reliability
DESCRIPTION
ReliabilityTRANSCRIPT
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Federal University of
Technology Owerri
Reliability
By
Prof. Chukwudebe G.N. and Diala U.H.
2nd Semester April. 2013 ECE 510 Reliability and Quality Assurance in Electronics
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RISK
Major accidents in recent years have taken a sad toll of lives:
Bhopal Chernobyl Piper Alpha Challenger
So have natural disasters:
Bam December 26 Tsunami
The immediate reaction is always “ It must never happen again”
We need to eliminate hazards as far as possible and reduce
the risks so that the remaining hazards are only a small
addition to the inherent risks of everyday life
RELIABILITY & RISK ANALYSIS TECHNIQUES are the
methods used to assess the safety of modern complex systems
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RELIABILITY
Definition Reliability is the ability of a product
to perform as intended ( that is without failure and
within specified performance limits )
for a specified mission time
when used in the manner and for the purposes
intended
under specified application and operational
conditions
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RELIABILITY
Alternative Definition
Reliability is the probability that a device or system
properly performs its intended function
over time
when operated within the environment for which it
is designed
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RELIABILITY
Definition stresses 4 elements
Probability quantitative
Adequate performance must be defined
Time the period over which we can expect a
certain degree of performance
Operating conditions temperature, humidity,
shock, vibration
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RELIABILITY
Characteristics of a Product
Estimated in Design
Controlled in Manufacturing
Measured during Testing
Sustained in the Field
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RELIABILITY
Importance of Reliability
In this modern day of science and technology where
complex devices are used for commercial, military,
scientific, consumer and pleasure purposes
A high degree of reliability is an absolute necessity
There is too much at stake in terms of cost and
human life to take any significant risks with devices
that might not function properly when needed most
2nd Semester April. 2013 ECE 510 Reliability and Quality Assurance in Electronics
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RELIABILITY
First we will deal with
Foundation of Reliability
Probability and Statistics
Then
In-depth reliability engineering considerations
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Objective
To give an overview of
The reliability issues
Techniques
Tasks
Limitations associated with
The design
Manufacture
Operation
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Probability & Statistics
Pragmatic approach
Discussion will include
Shape of failure distributions
Estimating parameters
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RELIABILITY
Focus on
Preventing failures through
Robust design and manufacturing practices
Based on
Life cycle loads and stresses
Product architecture
Potential defects and failure mechanisms
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RELIABILITY
There are 2 strands in Reliability
FAULT AVOIDANCE
Conservative Design
High Quality Components
FAULT TOLERANCE
Assumes despite all efforts components will fail
USE REDUNDANCY
Price in efficiency
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RELIABILITY
The Characteristics of a Product are:
Estimated in Design
Controlled in Manufacturing
Measured during Testing
Sustained in the Field
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RELIABILITY
Random input
Variables
Output
performance
Characteristics
Continuous
{x}
Discrete
{y}
Binary
{z}
Performance Characteristics of an engineering product
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Quality ProductionThe Quality of a Product
Performance characteristics may be Continuous. Fuel consumption
these are objective can be accurately establishedby independent measurements and not dependenton the opinion of an individual
Discrete. Visual appeal, body stylethese are subjective based on some scale like (5)excellent (4) Good……..
Binary Based on some feature that the productdoes or does not possess. Presence or absenceof sun roof…..
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Continuous {x} Discrete {y} Binary {z}
Urban fuel
consumption
Visual appeal of body and
style
Leaded/ unleaded petrol?
Time from 0 to
60m.p.h.
Visual appeal of interior Starts first time?
Braking distance
at 60m.p.h.
Comfort of ride Central locking?
Engine noise level Range of exterior colours Quad stereo?
% CO2 in exhaust Range of interior colours Tinted glass?
Maximum speed Power assisted steering?
Sun-roof?
PERFORMANCE CHARACTERISTICS
FOR A FAMILY CAR
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Specification
The manufacturer of an engineering product will need toproduce a specification
defines the product for a potential customer.Consists of a set of target values x1T, x2T, a target vector {xT}
Urban fuel consumption 40 miles per gallon
Maximum speed 100 miles per hour
Time from 0 to 60m.p.h. 13 seconds
Braking distance at 60m.p.h. 180 feet
Engine noise level 70dB
% CO2 in exhaust 1%
Random effects X1T + 1
Tolerance limits Tolerance vector {}
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RELIABILITY
Target performance {xT}
Tolerance {}
Reject if :
the actual performance {x} lies outside {xT }
Both manufacturer and customer need to know how the actual
random variations in a given performance characteristic {x} for a
given product, across different individual units and under different
environmental and operating conditions, compare with the target and
tolerance values {xT} and { }.
