Frequency Analysis

5/28/2018 Frequency Analysis

1/55

Frequency

Analysis


2/55

Objective

Frequency Analysis determines the likelihood of anevent to occur

The larger the number, the bigger the likelihood or

chance for the event to occur.


3/55

Techniques

Among others, two techniques are frequently used

1. Event-Tree analysis

2. Fault Tree Analysis


4/55

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 termedthe top event and fault tree is developed in

branches below this event showing it causes.,

connected by using logic gate


5/55

Example: Fault Tree of Pool Fire


6/55

Event Tree Analysis

An event tree is a visual representation of all the events

which can occur in a system.

The goal of an event tree is to determine the probability of

an event based on the outcomes of each event in the

chronological sequence of events leading up to it.

As the number of events increases, the picture fans out like

the branches of a tree.

By analyzing all possible outcomes, you can determine the

percentage of outcomes which lead to the desired result.


7/55

Example

This event tree was constructed to analyze the possible outcomes of a

system fire. The system has 2 components designed to handle this event:

a sprinkler system and an automated call to the fire department. If the fire

department is not notified, the fire will be mostly contained by the

sprinkler system. If the sprinkler system fails as well, the system will be

destroyed.


8/55

Fault Tree

Analysis


9/55

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


10/55

Instrument Faults/year

Controller 0.29

Control valve 0.60

Flow measurements (fluids) 1.14

Flow measurements (solids) 3.75Flow switch 1.12

Gasliquid chromatograph 30.6

Hand valve 0.13

Indicator lamp 0.044

Level measurements (liquids) 1.70

Level measurements (solids) 6.86

Failure Rates Data


11/55

Instrument Faults/year

Oxygen analyser 5.65

pH meter 5.88

Pressure measurement 1.41

Pressure relief valve 0.022Pressure 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


12/55

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


13/55

Frequency, Reliability and Probability

p = 1- e-mtwhere p is the annual probability of occurrence,mis the annual frequency and t is time period

(i.e., 1 year).

Component Failure Rate

(faults/year)

Reliability

R=e(-mt)

Failure

ProbabilityP=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)


14/55

Frequency and Probability - Example

taking the case of gasket failure and assuming

that we have 10 gaskets, the annual probability of

occurrence is:

137-

year10x8.7210

year

hr8760

hr

10x1exp1p


15/55

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.


16/55

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 instrumentationdiagram and design information

plant operation, human factors and

environmental factors

Fault Tree Analysis


17/55

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.


18/55

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


19/55

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


20/55

Underlying Principles

Causes of undesirable events can only be understoodwith 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


21/55

Example: Pump

A system to pump acetic acid from the supply tank to theprocess 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 detectedin 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?


22/55

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


23/55

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


24/55

PROBLEM 1 - SIMPLIFIED SYSTEM

NO FLOW TO

PROCESS

GENERAL PROBLEMS

PROBLEMS WITH

PUMPS

Regulator

fails

Tankslevel

too low

Power cut

ManifoldM

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


25/55

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


26/55

Boolean RulesDifferences to numericalmanipulation

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 basicevents 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


27/55


PUMP FAIL

PUMP A FAILS PUMP B FAILS

Failure ofPower

Supply

Pump AMechanic

al Failure

Failure of

Power

Supply

Pump B

Mechanic

al Failure

M W M Z

ExampleMinimal Cut Set


28/55

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


29/55


PUMP FAIL

FAILURE OFPOWER SUPPLY

MECHANICAL FAILURE OFPUMPS

Pump AMechanicalFailure

Pump BMechanicalFailure

M

W Z

Example -Minimum Cut Set


30/55

TOP EVENT

A B

DC E C

D E

Boolean Algebra-Minimum Cut Set


31/55

(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 )



32/55

TOP EVENT

A BC

D E



33/55

Event Tree

Analysis


34/55

Consequence spectrum

An accidental event is defined as the first significant

deviation from a normal situation that may lead to

unwanted consequences (e.g., gas leak, falling object, start

of fire)

An accidental event may lead to many different

consequences. The potential consequences may beillustrated by a consequence spectrum

Accidental

Event

C1

Cn

C2


35/55

Barrier

Most well designed systems have one or more

barriers that are implemented to stop or reduce the

consequences of potential accidental events.

The probability that an accidental event will lead to

unwanted consequences will therefore depend onwhether these barriers are functioning or not.

Barriers are also called safety functions or

protection layers, and may be technical and/oradministrative (organizational).


36/55

Cause of a Consequence

Failure of barrier

Other Factors

Whether a gas release is ignited or not

Whether or not there are people present when the

accidental event occurs Wind direction when the accidental event


37/55

Event Tree Analysis

An event tree analysis (ETA) is an inductive procedure that

shows all possible outcomes resulting from an accidental(initiating) event, taking into account whether installed

safety barriers are functioning or not, and additional events

and factors.

By studying all relevant accidental events (that have beenidentified by a preliminary hazard analysis, a HAZOP, or

some other technique), the ETA can be used to identify all

potential accident scenarios and sequences in a complex

system. Design and procedural weaknesses can be identified, and

probabilities of the various outcomes from an accidental

event can be determined.


