CN3135 PROCESS SAFETY, HEALTH AND ENVIRONMENT (RELIABILITY ENGINEERING TUTORIAL) Question 1: Given the fault tree gates shown in Figure 1 below and the following set of failure probabilities: AND T L1 1 2 OR L2 3 4 OR T 1 OR AND L1 3 2 AND T 1 L1 2 3 OR T 1 2 OR AND T 2 1 (i) (ii) (iii) (iv) (v) Figure 1 (a) Determine an expression for the probability of the top event in terms of the component failure probabilities. (b) Determine the minimal cut sets. (c) Compute a value for the failure probability of the top event. Use both the expression of part (a) and the fault tree itself. Component Failure Probability 1 0.1 2 0.2 3 0.3 4 0.4
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CN3135 PROCESS SAFETY, HEALTH AND ENVIRONMENT
(RELIABILITY ENGINEERING TUTORIAL)
Question 1:
Given the fault tree gates shown in Figure 1 below and the following set of failure
probabilities:
AND
T
L1
1 2
OR
L2
3 4
OR
T
1
OR
AND
L1
32
AND
T
1L1
2 3
OR
T
1 2
ORAND
T
21
(i) (ii) (iii) (iv)
(v)
Figure 1
(a) Determine an expression for the probability of the top event in terms of the component
failure probabilities.
(b) Determine the minimal cut sets.
(c) Compute a value for the failure probability of the top event. Use both the expression of
part (a) and the fault tree itself.
Component Failure Probability
1 0.1
2 0.2
3 0.3
4 0.4
Question 1 (SOLUTION):
Question 2:
The storage tank system shown in Figure 2 is used to store process feedstock. Overfilling of
storage tanks is a common problem in the process industries. To prevent overfilling, the
storage tank is equipped with a high-level alarm and a high-level shutdown system. The
high-level shutdown system is connected to a solenoid valve that stops the flow of input
stock.
Figure 2 – Level Control System with Alarm
(a) Develop an event tree for this system using the “failure of level indicator” as the
initiating event. Given that the level indicator fails 4 times / yr, estimate the number of
overflows expected per year. Use the data in the table provided above.
(b) Develop a fault tree for the top event of “storage tank overflows.” Use the data in Table
12-1 (from Textbook) to estimate the failure probability of the top event and the
expected number of occurrences per year. Determine the minimal cut sets. What are
the most likely failure modes? Should the design be improved?