Fault Tree Analysis

Failures in Process Industries

• Single Component Failure

– Data for failure rates are compiled by industry

– Single component or single action

• Multiple Component Failure

– Failures resulting from several failures and/or

actions

– Failure rates determined using FTA

Instrument Faults/year

Controller 0.29

Control valve 0.60

Flow measurements (fluids) 1.14

Flow measurements (solids) 3.75

Flow switch 1.12

Gas – liquid chromatograph 30.6

Hand valve 0.13

Indicator lamp 0.044

Level measurements (liquids) 1.70

Level measurements (solids) 6.86

Failure Rates Data

Instrument Faults/year

Oxygen analyser 5.65

pH meter 5.88

Pressure measurement 1.41

Pressure relief valve 0.022

Pressure switch 0.14

Solenoid valve 0.42

Stepper motor 0.044

Strip chart recorder 0.22

Thermocouple temperature meas. 0.52

Thermometer temperature meas. 0.027

Valve positioner 0.44

Failure Rates Data

Failure Rates Data

Component

Failure Frequency

(hr-1) Component

Failure Frequency

(hr-1)

Gasket Failure (leak) 1.00 x 10-06 Pump Seal Failure 8.00 x 10-07

Gasket Failure (total) 1.00 x 10-07 Alarm Failure 1.00 x 10-05

Pipe Rupture (> 3 in) 1.00 x 10-10 Operator Error 2.00 x 10-05

Pipe Rupture (< 3 in) 1.00 x 10-09 Hose Rupture 2.00 x 10-05

Valve Rupture 1.00 x 10-08

• Some data are per hour

Frequency, Reliability and Probability

p = 1- e-mt

where p is the annual probability of occurrence, m is the annual frequency and t is time period (i.e., 1 year).

Component Failure Rate m(faults/year)

Reliability R=e(-mt)

Failure Probability

P=1-R

Control Valve 0.6 0.55 0.45

Controller 0.29 0.75 0.25

DP Cell 1.41 0.24 0.76

Conversion is important in OR gate (dimensional homogeneity)

Frequency and Probability - Example

taking the case of gasket failure and assumingthat we have 10 gaskets, the annual probability ofoccurrence is:

137-

year 10 x 8.7210

year

hr 8760

hr

10 x 1exp1p

What is Fault Tree Analysis

• Fault Tree is a method by which a particular

undesired system failure mode can be

expressed in terms of component failure

modes and operator actions.

• 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.

• Fault tree analysis is typically carried out by

a group or people or an individual.

• These individuals must have knowledge on

the process so that causes of undesirable

events can be understood

• The following information is important

• process and equipment description and

specification

• process flow diagram, process instrumentation

diagram and design information

• plant operation, human factors and

environmental factors

Fault Tree Analysis

Two basic Element

• The two mostly used gate symbol are “and” &

“or” gates.

– “And” gate is used to indicate that output event

occurs if all input event occurs simultaneously.

– “Or” gate is used when output event occurs if any

one of the input event occurs.

• Event symbol mostly used is “Rectangle” to

show any event. Signify the TOP EVENT by a

double box.

FTA Procedure

1. Define top event

2. Choose events identified by hazard identification

method (i.e HAZOP) which can lead to this top

event.

3. Decide on the hierarchical construction of fault

tree

4. Construct fault tree. All inputs to a particular gate

should be completely defined before further

analysis of one of them is undertaken.

5. Quantify the base events

6. Quantify the top event

FTA Procedure

7. Analyze results to determine the

significance of particular base events or

combination events

8. Carry out sensitivity analysis to test the

following factors:

– uncertainty of basic data

– effect of improving reliability of plant and

control systems

– effect of varying method of operation on the

plant

– effect of plant modernization

– effect of improved training of operators

Underlying Principles

• Causes of undesirable events can only be

understood with knowledge on how the system

functions through:

– chemical/physical processes in the plant

– specific information on the whole process

– data on hazardous properties of materials

– process flow diagram and process instrumentation

diagram

– equipment specification

– plant operation

– human factors and environmental factors

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?

P1M

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

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

PROBLEM 1 - SIMPLIFIED SYSTEM

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

Cable C2 short circuits

Fault Tree

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

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

PROBLEM 1 - SIMPLIFIED SYSTEM

PUMP FAIL

PUMP A FAILS PUMP B FAILS

Failure of Power Supply

Pump A Mechanical Failure

Failure of Power Supply

Pump B Mechanical Failure

M W M Z

Example – Minimal Cut Set

Unit on FTA

• Quantify Fault Tree

• Electrical supply failure, P = 0.1

• Single pump failure, P = 0.25

• Referring to Fault Tree :

– Before minimal cut set, Probability of pump fail =

0.1225

– After minimal cut set, Probability of pump fail =

0.1625

PROBLEM 1 - SIMPLIFIED SYSTEM

PUMP FAIL

FAILURE OF

POWER SUPPLYMECHANICAL FAILURE OF

PUMPS

Pump A

Mechanical

Failure

Pump B

Mechanical

Failure

M

W Z

Example -Minimum Cut Set

TOP EVENT

A B

DC E C

D E

Boolean Algebra-Minimum Cut Set

(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 )

INDEMPOTENT LAW

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

ABSORPTION LAW

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

Boolean Algebra-Minimum Cut Set

TOP EVENT

A BC

D E

Boolean Algebra-Minimum Cut Set