#1. Fault tree diagram and quantitative analysis

Perform a fault tree analysis of the Containment Spray Injection System (CSIS).

(a) Construct a fault tree diagram with "insufficient fluid flow through the CSIS nozzles in containment" as the top undesirable event (UE). Include all relevant fault events in the diagram, even if some have a negligible probability. Your fault tree diagram should consist of these basic symbols:

 

i. Node text boxes that contain the text for all fault events, and

ii. "AND" or "OR" gates that connect them.

 

You don't need to include any more sophisticated symbols than these basic ones.

(b) Calculate and assign fault probabilities to each of the fault event nodes, from the bottom events to the top UE. Use the given constant probabilities for each component and fault event. Assign fault probability of zero to the events with a negligible probability. Show the main steps of your calculations.

 

#2. Quantitative analysis of fault tree by simulation

Instead of the given constant probabilities used in Question 1, assume the lifetimes/arrival time of all components/fault events follow exponential distributions, and that their failure rates, λ, are also uncertain and follow Weibull distributions with the parameters provided in the attached document.

 

(a) Find the distribution of the probabilities of the top UE occurring within one year by simulation, using 1000 replications. (Submit your Excel spreadsheet or JMP file used for simulation as attachment to your PDF file.)

Hints:

i. Follow the example on slide 38 and 39 of the .ppt file under Lecture 9 Fault Tree

Analysis on Blackboard. The corresponding Excel file Lec 10 Fault_Tree_for_Tank_Chart.pdf" is posted under the same lecture title.

 

Steps of simulation:

 

ii. Look up the Weibull distribution parameters for each of the component/fault events based on their constant probabilities and Table 1.

iii. Generate λ, the failure rate from Weibull distributions with the parameters found from the previous step.

iv. Calculate the failure probability of each component/fault event within one year, i.e. 12 months using exponential distribution with the failure rates generated in the previous step.