38/55

Event Tree Analysis

Simplerthan fault-tree analysis:

Sequence frequencies are products

Can combine sequences by taking sums

However, more judgmentis required in how to model

a system as an event tree Basic goal is to keep the model as simple as

possible:

By taking advantage of independence and conditional

independence relations

l l


39/55

Example: Explosion


40/55

Steps in Constructing Event Tree

1. Identify (and define) a relevant accidental (initial) event

that may give rise to unwanted consequences

2. Identify the barriers that are designed to deal with the

accidental event

3. Construct the event tree4. Describe the (potential) resulting accident sequences

5. Determine the frequency of the accidental event and the

(conditional) probabilities of the branches in the event tree

6. Calculate the probabilities/frequencies for the identified

consequences (outcomes)

7. Compile and present the results from the analysis


41/55

Accidental Event

When defining an accident event, we should answer thefollowing questions:

What type of event is it? (e.g., leak, fire)

Where does the event take place? (e.g., in the control room)

When does the event occur? (e.g., during normal operation, during

maintenance)

In practical applications there are sometimes discussions

about what should be considered an accidental event (e.g.,

should we start with a gas leak, the resulting fire or anexplosion). Whenever feasible, we should always start with

the first significant deviation that may lead to unwanted

consequences.


42/55

Accidental Event

An accidental event may be caused by:

System or equipment failure

Human error

Process upset The accidental event is normally anticipated. The

system designers have put in barriers that are

designed to respond to the event by terminating

the accident sequence or by mitigating theconsequences of the accident.


43/55

Accidental Event

For each accidental event we should identify:

The potential accident progression(s)

System dependencies

Conditional system responses


44/55

Barriers

The barriers that are relevant for a specificaccidental event should be listed in the sequence

they will be activated.

Examples include:

Automatic detection systems (e.g., fire detection)

Automatic safety systems (e.g., fire extinguishing)

Alarms warning personnel/operators

Procedures and operator actions

Mitigating barriers

/


45/55

Additional Events/Factors

Additional events and/or factors should be listedtogether with the barriers, as far as possible in the

sequence when they may take place.

Some examples of additional events/factors weregiven on a previous slide


46/55

Event Sequence

Each barrier should be described by a (negative) statement,

e.g., Barrier X does not function (This means that barrier Xis not able to performs its required function(s) when the

specified accidental event occurs in the specified context).

Additional events and factors should also be described by

(worst case) statements, e.g., gas is ignited, wind blowstoward dwelling area.

Accidental

Event

Additional

Accidental

Event

Barrier I

does not

function

Barrier II

does not

function

Barrier III

does not

function

Additional

Accidental

Event

Outcome /

Consequence

True

False

By this way the most severe consequenceswill come first


47/55

Outcome Alternatives

In most applications only two alternatives (trueand false) are considered. It is, however, possible

to have three or more alternatives, as shown in the

example below:

Wind toward residential area

Wind toward Factory

Wind toward empty area

Gas Release

d


48/55

End Outcomes

In practice, many event trees are ended before the final

consequences are reached

Including these final consequences may give very large

event trees that are impractical for visualization

This is solved by establishing a consequence distribution foreach end event and the probability of each consequence is

determined for each end event

In effect, this is an extension of the event tree, but it gives a

more elegant and simpler presentation and also eases thesummary of the end results

l i i i ki


49/55

Results in Decision Making

The results from the event tree analysis may be

used to:

Judge the acceptability of the system

Identify improvement opportunities Make recommendations for improvements

Justify allocation of resources for improvements

d


50/55

End Events

Out-

come

descr.

Freq-

uency

Loss of Lives

0 1-5 >5

Material Damage

N L M H

Environmental

Damage

N L M H

P d C


51/55

Pros and Cons Positive

Visualize event chains following an accidental event Visualize barriers and sequence of activation

Good basis for evaluating the need

Negative

No standard for the graphical representation of the event

tree

Only one initiating event can be studied in each analysis

Easy to overlook subtle system dependencies Not well suited for handling common cause failures in the

quantitative analyses

The event tree does not show acts of omission

G i E l


52/55

Generic Example

F i f O


53/55

Frequencies of Outcome

Let denote the frequency of the accidental (initiating) event.

Let Pr(Bi) denote the probability of event B(i).

When we know that the accidental event has occurred, the

probability of Outcome 1 is:

Note that all the probabilities are conditional given the result of the process

until barrier i is reached. The frequency of Outcome 1 is:

)BBBPr(BEvent)Accidental1Pr(Outcome 4321 )BBBBPr().BBBPr().BBPr().Pr(B 3214213121

The frequencies of the other outcomes are determined in a similar way.

)BBBBPr( 4321

Pi li L k E t T


54/55

Pipeline Leak Event Tree

G i li R t E t


55/55

Gas pipeline Rupture Event

Check for error

Frequency Analysis

Documents

Transcript of Frequency Analysis