N 2. a) Systems A and B failures are represented by fault trees with common basic...

  

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N 2. a) Systems A and B failures are represented by fault trees with common basic events (figure Q2a and Q2b respectively). These are standby systems that are required to mitigate the event of an initiating event. From historical records the initiating event has occurred 20 times in the past ten years. As these are standby systems, the preferred analysis method is using an Event Tree, shown in figure Q2c. The consequence of each of the four outcomes, 1 to 4, are 1, 20, 50 and 100 fatalities respectively. System A Failure 1) ii) Gate 1 Gate 2 52 Figure Q2a Initiating Event W Sys A Gate 1 A E B W Sys B F W System B Failure F 2 3 4 Outcome Gate 2 E G Figure Q2b Figure Q2c The probability of failure of each component is assumed fixed at 0.1. Using each of the methods below, calculate the frequency of each outcome (1 to 4). Note use the minimal cut set upper bound approximation for the probability evaluation of any outcome with more than three terms. using the coherent event tree method. using the exact event tree solution. [2 marks] [5 marks] iii) iv) What is the total risk using the exact method. [2 marks] Comment on any further analysis that might be carried out and how you might change the safety system set up to reduce the overall risk. [5 marks] b) Given the system shown in Figure Q2d, determine: i) ii) Birnbaum's importance ranking for each component (assuming probability of component failure is 0.1). The derivation of the rankings must be shown. [3 marks] A B D Figure Q2d C Comment on how you would interpret these results from the ranking in part bi) - explain what other factors or calculations you may need to consider. [3 marks] N 2. a) Systems A and B failures are represented by fault trees with common basic events (figure Q2a and Q2b respectively). These are standby systems that are required to mitigate the event of an initiating event. From historical records the initiating event has occurred 20 times in the past ten years. As these are standby systems, the preferred analysis method is using an Event Tree, shown in figure Q2c. The consequence of each of the four outcomes, 1 to 4, are 1, 20, 50 and 100 fatalities respectively. System A Failure 1) ii) Gate 1 Gate 2 52 Figure Q2a Initiating Event W Sys A Gate 1 A E B W Sys B F W System B Failure F 2 3 4 Outcome Gate 2 E G Figure Q2b Figure Q2c The probability of failure of each component is assumed fixed at 0.1. Using each of the methods below, calculate the frequency of each outcome (1 to 4). Note use the minimal cut set upper bound approximation for the probability evaluation of any outcome with more than three terms. using the coherent event tree method. using the exact event tree solution. [2 marks] [5 marks] iii) iv) What is the total risk using the exact method. [2 marks] Comment on any further analysis that might be carried out and how you might change the safety system set up to reduce the overall risk. [5 marks] b) Given the system shown in Figure Q2d, determine: i) ii) Birnbaum's importance ranking for each component (assuming probability of component failure is 0.1). The derivation of the rankings must be shown. [3 marks] A B D Figure Q2d C Comment on how you would interpret these results from the ranking in part bi) - explain what other factors or calculations you may need to consider. [3 marks]

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