Why Risk Models Should be Parameterised

1. Why Risk Models Should be Parameterised William Marsh, william@dcs.qmul.ac.uk Risk Assessment and Decision Analysis Research Group

2. Acknowledgements • Joint work with George BearfieldRail Safety and Standards Board (RSSB), London

3. Aims • Introduce idea of a ‘parameterised risk model’ • Explain how a Bayesian Network is used to represent a parameterised risk model • Argue that a parameterised risk model is • Clearer • More useful

4. Outline • Background • Risk analysis using fault and event trees • Bayesian networks • An example parameterised risk model • Using parameterised risk model

5. no 80% no 95% no 95% yes 20% yes 5% no 75% yes 5% no 95% yes 25% yes 5% Fault and Event Trees Outcome • Quantitive Risk Analysis Hazardous event OR Events AND AND Base event

6. RSSB’s Safety Risk Model • 110 hazardous events • Fault and event trees • Data from past incidents • UK rail network • Average • Used to monitor risk for rail users and workers • Informs safety decision making

7. Mild Normal Severe 70% 20% 10% Conditional Probability Table Yes No 80% 20% Bayesian Networks • Uncertainvariables • Probabilistic dependencies Bayes’ Theorem Incline Speed Fall

8. Bayesian Networks • Uncertainvariables • Probabilistic dependencies • Efficient inference algorithms Bayes’ Theorem Mild Normal Severe 0% 0% 100% Incline Speed Fall Yes No 60% 40%

9. Example Parameterised Risk Model

10. Falls on Stairs • Falls on stairs common accident • 500 falls on stairs / year (2001) • Influenced by • stair design & maintenance • the users’ age, gender, physical fitness and behaviour • Injuries • Non fatal: bruises, bone fractures and sprains … • Fatal injuries: fractures to the skull, trunk, lower limbs

11. Fault Tree Lose Footing OR GATE 2 AND AND Misstep GATE 3 GATE 4 TripHazard Imbalance Slip Inattention

12. Events and Outcomes Break LoseFooting Holds Falls sideways Vertical yes Forward-short forward no Forward-long drops yes Backward-short backward no Backward-long holds Startled

13. Events and Outcomes Break LoseFooting Holds Falls sideways Vertical yes Forward-short forward no Forward-long drops yes Backward-short backward no Backward-long holds Startled

14. Can the Model be Generalised? • Logic of accidents same (nearly) but numbers vary with design • Reuse logic • Estimating probabilities once only

15. Factors – Risk Model Parameters • Factors with discrete values

16. Factors to Base Events • Base event probabilities depend on factors

17. Factors to Events • Probabilities of event branches depend on factors • … also on earlier events

18. FT Bayesian Network

19. Event Tree Bayesian Network

20. Accident Injury Score (AIS) • Harm from accident

21. Complete Bayesian Network AgenaRisk see: http://www.agenarisk.com/

22. Explicit Factors make Clearer Models • Are there factors in the fault or event tree? Age Break LoseFooting Holds Falls sideways Vertical yes Forward-short forward no Forward-long yes Backward-short backward no drops Backward-long yes Forward-short forward no Forward-long yes Backward-short backward no holds Backward-long Startled

23. Using the Parameterised Model Reuse of the model Modelling multiple scenarios

24. Prior probability distribution Using the Parameterised Model • Observe (some) factors

25. Using the Parameterised Model • Suppose 3 stairs • Value of each observed factor

26. Results – Outcome • Probability distribution • Outcome of a ‘stair descent’ • Hidden ‘nothing happens’ outcome

27. Results – Accident Injury Score

28. System Risk • University has many stairs in different buildings • How to assess the total risk? • Solution 1 • Used parameterised model for each stairs • Aggregate results • Solution 2 • Model ‘scenario’ in the Bayesian Network • Scenario: each state has shared characteristics e.g. geographical area

29. Scenario • Each value is a ‘scenario’ for which we wish to estimate risk Could be each staircase

30. Imprecise Scenarios • Imagine three departments • Factors do not have single value • Probability distribution over factor values

31. Departments Proportion of events in each scenario Exposure • Some scenarios more common • Distribution of ‘stair descents’

32. Using the System Model • Use 1 • Select a scenario • … like the parameterised model • Scaled by total system events

33. Using the System Model • Use 2 • Whole system risk, • … weighted by exposure for each scenario

34. Parameterised Risk Models in Practice Improving Safety Decision Making

35. Better Safety Decision Making • Safety benefits of improvements • Existing models only support system-wide improvements • Detection of local excess risk • E.g. poor maintenance in one area • Requires risk distribution (not average) • … variations in equipment type and condition • … procedural and staffing variations

36. Risk Profile: Sector and Network

37. Derailment Event tree Investigation found the cause to be: ‘the poor condition of points 2182A at the time of the incident, and that this resulted from inappropriate adjustment and from insufficient maintenance ….’ Factors Fault tree

38. Summary • Parameterised ET + FT • Using Bayesian Networks • Factors made explicit • Clearer and more compact • Reuse of risk model • Risk profiles • Guide changes to reduce risk • Challenge of including more causes Thank You