causal & frequency analysis · 2016-10-18 · the cause and effect (ce) diagram (ishikawa...

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

[email protected]

Causal & Frequency Analysis

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

Fishbone Diagram

2

innovative ● entrepreneurial ● global www.utm.my

The Cause and Effect (CE) Diagram (Ishikawa Fishbone)

§  Created in 1943 by Professor Kaoru Ishikawa of Tokyo University §  Used to investigate a problem, exploring, identifying, and displaying

the possible causes. §  Main Objective

•  To identify the causes of a defined critical event in a system. •  To classify the causes into groups. •  To acquire and structure the relevant knowledge and experience of the study team.

§  The cause and effect diagram analysis is done by a study team as a brainstorming session.


Fishbone Diagram

Cause 4 Cause 1

Cause 3 Cause 2

EFFECT


Reliability Block Diagram

5


Reliability Block Diagram

§  A reliability block diagram shows the logical connections of functioning items that are needed to fulfill a specified system function.

§  Each function is represented as a functional block and is drawn as a square

§  The RBD Systems can be connected in series or parallel configuration

6


Reliability of Series Systems

ns RRRR ...21 ••= ∏=

=n

iis RR

1

0.99 0.85 0.98 825.0=sR

!!

Ri(t)= e−λit !!!!!!!!!!!!!!!

Rsystem = e−λit∏ !!!!!!!!!!!Rsystem = e−Λt !!!!!!!!!!!!!!Λ = λi∑

For constant per-unit failure rates

innovative ● entrepreneurial ● global www.utm.my EML4550 -- 2007

Reliability of Parallel Systems

( ) ( ) ( )[ ]nnss

RRRFFFFR−•−•−−=⋅⋅⋅••−=−=1...111

11

21

21

( )∏=

−−=n

iis RR

1110.99

0.85

0.98

99997.0=sR


Example §  Find the system reliability of the following combinational system with both serial and

parallel arrangements. Assume all sub-systems have a reliability of 0.9

1

2

3

4

5 6

[ ][ ][ ][ ]

889.0)9.0)(99.0)(999.0(]9.0[)1.0)(1.0(1)1.0)(1.0)(1.0(1

)1)(1(1)1)(1)(1(1))()((

654321

654321

==−−=

−−−−−−−== +++

RRRRRRRRRRs


For constant per-unit failure rates (example: two systems in parallel)

( )( )( )ttt

system

ttsystem

2121

21

eeeR

e1e11Rλ+λ−λ−λ−

λ−λ−

−+=

−−−=

§  System does not have constant per-unit failure rate even if components do §  System reliability for parallel systems is always greater than the most reliable

component §  Most systems are not designed in parallel (redundancy) due to cost considerations

(unless needed due to safety and life-protection considerations) •  Series

•  Transmission line, Power train •  Parallel

•  Multiple airplane engines, Two headlights


Reliability of Large Systems

§  Most systems are neither parallel nor series, but a hybrid combination

§  Calculation of overall system reliability, however, is done following the simple principle shown before

§  Parallel systems are used when extremely high reliability is needed (by use of redundancy)


Fault Tree Analysis

12


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

13


Basic Fault Tree Structure

BASIC EVENTS

TOP EVENT

INTERMEDIATEEVENT

INTERMEDIATEEVENT

BASIC EVENTS

14

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 Elements of Fault Tree Event Symbol Meaning of Symbols

Undeveloped event.

Not analyzed for various reasons

Event represented by a gate

Diamond

Rectangle

Transfer symbolTriangles

Basic event with sufficient dataCircle

AND gate

OR gate

Output event occurs if all input events occur simultaneously.

Output event occurs if any one of the input events occurs.


Understanding the GatesAND 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

16

innovative ● entrepreneurial ● global www.utm.my 17

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


P1

M

S

P2

F1

F2

E

C1 C2

R

E : ELECTRICITYF1,F2 : FEED PIPES M : MANIFOLD

P1,P2 : PUMPSR : REGULATORS : SUPPLY TANK

Example: Pump

C1, C2 : CABLES

•  Acetic acid is pumped automatically from the supply tank to the process. •  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”.

P1


Component Symbol Failure Mode

Cables C1 + C2 short-circuitElectricity supply E power cutFeed pipes F1 + F2 rupture of pipeManifold M rupturePumps P1 + P2 fail to startRegulator R fail to open Supply tank S level too low

Failure Modes to Consider

19


Fault TreeNO 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 F1 ruptures

Pump P1 fails to start

Cable C1 short circuits

Pipe F2 ruptures

Pumps P2 fails to start

Cable C2 short circuits

20


Class Workshop

21


Class Workshop

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

1.  Explosion of a Diesel Tank2.  A car hitting the rear bumper of another car on a highway3.  Flash fire at a gas station

§  Draw the fault tree and present to the class

22


RBD & Fault Tree

23


FT & its equivalent RBD

24

FAULT TREE ANALYSIS 277

(i)

(ii)

(iii)

Figure 10.6 Relationship between some simple fault tree diagrams and reliability block diagrams.

cut set can be represented as a single parallel structure with r items, where r is the order of the minimal cut set. All the r items in this parallel structure have to fail for the minimal cut set to fail.

Let C j (t) be the event where minimal cut set C j is failed at time t, for j = 1,2, ... , k. The TOP event occurs at time t when at least one of the minimal cut sets fails at t, and can therefore be expressed as

(l D.I)

The fault tree can therefore be represented by an alternative top structure, the minimal cut set fault trees connected through a single OR-gate, as illustrated in Figure I D. 7.

To save space, the rectangles describing the basic events are omitted in Figure 1 D. 7. Each minimal cut set is drawn here with three basic events. The basic events in min-imal cut set j are illustrated by the symbols j.l, j.2, and j.3, for j = I, 2, ... , k. In a real fault tree, the minimal cuts sets will be of different orders and the same basic event may be a member of several minimal cut sets.


FT & RBD

d a b

c b

b

a

d b

c


Class Workshop

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

FAILURE OF SMOKE DETECTORThe 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

26


Class Workshop 1 Functional Block Diagram for Smoke Detector

27

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


Class Workshop 2

28

Top Event: No Fuel to Pump When RequestedDraw the equivalent Fault Tree Diagram

FUEL DELIVEREDFUEL SUPPLY

Block Valve A

Block Valve B

Control Valve A

Control Valve BPump


END OF LECTURE

29

causal & frequency analysis · 2016-10-18 · the cause and effect (ce) diagram (ishikawa...

Documents