RASM Chapter 6a

Information about RASM Chapter 6a

Published on July 21, 2014

Author: pthomp

Source: authorstream.com

Content

PowerPoint Presentation: Risk Assessment and Safety Management QUANTITATIVE RISK ASSESSMENT TECHNIQUES Dr Pauline Thompson PowerPoint Presentation: Aims It is essential that all safety professionals understand the basic concepts of probability Those studying SRRE will undertake more complex techniques in other courses But all students need to understand the basics of quantitative assessment so it is used properly PowerPoint Presentation: Basics of Probability The chance of an event happening Formally measured on a scale of 0-1 Close to 0 means unlikely to happen Close to 1 means very likely to happen Informally measured on a percentage scale PowerPoint Presentation: Concepts of Probability Revision from Chapter 1 = Concept: 0 < P < 1, P = 0 = cannot happen, P = 1 = will definitely happen Classical: Theory or reason e.g. coins = chance of heads = ½ = 0.5 Not much use in complex systems Relative frequency Comparison with measured data e.g. use historical data on failure of equipment per year Only possible with lots of data Subjective For unique events where probability must be guessed Guess can be improved by a panel of experts PowerPoint Presentation: Estimating Probability Values Relative frequency most often used in real world From empirical data e.g. Light bulbs designed to last 1000h. Tests show 1 in 400 fail before this. Probability that a light bulb does not last 1000 hours is 1/400 = 0.025 A frequentist approach – e.g. collection of data for RIDDOR By subjective estimate e.g. Neighbour estimates a shop is open 95% of normal working hours Used if reasoning not possible and no data available Beware of bias NOT the same as subjective probability for unique events By probabilistic modelling e.g. Variety of component parts in a system Combine likelihood of parts working needed for successful operation Often use a combination PowerPoint Presentation: Example Estimate: the likelihood of a lifting operation leading to a ‘lost time injury. Operations are carried out 60 times a year in each plant In your 13 years experience you have only heard of 2 accidents which might be attributable to lifting in 28 similar plants you have visited. You would need to make a subjective judgement about which plants to include based on the degree of similarity, and whether both accidents were attributable primarily to the nature of the lifting operation rather than some other cause. PowerPoint Presentation: Example Estimate: the likelihood of a lifting operation leading to a ‘lost time injury. If you decided everything should be included, the following estimates : Number of opportunities on which an accident could have happened during the 13 years, considering all plants, ( N ), N = 60  13  28 = 21 840 Estimated probability of a ‘lost time’ accident in any lifting operation ( P ), - or just over 9 per 100 000 operations. Probability of occurrence of such an accident in any single plant in a year, given about 60 such lifting operations per year ( P ANNUAL ), P ANNUAL = P  60 = 5.5  10 -3 = 5 to 6 per 1000 years , in a single plant PowerPoint Presentation: Probability and Event it relates to Probability is a number between 0<1 (no units). Important to relate it to an event and conditions/time period e.g. probability of a person being killed in a road accident would normally relate to the period of a year A probability of 10 -4 (1 in 10 thousand), might relate to the event ‘any single member of the population is killed by a car in a road accident during a period of one year’ PowerPoint Presentation: The System Changes Things change with time: e.g. probability of a person being killed in a road accident would be much more now than when there were fewer cars on the road Data from previous periods may not be valid If make assumptions about data it must be clear PowerPoint Presentation: Frequency Must distinguish probability from frequency: Frequency expressed in number of events per time period e.g . if for a member of the population: probability of being killed by a car in a road accident in a year is 10 -4 the frequency is the number of people killed by cars in road accidents in a year. Frequency = the probability (10 -4 ) x the population, (50 million) = 5000. Not necessarily between 0 and 1, although sometimes it may be. e.g., if 10 people are killed over a period of 20 years, the frequency is 0.5 deaths per year. This is not a probability. Frequency is a more useful concept when trying to convey to the general public what a probability might mean as it is more imaginable. PowerPoint Presentation: Relation to set theory ‘ Universal Set’, Ω (‘omega’), = the set of all possible outcomes and is referred to as the ‘sample space’. An event is, therefore, a sub-set of the sample space Probability of X = area of subset/area of Ω e.g. roughly half of the readers of this course might be female PowerPoint Presentation: Axioms of probability Three basic axioms of probability i.e . all probabilities must lie between 0 and 1 . where means not X. (i.e. the unshaded area ( Ω - X )) P(X∩Y ) = P(X/Y) P(Y) i.e. the intersection of two events The probability P(X/Y) is the conditional probability of event X occurring, given that event Y has occurred and P(X∩Y ) is the probability of both X and Y happening. PowerPoint Presentation: Intersections X ∩ Y is an intersection of X and Y = ‘ both X and Y occur P(X ∩ Y ) is the probability of both X and Y occurring. E.g.: P(Y) is the probability of the event ‘person falls from ladder in a year ’ P(X) is the probability of the event ‘person is killed in a year’ Part of the set X which is within Y represents a person being killed given that they fall from a ladder, in a year P(X∩ Y) is the probability of a person falling from a ladder AND being killed as a result P(X/Y) is the proportion of people killed that have fallen off a ladder Easier to follow in a rearranged version of Axiom 3: PowerPoint Presentation: Intersections Alternatively as shown by a Venn Diagram: PowerPoint Presentation: Independent Events If the probability of event X is not influenced by the event Y then P(X/Y) = P(X) In this case axiom 3 above becomes equivalent to X and Y are then called independent events. CAVEAT: it is extremely important to distinguish between conditional events and independent events and not to regard events as independent if they are in fact conditional or else wrong probabilities will result at the end. PowerPoint Presentation: Independent Events For example, consider the two probabilities: P(A) = Probability of explosion in facility Z in a year P(B) = Probability of gas leak in facility Z in a year If one wished to know the probability of an explosion and a gas leak occurring in facility Z in a year it would not be given by because an explosion depends upon a gas leak occurring first The probability of an explosion and a gas leak occurring in a year is where: P(C) = P(Explosion in facility Z in a year/ gas leak in facility Z in a year) = P(A/B) PowerPoint Presentation: Independent Events To put some numbers on it: P(B) may be, say, 10 -3 and P(C) may be 0.5, The probability of a gas leak and an explosion in facility Z in a year would be = 0.5 x 10 -3 = 5 x 10 -4 However , if the only fuel source for an explosion is a gas leak, then the whole of subset A lies within subset B and so P(A ) = 5 x 10 -4 Had we erroneously considered A and B to be independent events and had not used the conditional probability but instead simply multiplied P(A) and P(B) we would have got P(A ) P(B) = 5 x 10 -4 x 10 -3 = 5 x 10 -7 which would not be the probability of an explosion and a gas leak in facility Z in a year and would seriously underestimate the probability. PowerPoint Presentation: AND gates The probability of an intersection of events = AND gate In general, P(C ) = P(A/B) P(B ) Independent events P(C) = P(A) P(B)