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RELIABILITY
A statistical analysis of the variations is required.
This involves calculating:
Mean
Standard deviation
Probability
Probability density function
To do this we require N sample values of the
performance characteristic {x} specified by xi where
i = 1,2,………N
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RELIABILITY
xi i = N
i = 1
1 N
Mean x =
Standard Deviation = (xi - x)2 i = N
i = 1
1 N
Root mean square xRMS = (xi)2
i = N
i = 1
1 N
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RELIABILITY
F
a
I
l
u
r
e
R
a
t
e Time
Infant Mortality
Period Operating Period Wear-out Period
System Failure Rate The Bathtub Curve
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The infant mortality period or debugging stage
Failures typically caused by manufacturing flaws
Damage received in transit
Damage received in handling
The operating period
Smaller failure rate
Failure rate tends to remain constant
Failure typically due to only to chance
Failure generally results from severe, unpredictable and
usually unavoidable stresses that arise from environmental
factors such as vibrations, temperature, shock and pressure.
THE BATHTUB CURVE
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The wear-out period
Failure rate increases rapidly
Failure as a result of gradual degradation of some
property of the system essential to proper operation
The degradation may occur from causes such as
fatigue, creep, corrosion and abrasion
We are most interested in the period between infant
mortality and wear-out.
In this period we have
Constant failure rate
Exponential failure time density function
THE BATHTUB CURVE
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RELIABILITY
Failure Rate
Assume at t = 0 we have N0 articles
At time t = t we observe Ns have survived
The number failed is NF
So
N0 = NS(t) + NF (t)
And
R(t) = NS(t) / N0
R(t) is the Reliability as a function of time
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Ns
N0
Ns(t)
Time t t+t
Graph of NS vs t
The failure rate is the limit
as t 0 of
(the gradient at t) NS
RELIABILITY
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RELIABILITY
The reliability R of a product can be defined
as the probability that the product continues to meet
some specification
The unreliability F of a product can be
defined as the probability that the product fails to
meet the specification
Both reliability and unreliability vary with time
R(t) decreases with time
F(t) increases with time
R(t) + F(t) = 1
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PRACTICAL RELIABILITY
DEFINITIONS
Non- repairable items
Suppose that N individual items of a given non-repairable
product are placed in service and the times at which failures
occur are recorded during a test interval T
Further assume that all N items fail during T and the ith failure
occurs at time Ti
i.e. Ti is the survival time or up time for the ith failure
The total up time for N failures is therefore
and the mean time to failure is given by
I =N
I =1 Ti
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PRACTICAL RELIABILITY
DEFINITIONS
Mean Time To Fail = Total up time
Number of failures
Ti i = N
i = 1
1
N MTTF =
i.e.
Mean Failure Rate = Number of Failures
Total up time
= Ti i = N
i = 1
N
i.e. The mean failure rate is
the reciprocal of MTTF
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Mean Time To Failure & Mean Time Between Failures
MTTFN
fti
i
N
1
1
fti is TTF
MTTFN
t Nf t dt tf t dt
1
0 0
[ ( ) ] ( )
or total life for N devices = N MTTF
and between t and t+t the number live is NR(t)
MTTF R t dt( )0
Repair
Time
LIVE
Under
Repair
TTF
TBF
REPAIRABLE SYSTEMS
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PRACTICAL RELIABILITY
DEFINITIONS
T1
T2
TN
There are N survivors at
time t = 0, N - i at t = Ti,
decreasing to zero at
time t = T. The figure
shows the probability of
survival, i.e. the
reliability, Ri = (N-i) / N
decreases from Ri = 1 at
t = 0, to Ri = 0 at t = T.
MTTF = Total area under
graph
1
R
t 0 1/N
2/N
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Quantification of Reliability
Reliability⇛The probability that a system/component
works Availability⇛The probability that a system/component
works on demand Availability at time t ⇛The probability that a system /
component works on demand Availability⇛The fraction of the total time that a system /
component can perform its required function
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t
dttftF0
)()(
Quantification of Reliability
Unavailability = 1 - Availability
Unreliability = 1 - Reliability
For the failure process let
F(t) = P[a given component fails in [0,t)]
The corresponding probability density function f(t) is therefore
dt
tdFtf
)()(
So f(t)dt = P[a component fails in time period [t, t + dt)]
So
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Quantification of Reliability
Transition to the failed state can be characterised by the
conditional failure rate h(t).
