Religious-pilgrimage system

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LECTURE 3.1 NATURAL HAZARD RISK HRVA, FALL 2020

Administrative Review

Homework 2.3

•  Lots of plagiarism and use of Google Translate •  A fire extinguisher is not a fire-fighting system, it is a component or “weapon” of

that system

•  Fire-fighting systems include fire stations, fire fighters, water-supply pipes

•  Sources? Squad discussion? Many ignored these requirements. Why? Homework 3.1

Quiz 3.2 will be given next week. It will cover Weeks 6 and 7

Midterm Exam: Week 8.

It will cover Modules 1, 2 and 3. DD/MM/YYYY DOCUMENT TITLE 2

Risk Analysis

1. Today we will address the risk analysis of natural hazards.

This means situations where the hazard’s magnitude and frequency is

independent of the asset’s vulnerability.

2.  We will first look at different definitions of risk in history. 3.  Then we will show which approach is most appropriate for natural hazards.

4.  We will analyze risk with vulnerable measured by the probability that the asset’s external defenses and internal resistance will fail.

5.  This will then permit us to analyze a wide variety of risk analysis problems.

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What is risk?

The definition has changed over time.

1.  17th century: it was another word for hazardous. 2.  18th century: it meant the probability of a hazardous impact.

3.  Early 20th century: it mean the probability that a loss will occur. 4.  1975 in the nuclear-power industry: the expected loss from a hazard.

For natural hazards

Risk = probability: won’t indicate how big the hazard magnitude will be.

Risk = hazard; doesn’t consider how well protected or vulnerable the asset may be

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Risk as Expected Negative “Utility” or Loss

Risk as expected loss, R probability of loss x loss

Let probability of loss = p

Let loss = L

So Risk, R = p x L

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Risk Analysis Example

Example:

If the probability, p, of an earthquake each year is 0.05 or 5%

The loss, L, from the earthquake’s impact is $100 million

Then the risk each year is p X L or 0.05 x $100 million = $5 million.

Meaning?

Risk of 5% each year means that you will have an earthquake every 20 years.

So, you need to save $5 million every year so you can pay for the loss of the

earthquake when it strikes.

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Risk, Hazard and Vulnerability

How then are risk, hazard and vulnerability related?

1.  Probability of loss, p is directly related to the probability of the hazard occurring. But also related to the external vulnerability of the asset.

2.  The loss, L, is directly related to the magnitude of the hazard.

3.  Example: Flooding in Jeddah 1.  Probability of harm, p is directly related to probability of rain occurring and the probability

that the sewer drainage system will fail and allow the flood waters to rise.

2.  Loss, L, is directly related to the hazard’s magnitude or amount of rain falling.

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Basic relationship between Risk, Vulnerability and Hazard

Risk, R = p(h, v) x L(z)

Where

h = probability of hazard

v = probability that protections of asset will fail or vulnerability

z = magnitude of hazard

Question 1: What has a higher probability of network failure (vulnerability) when

subject to a random attack of its nodes? Scale-free network or random network?

Question 2: What has higher probability of vulnerability from a sandstorm: a truck-

driver with orders to pull over and wait for the storm to pass, or a truck driver with

orders never to be late with his delivery? DD/MM/YYYY DOCUMENT TITLE 8

Basic Review of Probability Theory

Before we proceed, we need to review some basic probability theory

What is the probability of tossing a coin twice and getting heads each time?

This is a situation where each coin toss is completely independent of the previous coin

toss.

In other words, what happens in the first coin toss has no effect on the second coin

toss.

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Coin Toss #1

p(H) = 0.5

Tails

Heads

p(T) = 0.5

Heads

p(H/H) = 0.5

Tails

p(T/H) = 0.5

Heads

p(H/T) = 0.5

Tails

p(T/T) = 0.5

p(H and H) = 0.5 x 0.5 = 0.25

p(H and T) = 0.5 x 0.5 = 0.25

p(T and H) = 0.5 x 0.5 = 0.25

p(T and T) = 0.5 x 0.5 = 0.25

Calculating probability of loss

When the probability of the hazard is completely independent of the probability of

vulnerability (when protections fail), then

p(h, v) = h x v

Why? Basic probability theory: the hazard probability is independent of vulnerability

probability when you have a natural hazard, but not with an intentional hazard.

So, R = h x v x L(z)

What does this mean?

When the probability of a lightning strike on a mosque, h, is 1% or 0.01 each year.

The probability that the sprinkler system in the mosque won’t stop the resulting fire, v

is 5% or 0.05 for each lightning strike.

Then the probability of fire loss is 0.01 x 0.05 = 0.0005 or 0.05% DD/MM/YYYY DOCUMENT TITLE 11

Probability an Accident will occur each day?

p(S) = 0.01

Driver faces open road

Driver faces stopped car In road

p(R) = 0.99

Driver avoids collision

p(A/S) = 0.80

Driver collides into stopped car

p(C/S) = 0.2

p( S and A) = 0.01 x 0.8 = 0.008

p(S and C) = 0.01 x 0.2 = 0.002

So, probability an accident will not occur, p(R) + p(S and A) = 0.008 + 0.99 = 0.998 Probability an accident will occur each day is p(S and C) = 0.002

Calculating Risk with Hazard and Vulnerability Probabilities

Given: If you have a 30% probability that a fire will cause $1 million worth of damage,

a 40% probability that it will cause $2 million worth of damage.

Question: What is the risk of this fire?

Answer: 0.3 x $1 million + 0.4 x $2 million = $300,000 + $800,000 = $1,100,000

Or $1.1 million

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Blackout Problem

Given: A business earns $10,000 per day in revenue. Should it lose electricity, it will

not be able to operate and will lose that revenue. There is a 30% chance that a

blackout for a will last one day, a 10% chance a blackout will last two days, and a 5%

chance it will last 3 days. But the business also owns an old electrical generator that

allows it to supply its own electricity. Unfortunately, it isn’t very reliable. It has a

70% chance of operating for just one day, a 30% change of operating for two days.

Object: Determine the risk the business faces from blackouts.

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Probability an Blackout will occur each Summer

P(1B) = 0.3

One Day Blackout

Two Day Blackout

Three Day Blackout

P(2B) = 0.1

P(3B) = 0.05

One Day of Generation

P(1G/1B) = 0.70

Two Days of Generation

P(2G/1B) = 0.2

p( 1B and 1G ) = 0.3 x 0.7 = 0.21 Risk = 0

p(1B and 2G) = 0.3 x 0.2 = 0.06 Risk = 0

One Day of Gen.

P(1G/2B) = 0.70

Two Days of Gen

P(2G/2B) = 0.2

p( 2B and 1G ) = 0.1 x 0.7 = 0.07 Risk = 0.07 x 1 x $10,000 = $700

p(2B and 2G) = 0.1 x 0.2 = 0.02 Risk = 0

P(1G/3B) = 0.70

Two Days of Gen

P(2G/3B) = 0.2

p( 1G and 3B ) = 0.05 x 0.7 = 0.035 Risk = 0.035 x 2 x $10,000 = $700

P(1B and 3G) = 0.05 x 0.2 = 0.01 Risk = 0.01 x 1 x $10,000 = $100