Part 2 – Lecture 3 Fault Tree Analysis - FCEEfcee.utm.my/.../blogs.dir/86/files/2015/03/RAAM-P2L3Fault-Tree.pdf · The fault tree developed consists of many levels of basic events

innovative ● entrepreneurial ● global www.utm.my innovative ● entrepreneurial ● global www.utm.my

Part 2 – Lecture 3 Fault Tree Analysis

Dr. Arshad Ahmad Email: [email protected]

1


What is Fault Tree Analysis

2

innovative ● entrepreneurial ● global www.utm.my

Fault Tree Analysis (FTA) §  FTA is an effect and cause diagram that uses standard

symbols developed in the defense industry and is used heavily in safety engineering.

§  FTA is a structured approach for analyzing the root causes of a failure mode not yet fully understood

§  In Fault Tree, undesired system failure mode can be expressed in terms of component failure modes and operator actions.

§  FTA is an alternative to Ishikawa (Fish Bone) Diagrams. Many feel that FTA is better suited to understanding layers and relationships of causes of equipment failures.

3


Fault Tree Analysis (FTA)

4

§  FTA is used to model the failure of a system resulting from multiple components

§  In FTA, the system failure mode to be considered is termed the “top event” and fault tree is developed in branches below this event showing it causes., connected by using logic gate


Basic Fault Tree Structure

TOP EVENT

BASIC EVENTS

INTERMEDIATE EVENT

INTERMEDIATE EVENT

BASIC EVENTS

5


Basic Elements of FTA

“OR” gate is used when output event occurs if any one of the input event occurs.

TOP EVENT is often signified by a double box.

“And” gate is used to indicate that output event occurs if all input event occurs simultaneously.

TOP EVENT

INTERM. EVENT

INTERMEDIATE EVENT is signified by a single box.

Base Event: Potential root failure which cannot be broken down into lesser failures

Event: Potential Failures which is not analyzed for various reasons

6


Understanding the Gates

AND gate means, for this upper failure to occur, all of these failures must occur

Failure

Failure

OR gate means that for this upper failure to occur, only one of these failures must occur

7

innovative ● entrepreneurial ● global www.utm.my 8

Developing FTA

Step 1 Identify Top Level Fault

Step 2 Brainstorm first level contributors

Step 3 Link contributors to top by logic gates

Step 4 Brainstorm second level contributors

basic event cannot be broken down any further

event that is not analyzed for various reasons

Step 5 Link contributors to upper level by logic gates

Step 6 Repeat / continue for each lower level failure


Example: Pump

§  A system to pump acetic acid from the supply tank to the process is illustrated in figure.

§  The system function automatically. §  When the regulator is energized, one of the pumps is started and

acid passes through the feed pipes; if no acid is detected in the feed pipe the second pump is started.

§  Construct a fault tree with the top event “no flow to the process”. §  To make your life easier, consider failure modes listed here.

§  Is there any other notable failures not listed should be considered?

9


P1

M

S

P2

F1

F2

E

C1 C2

R

E : ELECTRICITY

F1,F2 : FEED PIPES

M : MANIFOLD

P1,P2 : PUMPS

R : REGULATOR

S : SUPPLY TANK

Example: Pump

C1, C2 : CABLES

10


Component Symbol Failure Mode

Cables C1 + C2 short-circuit

Electricity supply E power cut Feed pipes F1 + F2 rupture of pipe

Manifold M rupture Pumps P1 + P2 fail to start

Regulator R fail to open on Supply tank S level too low

Failure Modes to Consider

11


Fault Tree

NO FLOW TO PROCESS

GENERAL PROBLEMS PROBLEMS WITH PUMPS

Regulator fails

Tanks level

too low

Power cut

Manifold M

fails

PUMP P1 PROBLEMS PUMP P2 PROBLEMS

Pipe P1 ruptures

Pump P1 fails to start

Cable C1 short circuits

Pipe P2 ruptures

Pumps P2 fails to start


12


Class Workshop

Work in your Group to draw a fault Tree for the following accident scenario

1.   Explosion of a Diesel Tank 2.   A car hitting the rear bumper of another car

on a highway

3.   Flash fire at a gas station

Draw the fault tree and present to the class

13


FTA Computations

14


Fault Tree Computations

§  The objective is to determine the failure rates of the top event, either expressed as probability or frequency of failure.

