =  D_Isc\n",
    "\n",
    "# Design c (both detection system and extra staircase)\n",
    "Dc  =  (1-p_det) * D_Isc + p_det * ((1-p_occ) * D_IIsc + p_occ * D_IIIsc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "## PNV of design a, b and c\n",
    "D_a = Da *lambda_fi/g  # [USD] PNV expected risk for alternative design a\n",
    "D_b = Db *lambda_fi/g  # [USD] PNV expected risk for alternative design b\n",
    "D_c = Dc *lambda_fi/g  # [USD] PNV expected risk for alternative design c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### III.2.c PNV net benefit, *B-D*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "netB_a = B - D_a # [USD] Net benefit for alternative design a\n",
    "netB_b = B - D_b # [USD] Net benefit for alternative design b\n",
    "netB_c = B - D_c # [USD] Net benefit for alternative design c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV. Cost-Benefit evaluation, Z (USD, Present net value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The PNV for alternative design a (detection system only) is -264,504 [USD]; the BCR is 0.10\n",
      "\n",
      "The PNV for alternative design b (extra staircase only) is -515,824 [USD]; the BCR is 0.00\n",
      "\n",
      "The PNV for alternative design c (both detection system and extra staircase) is -780,438 [USD]; the BCR is 0.04\n"
     ]
    }
   ],
   "source": [
    "## PNV of proposed alternative design\n",
    "Z_a = netB_a - net_C_a # [USD] Present net value for alternative design a (detection system only)\n",
    "Z_b = netB_b - net_C_b # [USD] Present net value for alternative design b (extra staircase only)\n",
    "Z_c = netB_c - net_C_c # [USD] Present net value for alternative design c (both detection system and extra staircase)\n",
    "\n",
    "## Benefit cost ratio of proposed alternative design\n",
    "BCR_a=netB_a/net_C_a \n",
    "BCR_b=netB_b/net_C_b\n",
    "BCR_c=netB_c/net_C_c\n",
    "\n",
    "## Print to screen\n",
    "print(\"\\nThe PNV for alternative design a (detection system only) is {0:,.0f} [USD]; the BCR is {1:.2f}\".format(Z_a,BCR_a))\n",
    "print(\"\\nThe PNV for alternative design b (extra staircase only) is {0:,.0f} [USD]; the BCR is {1:.2f}\".format(Z_b,BCR_b))\n",
    "print(\"\\nThe PNV for alternative design c (both detection system and extra staircase) is {0:,.0f} [USD]; the BCR is {1:.2f}\".format(Z_c,BCR_c))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 3 - Parameter study"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Impact of parameter choices - detection system only"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Function definition PNV Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function combining above model assumption for parameter study\n",
    "def Zvalue(p_det,p_occ,eps_loss_indirect,reduxDET_civ,reduxSup_civ):  \n",
    "    ## I. Input ##\n",
    "    ##############\n",
    "    ## parameters provided as function input\n",
    "    # p_det = 0.90 # [-] probability of succesful detection and alarm; 0.90 based on PD7974-7:2019\n",
    "    # p_occ = 0.5 # [-] probability of succesful fire suppression by occupants; 0.5 based on (Albrecht and Hosser, 2010)\n",
    "    # eps_loss_indirect = 1.25 # [-] total property loss multiplication factor accounting for indirect costs; 1.25 based on (Ramachandran and Hall, 2002)\n",
    "    # reduxDET_civ=0.4 # in case of early warning\n",
    "    # reduxSup_civ=0.5 # injuries only - very low (effectively zero) fatality rate   \n",
    "    \n",
    "    ## II. Design fire risk evaluation ##\n",
    "    #####################################    \n",
    "    ## II.2.a Scenario I \"No detection system warning\"\n",
    "    ### Material loss\n",
    "    xi_d_I = S_loss_0 * Replace_cost * eps_loss_content * eps_loss_indirect # [USD] property loss\n",
    "    ### Total loss valuation\n",
    "    D_I=Df_I+Din_I+xi_d_I # [USD] expected value fire-induced loss, scenario I \"no detection system warning\"\n",
    "    \n",
    "    ## II.2.b Scenario II \"Detection system warning, no occupant suppression\"\n",
    "    ### fatalities and injuries\n",
    "    Nf_II = Nf_civilian*(1-reduxDET_civ) + Nf_firefighter_onground + Nf_firefighter_response # [fatality/fire] total fatality rate\n",
    "    Nin_II = Ni_civilian*(1-reduxDET_civ) + Ni_firefighter_onground + Nf_firefighter_response # [injury/fire] total injury rate\n",
    "    ### Valuation of fatalities and injuries\n",
    "    Df_II=Nf_II*VSL # [USD/fire] valuation expected life loss\n",
    "    Din_II = Nin_II*xi_in # [USD/fire] valuation expected injuries\n",
    "    ### Material loss\n",
    "    xi_d_II = S_loss_0 * Replace_cost * eps_loss_content * eps_loss_indirect # [USD] property loss\n",
    "    ### Total loss valuation\n",
    "    D_II=Df_II+Din_II+xi_d_II # [USD] expected value fire-induced loss, scenario I \"no detection system warning\"\n",
    "\n",
    "    ## II.2.c Scenario III \"Detection system warning and succesful suppression by occupants\"\n",
    "    ### fatalities and injuries\n",
