Risk Analysis Introduction

Transcription

1 Risk Analysis Introduction Aron Larsson SU/DSV and ITM/MIUN What is risk? An awkward feeling? An uncertainty? A probability? A measure? A numerical value? 1

2 Risk A pertinent event for which there is a textual description [Koller, 2005] the risk is that we will face severe damage in the left turbin leaving it unusable for 14 days. Risk acceptance A decision to accept arisk Risk acceptance criteria categories Threshold (absolute) values the probability of a certain accident should not exceed a certain number p Three regions Negligible ALARP Intolerable ALARP: Risk should be reduced as low as reasonably practibale Involves considerations of costs and benefits 2

3 SRA Definition The potential for realization of unwanted, adverse consequences to human life, health, property, or the environment; estimation of risk is usually based on the expected value of the conditional probability of the event occurring times the consequence of the event given that it has occurred. Society for Risk Analysis Decision making and risk Decisions under certainty Each decision alternative will lead to a known consequence Decisions under uncertainty Each decision alternative may lead to several consequences, but we cannot quantify their likelihoods Decisions made under risk Each decision alternative may lead to several consequences, and we can use probabilities biliti to quantify their likelihood lih Value consequences, obtain probabilities Risk attitudes Acceptance levels Value of risk, value of decreased risk 3

4 Risk acceptance A decision to accept arisk Risk acceptance criteria categories Threshold (absolute) values the probability of a certain accident should not exceed a certain number p Regions of tolerance ALARP: Risk should be reduced as low as reasonably practibale Involves considerations of costs and benefits Risk management principles ALARA Risks should be reduced as low as reasonably achievable ALARP Risks should be reduced as low as reasonably practicable Basic safety limit (BSL) Basic safety objective (BSO) 4

5 Tolerable region Need some risk analysis in order to position risks on this scale BSL BSO Risk analysis A detailed examination including risk assessment, risk evaluation, and risk management alternatives, performed to understand the nature of unwanted, negative consequences to human life, health, property, or the environment; an analytical process to provide information regarding undesirable events; the process of quantification of the probabilities and expected consequences for identified risks. Society for Risk Analysis 5

6 Risk analysis (cont d) Used to describe and inform on risk Establish risk picture, understand risk context Compare different decision alternatives Identify critical factors, systems, components Investigate effects of various preventive measures Determine if a risk is tolerable, put a value on the risk (assign risk index) Risk analysis (cont d) Basic - two sources of information: The likelihood of something bad occurring (for example a probability measure) The consequence, or impact, of occurence (for example a value or a description) 6

7 Risk analysis categories Main category Type of analysis Description Simplified RA Qualitative Informal procedure, establish risk picture, brainstorming, discussions. Standard RA Qualitative or Formalised procedure, quantitative recognised methods, HAZOP/coarse/matric es. Model-based RA Primarily quantitative Formal methods, calculations, eventtree, fault-tree, probability theory. Common idea of risk analysis Risk = Probability Consequence risk is given by (in some meaningful way) aggregating the value of a certain consequence with its probability of occuring. 7

8 Simple standard model Probability Consequence Risk index level 1 Low Small loss or damage Acceptable May be allowed Should be treated 2 Medium Larger loss or damage Unacceptable Not allowed Must be treated 3 High Very large loss or damage Bankruptcy Catastrophe Unforgivable Must be treated immediately Simple standard model (cont d) Risk index level is given by the sum S = Probability + Consequence S can assume integer values from 2 to 6 If S equals 2 the risk level is 1 If S equals 3 or 4 the risk level is 2 If S equals 5 or 6 the risk level is 3 often considered a too simplified approach and an informal model. A better version is by replacing + with x 8

9 A more formal model to risk index Risk is a function of unknown parameters to be estimated [Aven, 2003] A formal risk model: r = f(q 1, q n ) where r is called the risk index (a measure of risk) and the q i :s are assessed parameters Example of risk indexes: Expected number of fatalities per year (potential loss of lives - PLL) Classical approach to risk analysis using risk index Estimate each q i then r^ = f(q 1^, q n^) is the estimated risk index r^ is a function of parameters (q 1^, q n^) A very simple example could be A very simple example could be r^ = f(q 1^, q 2^) = q 1^ + q 2^ 9

10 Commonly used risk indices In safety: Potential Loss of Lives (PLL) Fatal Accident Rate (FAR) Average Individual Accident Rate (AIR) In business: Expected Value and Variance of the Portfolio Value-at-Risk (VaR) Net Risk-Weighted (Resource) Value Safety risk indices often related to an F-N curve Frequency of accidents per year (F) Number of deaths per accident (N) 10

