Working Capital Management - Questions and AnswersFull description
Working Capital Management - Questions and Answers
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: (i)
(ii)
T
(v)
2
L1
2
L1
L2
OR
OR
3
2
AND
1
1
L1 OR
AND
T AND
1
T
OR
1
2
(iv)
T
OR
AND
1
(iii)
T
3
2
3
4
Figure 1 Component
Failure Probability
1
0.1
2
0.2
3
0.3
4
0.4
(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.
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. System High-level alarm Operator stops flow High-level switch system
Failures / demand 0.01 0.1 0.01
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?
Question 2 (SOLUTION):
(-mt)
1 2 3 4 5 6 7
Fl ow control val ve Le ve l me asure me nt Chart re corde r Le ve l me asure me nt Al arm Sol e nol d val ve Le ve l Swi tch / me asure me nt
Question 3: Using the system shown in Figure 3 below, draw the fault tree and determine the failure characteristics of the top event (vessel pressure exceeds MAWP)
Figure 3 – A control system to prevent the pressure from exceeding the MAWP
Question 3 (SOLUTION):
1 Le vel me asure me nt 2 Control l er 3 Pre ssure Swi tch 4 5 6 7 8
Val v e Pre ssure Me asure me nt Control l er Pre ssure Swi tch Val v e LIC = PIC = Probabili ty of top event = reli abili ty, R of top event = m of top event = MTBF =
Relia eliabilit bility y (R = e 0.779 0.670 0.741 0.670 0.368
0.076 0.7 1.7 1.776
0.927 0.497 0.183 0.169
MBTF = 1/m =
0.563
(-mt)
)
Probabi li ty (P = 1 - R) 0.221 0.330 0.259 0.330 0.632 0.073 0.503 0.817 0.831
Question 5: Using the system shown in Figure 5, draw the fault tree and determine the failure characteristics of the top event (vessel overflow). In this problem you have human intervention; that is, when the alarm sounds, someone turns off valve 7.
Figure 5 – Control system to prevent vessel overflow
Question 5 (SOLUTION):
1 2 3 4 5 6 7 12 12 & 3 & 7 456 1237 & 456
Chart Al arm Leve l me asure ment Sol enoid valve Control l e r Leve l me asure ment Hand V al ve