15

Intermediate Event, C

Base Event 2, B Base Event 1, A

For OR gate, C= A+B

Intermediate Event, C

Base Event 2, B Base Event 1, A

For AND gate, C= A.B


Frequency (failure/year) = probability of failure per operation × number of operation per year

AND GATE rules :

can multiply P and P = unit of probability

can multiply P and F = unit of F

cannot multiply F and F = unit F2 (for example failure/yr2)

OR GATE rules :

can add P and P = unit of P

can add F and F = unit F

cannot add F and P =different unit

RULES for AND GATES

P(A.B) = PA.PB F(AB) = FA.PB

Unit on Fault Tree and Rules

16


Fault Tree Example NO FLOW TO

PROCESS

GENERAL PROBLEMS PROBLEMS WITH PUMPS

Regulator fails

Tanks level

too low

Power cut

Manifold M

fails

PUMP P1 PROBLEMS PUMP P2 PROBLEMS

Pipe P1 ruptures

Pump P1 fails to start


Pipe P2 ruptures

Pumps P2 fails to start


0.1 0.01

0.02 0.02

0.05 0.01 0.1 0.02

0.02

0.01+0.02+0.1 =0.13

0.01+0.02+0.1 =0.13

0.13(0.13)= 0.0169 0.02+0.05+0.02+0.01 =0.1

0.01

0.1+0.0169=0.1169


Class Workshop

Work in your Group to draw a fault Tree for the following accident scenario

FAILURE OF SMOKE DETECTOR The indicator light is on… yet even with sufficient

amounts of smoke directly below the detector vents the alarm does not signal.

Draw the fault tree, compute the probability and present to the class

18


Class Workshop Functional Block Diagram for Smoke Detector

19

Inputs Presence of

smoke

Process Detection of smoke

Outputs Alarm signaling

Smoke enters through vent

Smoke is ionized and causes

increase in voltage

Signal sent from smoke detector triggers control box

circuit

Signal/power to siren turns motor

Smoke enters ionization chamber

Control Box sends signal/power to siren

Motor causes siren to sound

Alarm signals

Battery powers control box, indicator light, and smoke

detector


CUT SET

20


Cut Set

§  A CUT SET is a combination of basic events which will produce TOP EVENT

§  A cut set is said to be a minimal cut set if, when any basic event is removed from the set, the remaining events collectively are no longer a cut set

21


Minimal Cut Set

§  The fault tree developed consists of many levels of basic events and sub-events linked together by AND gates and OR gates.

§  Minimal cut set analysis rearranges the fault tree so that any basic event that appears in different parts of the fault tree is not "double counted" in the quantitative evaluation.

§  The result of minimal cut set analysis is a new fault tree, logically equivalent to the original, consisting of an OR gate beneath the top event, whose inputs are the minimal cut sets.

§  Each minimal cut set is an AND gate containing a set of basic inputs necessary and sufficient to cause the top event.

§  Software is available to produce minimal cutset. Boolean Algebra is used for the analyses

22


Boolean Algebra Rule Mathematical Form

Idempotent Rule A.A=A A+A=A

Absorption Rule A.(A+B)=A A+A.B = A

Commutative Rule A.B = B.A A+B = B+A

Associative Rule A.(B.C) = (A.B).C A+(B+C)=(A+B)+C

Distributive Rule A.(B+C)=A.B+A.C

23

CUTSETS ARE ANALYZED/FORMULATED USING BOOLEAN ALGEBRA

A ∩ A = A A ∪ A = A

A ∩ ( B ∩ C ) = (A ∩ B) ∩ C A ∪ ( B ∪ C ) = (A ∪ B) ∪ C

A ∩ B = B ∩ A A ∪ B = B ∪ A

A ∩ (A ∪ B) = A A ∪ (A ∩ B) = A

A ∩ ( B ∪ C ) = (A ∩ B) ∪ (A ∩ C)


Example 1 :Cut set

PUMP FAIL

PUMP B FAILS

Failure of Power Supply

Pump A Mechanical Failure


Pump B Mechanical Failure

M W M Z

PUMP A FAILS

M, M.Z, W.M, W.Z are all cut set

Why?

