Lecture 1 – Putting Safety Into Perspective– Single component or single action
• Multiple Component Failure
actions
Instrument Faults/year
Controller 0.29
(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)
Controller 0.29 0.75 0.25
Conversion is important in OR gate (dimensional homogeneity)
Frequency and Probability - Example
taking the case of gasket failure and assuming that we have 10 gaskets, the annual probability of occurrence is:
13 7-
year
• 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.
developed in branches below this event
showing it causes.
a group or people or an individual.
• These individuals must have knowledge on
the process so that causes of undesirable
events can be understood
specification
diagram and design information
environmental factors
“or” gates.
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
method (i.e HAZOP) which can lead to this top
event.
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
combination events
following factors:
control systems
plant
Underlying Principles
functions through:
– specific information on the whole process
– data on hazardous properties of materials
– process flow diagram and process instrumentation
diagram
Example: Pump
• A system to pump acetic acid from the supply tank
to the process is illustrated in figure.
• The system function automatically.
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”.
listed here.
be considered?
P1 M
Feed pipes F1 + F2 rupture of pipe
Manifold M rupture
Regulator R fail to open on Supply
tank S level too low
Failure Modes to Consider
PROBLEM 1 - SIMPLIFIED SYSTEM
NO FLOW TO PROCESS
Pipe P1 ruptures
Cable C1 short circuits
Cable C2 short circuits
AND GATE rules :
cannot multiply F and F = unit F2 (for example failure/yr2)
OR GATE rules :
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
Boolean Rules
= M+ W.Z
A CUT SET = combination of basic events which will produce TOP EVENT
In the example :
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
Failure of Power Supply
Failure of Power Supply
M W M Z
Example – Minimal Cut Set
• Referring to Fault Tree :
0.1225
0.1625
PUMPS
INDEMPOTENT LAW
ABSORPTION LAW