11 Risk index in safety: Potential loss of lives (PLL) Represents average number of fatalaties in year An expectation Relative to a given system, business unit or activity Risk index in safety: Average individual risk (AIR) AIR = PLL/n 11

12 Risk index in safety: Fatal accident rate (FAR) Represents the average number of fatalaties per 100 million exposed hours FAR = [PLL / (n t)] 10 8 when n persons are at risk at any time so that the total hours of risk exposure is n*t per year refers to the time of 1000 persons present at work through a full life span. How to assess? Best-estimate estimate approaches Estimates with uncertainty analysis As the assessment are subject to uncertainty. 12

13 Best-estimateestimate approaches Results are based on cautious bestestimates of parameter values (q 1^, q n^) Typically deliberatively conservative (overestimates the risk) Event tree example: Best-estimateestimate approach with PLL X = Number of gas leakages I A Not A B Not B Y = 0 Y = 2 Y = 1 Y: number of fatalities Estimate frequency of leakages, obtain P(A) and P(B A) from data. Assume P(A) = 0.005, P(B A) = 0.1, and frequency of leakages has mean ml of 1. Then simply compute average number of fatalities per year (PLL), PLL = 1*0.005*0.1*2 + 1*0.005*0.9*1 =

14 Uncertainty analysis Two kinds of uncertainties in risk analysis Stochastic/Aleatory Variability in observable data, randomness in samples Estimates q^ with random errors Confidence intervals Epistemic/Knowledge-based Lack of knowledge about studied d phenomena, uncertainty t in the model, uncertainty in our uncertainties. Model f may be bad for various reasons Subjective probabilities Uncertainty analysis (cont d) Given probability distributions over uncertain parameters q = (q 1,, q n ) Parameters such as P(A) and P(B A) and m L We may determine the distribution over a risk index r H PLL (p) = P(PLL p) when PLL is the risk index used 14

15 Event tree example with uncertainty analysis What if we re uncertain of P(A) ( ) and P(B ( A) ) and m L? Express degrees-of-beliefs or subjective probabilities Probability distribution over possible values of P(A) and P(B A) and m L For example: P(m L = 1) = 0.5, P(m L = 0.5) = 0.25, P(m L = 2) = 0.25 Note: = 1 P(PLL ) = 0.25 P(PLL ) = 0.75 P(PLL 0.011) 011) = 1 Yields uncertainty distributions for the risk index used, not a single value r! Uncertainty analysis (cont d) Instead of a single number for r, we may use credibility intervals P(a r b) = H r (b) - H r (a) P(a r b) = 90% meaning that our probability is 90% that the value for r is contained in the interval [a, b] 15

16 Uncertainty analysis (cont d) m L P(A) = p A P(B A) = p B A P(m L = 0.5) = 0.25 P(p A = 0.001) = 0.25 P(p B A = 0.05) = 0.25 P(m L = 1) = 0.5 P(p A = 0.005) = 0.5 P(p B A = 0.1) = 0.25 P(m L = 2) = 0.25 P(p A = 0.01) = 0.25 P(p B A = 0.2) = 0.25 m L = Number of expected gas leakages A B Y = 2 Not B Y = 1 Y = 0 Y: number of fatalities Uncertainty analysis (cont d) Uncertainty distribution for FAR value 16

17 Uncertainty analysis (cont d) FAR distribution given by this event tree modelled in DecideIT. Risk analysis process model Quantitative work Model r = f(q) Risk description Best estimates of r Uncertainty assessments of r, P(r r ) Predictions E(r) Sensitivity analysis Probability calculus Uncertainty Assessments P( q q ) Qualitative work Risk analyst s understanding of the world Background information, knowledge, experience, data The world Observable quantitie Probabilities Consequences 17

18 Sensitivity analysis the core theme [of sensitivity analysis] is the variation of input variables to a model to investigate their effect on the output variables (S. French: Modelling, Making Inferences and Making Decisions: The Roles of Sensitivity Analysis, TOP 11/2, 2003) Sensitivity analysis Although this holds: E(r) = E(f(q)) = f(e(q)) So, in our simple case only modelling uncertainty of m L : E(PLL) = 1.125*0.005*0.1* *0.005*0.9*1 = It is wise to study changes in input parameters of the risk model Typical approach: One-way sensitivity analysis Study effects of varying one parameter More advanced: Multi-way sensitivity analysis Study effects of varying more than one paratemer simultaneously 18

19 Readings Aven Chapters (not 2.1.3)