causal & frequency analysis · 2016-10-18 · the cause and effect (ce) diagram (ishikawa...
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innovative ● entrepreneurial ● global www.utm.my Arshad Ahmad
arshad@utm.my
Causal & Frequency Analysis
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Fishbone Diagram
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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.
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Fishbone Diagram
Cause 4 Cause 1
Cause 3 Cause 2
EFFECT
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Reliability Block Diagram
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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
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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
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Reliability of Parallel Systems
( ) ( ) ( )[ ]nnss
RRRFFFFR−•−•−−=⋅⋅⋅••−=−=1...111
11
21
21
( )∏=
−−=n
iis RR
1110.99
0.85
0.98
99997.0=sR
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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
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For constant per-unit failure rates (example: two systems in parallel)
( )( )( )ttt
system
ttsystem
2121
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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
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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)
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Fault Tree Analysis
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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
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Basic Fault Tree Structure
BASIC EVENTS
TOP EVENT
INTERMEDIATEEVENT
INTERMEDIATEEVENT
BASIC EVENTS
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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
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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.
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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
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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
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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
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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
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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
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Class Workshop
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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
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RBD & Fault Tree
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FT & its equivalent RBD
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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.
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FT & RBD
d a b
c b
b
a
d b
c
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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
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Class Workshop 1 Functional Block Diagram for Smoke Detector
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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
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Class Workshop 2
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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
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END OF LECTURE
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