Related presentations


Other presentations created by pthomp

RASM Chapter 3
30. 05. 2014
0 views

RASM Chapter 3

RASM Chapter 2
30. 05. 2014
0 views

RASM Chapter 2

RASM Chapter 1a
30. 05. 2014
0 views

RASM Chapter 1a

RASM Chapter 1b
30. 05. 2014
0 views

RASM Chapter 1b

IntroCourse2014a
13. 06. 2014
0 views

IntroCourse2014a

IntroCourse2014b
13. 06. 2014
0 views

IntroCourse2014b

RASM Chapter 4
13. 06. 2014
0 views

RASM Chapter 4

RASM Chapter 5
11. 07. 2014
0 views

RASM Chapter 5

RASM Chapter 6b
21. 07. 2014
0 views

RASM Chapter 6b

RASM Chapter 7
23. 07. 2014
0 views

RASM Chapter 7

RASM Chapter 8
23. 07. 2014
0 views

RASM Chapter 8

RASM Chapter 9
24. 07. 2014
0 views

RASM Chapter 9

RASM Chapter 10
24. 07. 2014
0 views

RASM Chapter 10

Fire Chapter 1
28. 07. 2014
0 views

Fire Chapter 1

Fire Chapter 2
28. 07. 2014
0 views

Fire Chapter 2

Fire Chapter 3
30. 07. 2014
0 views

Fire Chapter 3

Fire Chapter 4
31. 07. 2014
0 views

Fire Chapter 4

Fire Chapter 6b
14. 08. 2014
0 views

Fire Chapter 6b

LFD Chapter 4
08. 03. 2015
0 views

LFD Chapter 4

IntroCourse2015b
29. 04. 2015
0 views

IntroCourse2015b

IntroCourse2015a
29. 04. 2015
0 views

IntroCourse2015a

GeologySoils1_Intro
21. 06. 2016
0 views

GeologySoils1_Intro

GeologySoils13_Cohesive
21. 06. 2016
0 views

GeologySoils13_Cohesive

GeologySoils12_Granular
21. 06. 2016
0 views

GeologySoils12_Granular

GeologySoils16A_SlopeFailure
23. 06. 2016
0 views

GeologySoils16A_SlopeFailure

GeologySoils16B_SlopeFailure
23. 06. 2016
0 views

GeologySoils16B_SlopeFailure

GeologySoils15B_Subsidence
23. 06. 2016
0 views

GeologySoils15B_Subsidence

GeologySoils15A_Subsidence
23. 06. 2016
0 views

GeologySoils15A_Subsidence

GeologySoils17B_SlopeFailure
27. 06. 2016
0 views

GeologySoils17B_SlopeFailure

GeologySoils17A_SlopeFailure
27. 06. 2016
0 views

GeologySoils17A_SlopeFailure

GeologySoils16B_Subsidence
27. 06. 2016
0 views

GeologySoils16B_Subsidence

GeologySoils16A_Subsidence
27. 06. 2016
0 views

GeologySoils16A_Subsidence