    "    Nin_III = Ni_civilian*(1-reduxSup_civ)  + Nf_firefighter_response # [injury/fire] total injury rate\n",
    "    ### Valuation of fatalities and injuries\n",
    "    Din_III = Nin_III*xi_in # [USD/fire] valuation expected injuries\n",
    "    ### Material loss\n",
    "    xi_d_III = S_loss_sup * Replace_cost * eps_loss_content * eps_loss_indirect # [USD] property loss\n",
    "    ### Total loss valuation\n",
    "    D_III=Df_III+Din_III+xi_d_III # [USD] expected value fire-induced loss, scenario I \"no detection system warning\"\n",
    "    \n",
    "    ## III. PNV calculation ##\n",
    "    ##########################\n",
    "    ## III.2.a Fire-induced losses reference design, B\n",
    "    # Expected loss reference design\n",
    "    Dref  =  D_I\n",
    "    # Present net value of reference design\n",
    "    B = Dref * lambda_fi/g # [USD] PNV fire-induced losses reference design\n",
    "    \n",
    "    ## III.2.b Fire-induced losses trial designs\n",
    "    ## Expected losses with design a (detection system only)\n",
    "    Da = (1-p_det) * D_I + p_det * ((1-p_occ) * D_II + p_occ * D_III)    ## PNV evaluation\n",
    "    D_a = Da *lambda_fi/g  # [USD] PNV expected risk for alternative design a\n",
    "    \n",
    "    ## III.2.c PNV net benefit, B-D\n",
    "    netB_a = B - D_a # [USD] Net benefit for alternative design a\n",
    "    \n",
    "    ## IV. Cost-Benefit evaluation ##\n",
    "    #################################  \n",
    "    ## PNV of proposed alternative design\n",
    "    Z_a = netB_a - net_C_a # [USD] Present net value for alternative design a (detection system only)\n",
    "    ## Benefit cost ratio of proposed alternative design\n",
    "    BCR_a=netB_a/net_C_a \n",
    "    \n",
    "    return Z_a,BCR_a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Example of usage function Zvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The PNV for alternative design a (detection system only) is -264,504 [USD]; the BCR is 0.10\n"
     ]
    }
   ],
   "source": [
    "## Example application of function Zvalue - verification base values\n",
    "\n",
    "# input values\n",
    "p_det = 0.90 # [-] probability of succesful detection and alarm; 0.90 based on PD7974-7:2019\n",
    "p_occ = 0.5 # [-] probability of succesful fire suppression by occupants; 0.5 based on (Albrecht and Hosser, 2010)\n",
    "eps_loss_indirect = 1.25 # [-] total property loss multiplication factor accounting for indirect costs; 1.25 based on (Ramachandran and Hall, 2002)\n",
    "reduxDET_civ=0.4 # in case of early warning\n",
    "reduxSup_civ=0.5 # injuries only - very low (effectively zero) fatality rate  \n",
    "    \n",
    "# CBA \n",
    "Z_a,BCR_a = Zvalue(p_det,p_occ,eps_loss_indirect,reduxDET_civ,reduxSup_civ)\n",
    "\n",
    "## Print to screen\n",
    "print(\"\\nThe PNV for alternative design a (detection system only) is {0:,.0f} [USD]; the BCR is {1:.2f}\".format(Z_a,BCR_a))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Parameter study and visualization for design alternative a\n",
    "Investigation of conditions under which the investment into the advanced detection system becomes cost-efficient.  \n",
    "Generous input values for reliability and life risk reduction to explore best case scenario.  \n",
    "==> Conclusion : even under generous assumptions, an indirect cost factor of 6.4 (i.e., approx. 540% additional indirect costs) needed before the investment becomes efficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Present net value, Z [$10^3$ USD]')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Exploration of best case scenario for detection system efficiency\n",
    "# %matplotlib qt \n",
    "%matplotlib inline\n",
    "\n",
    "## generous input values reliability and efficiency\n",
    "p_det = 1.0 # [-] probability of succesful detection and alarm; 0.90 based on PD7974-7:2019\n",
    "p_occ = 1.0 # [-] probability of succesful fire suppression by occupants; 0.5 based on (Albrecht and Hosser, 2010)\n",
    "reduxDET_civ=1.0 # in case of early warning\n",
    "reduxSup_civ=1.0 # in case of occupant suppression; applies to injuries only, considering very low (effectively zero) fatality rate  \n",
    "\n",
    "## values to explore for parameter study\n",
    "eps_loss_indirect_list=np.arange(1,21,1)\n",
    "\n",
    "## CBA \n",
    "Z_a,BCR_a = Zvalue(p_det,p_occ,eps_loss_indirect_list,reduxDET_civ,reduxSup_civ)\n",
    "\n",
    "## Visualization\n",
    "legends = []\n",
    "fig,ax = plt.subplots(1,1)   \n",
    "ax.plot(eps_loss_indirect_list,Z_a/1000,label='Detection system only')\n",
    "ax.legend(legends,fontsize=12)\n",
    "ax.plot([0,20],[0,0],linestyle='solid',color='k',linewidth=3.0)\n",
    "ax.set_xlim([1.0,20])\n",
    "ax.grid(which='both',axis='both')\n",
    "fig.set_size_inches(9,6)\n",
    "ax.set_xlabel('Indirect cost as factor of direct cost');ax.set_ylabel('Present net value, Z [$10^3$ USD]')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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