Because, from the base element, the path will lead to the top event

A CUT SET is a combination of basic events which will produce TOP EVENT

Minimal CUT SET is a CUT SET if any basic event is removed the TOP EVENT will not occur

24


Example 1 – Minimal Cut Set

PUMP FAIL

PUMP B FAILS





M W M Z

PUMP A FAILS

Original Cutset

PUMP FAIL

Mechanical Failure of Pumps



M

W Z


Minimal Cutset

25


Boolean Rules Differences to numerical manipulation Indempotent A+A=A

A.A=A Absorption A+A.B=A

A.(A+B)=A For example : (M+W) . (M+Z) = M.M + M.Z +W.M +W.Z = M + M.Z +W.M +W.Z = (M + M.Z +M.W) + W.Z = M+ W.Z

A CUT SET = combination of basic events which will produce TOP EVENT

In the example :

M, M.Z, W.M, W.Z are all cut set

But

Minimal CUT SET is a CUT SET if any basic event is removed the TOP EVENT will not occur

Therefore MINIMAL CUT SET is M and W.Z

……can redraw the FAULT TREE…..

Boolean Algebra and Minimal Cut Set

26


Example 1 – Minimal Cut Set

PUMP FAIL

PUMP B FAILS





M W M Z

PUMP A FAILS

Original Cutset

Consider the following probability -  Electrical supply failure M=0.1 -  Single Pump Failure, W= Z=0.25

PUMP FAIL

Mechanical Failure of Pumps



M

W Z


Minimal Cutset

P=M+(W.Z) P=0.1+(0.25)(0.25) P=0.1625

P=(M+W)(M+Z) P=(0.1+0.25)(0.1+0.25) P=0.1225

27


§  Observation from Example 1: •  Before minimal cut set, Probability of pump fail = 0.1225

•  After minimal cut set, Probability of pump fail = 0.1625

28


TOP EVENT

A B

D C E C

D E

–

29


(A + B) . [ (C + D) . (E + C) + (D.E) ]

= (A + B) . (C.E + D.E + C.C + D.C + D.E )

= (A + B) . (C.E + D.E + C + D.C + D.E )

= (A + B) . (C + C.E + D.E + D.C + D.E )

= (A + B) . (C + C.D + C.E + D.E + D.E )

= (A + B) . (C + C.D + C.E + D.E)

= (A + B) . (C + C.E + D.E)

= (A + B) . (C + D.E )

–

30

IDEMPOTENT LAW

ABSORPTION LAW


TOP EVENT

A B C

D E

–

31


Class Workshop

Work in your Group to draw to develop the Minimal Cut Set for the given fault tree

Draw the fault tree and present to the class

32


FTA’s Do’s and Don’ts

§  Do’s •  Start at the Top

•  Think Categories

•  Brainstorm, then organize

•  Facilitate proper brainstorming

•  Know when to stop •  Have action plans for all circles

•  Check that branches terminate with a circle or diamond

•  Revisit the FBD or FTA when new data is found

•  Use yellow stickies to capture the brainstormed causes

§  Don'ts •  Don’t get bogged down

•  Don’t jump to solutions!


FTA and FMEA

34

PRODUCT FAILURE

PART FAILURE

Failure Mode & Effect Analysis (FMEA)

Fault Tree Analysis (FTA)


END OF LECTURE

35

Documents

Part 2 – Lecture 3 Fault Tree Analysis - FCEEfcee.utm.my/.../blogs.dir/86/files/2015/03/RAAM-P2L3Fault-Tree.pdf · The fault tree developed consists of many levels of basic events