This function is sometimes referred to as the hazard rate or
hazard function.
This parameter is a measure of the rate at which failures
occur taking into account the size of the population with the
potential to fail, i.e. those that are still functioning at time t:
So
h(t)dt = P[a component fails in time period t, t + dt| it has
not failed in [0, t)]
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Quantification of Reliability
For conditional probabilities we can write:
)( BAP)(
)(
BP
BAP
Since h(t)dt is a conditional probability we can define events A
and B as follows by comparing this with the equation above:
A — Component fails between t and t + t+dt
B — component has not failed in[0, t)
With events defined like this P(A B) = P(A) since if the
component fails between t and t+dt it is implicit that it cannot
have failed before time t
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Quantification of Reliability
P[component fails between t and t+dt]
P[component not fail in [0, t)] h(t)dt =
= )(1
)(
tF
dttf
Integrating gives ')'(1
)'(')'(
00
dttF
tfdtth
tt
t
dtth0
')'( = -ln[1-F(t)]
F(t) = 1-exp
t
dtth0
')'(
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Quantification of Reliability
F(t) = 1-exp
t
dtth0
')'(
If h(t), the failure rate or hazard rate for a general system or
component is plotted against time we get the bathtub curve.
In the useful life period h(t) = is constant.
So after integration F(t) = 1-e-t
And the reliability, the probability that the component works
continuously over (0, t] is the exponential function
R(t) = e-t
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System Mean Time to Failure
When system failure can be tolerated and repair can
be instigated an important measure of the system
performance is the system availability
A = MTBF + MTTR
MTBF
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QUANTIFIED RISK ASSESSMENT
SYSTEM LIFE CYCLE
MANUFACTURING PHASE
SYSTEM
DEFINITION
PHASE
CONCEPT
DESIGN
PHASE
DETAIL
DESIGN
PHASE
OPERATING PHASE
Establish
reliability
requirements
Set provisional
reliability/
availability
targets
Prepare
reliability
specification
Perform global
safety/
availability
assessment
Identify critical
areas and
components
Confirm /
review targets
FMEA / FTA of
critical systems
and components
Review reliability
database
Carry out
detailed system
reliability
assessment
Prepare safety
case
Prepare and
implement
reliability
specifications
Review reliability
demonstrations
Audit reliability
performance
Collect and
analyse
reliability, test
and
maintenance
data
Assess reliability
impact of
modifications
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RELIABILITY
CRITICAL FAILURES
Where failure causes total loss of function
MAJOR FAILURES
Where failure causes major loss of function but
the product can still be used to some extent
MINOR FAILURES
Where failure leaves the product still able to be
used to perform the major function but with the
loss of some convenience function
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A reliability network is a representation of the reliability dependencies between components of a system
Dependencies are used in such a way as to represent the means by which the system will function
Such a network can be used to assess the probability of failure of a system
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The functional behaviour of most systems can be
characterised by a network diagram
Nodes denote the subsystems
Branches of the network represent the functional
relationship between these subsystemsExample
A high voltage supply system consisting
of two transmitters A and B and
a power supply.
For the system to work
the power supply and at least one of
the transmitters must operate
A path must exist between C and D for the system to work.
Power
Supply
Transmitter A
Transmitter B
C D
TOPOLOGICAL RELIABILITY
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The question of what constitutes proper operation or proper function for a particular type of equipment is usually specific to the equipment
Rather than attempt to suggest a general definition for proper function we assume that the appropriate definition for a device of interest has been specified
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We can represent the functional status of the device as
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Φ { 1 if the device functions properly
0 if the device has failed
Note that this representation is intentionally binary.
We assume that the status of the equipment of interest is either
satisfactory or failed.
There are many types of equipment where one or more de-rated
states are possible and methods have been developed to cope.
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We presume that most equipment is comprised of components and that the status of the device is determined by the status of the components.
Let n be the number of components that make up the device and define the component status
variables xi as
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xi{ 1 if the device functions properly
0 if the device has failed
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The set of n components that make up the device is represented by the
component status vector: x = { x1, x2,…………, xn } The dependence of the device status on the
component status is represented by the function
Φ = Φ(x) referred to as a “system structure function” or a “system status function” or simply as a “structure”
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There are 4 generic types of structural relationships between a device and its components.
1. Series
2. Parallel
3. k out of n
4. All others
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SERIES SYSTEMS Definition
A series system is one in which all components must function properly in order for the system to function properly.
Reliability block diagram of a series system
Conceptual analogue Series electrical circuit
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1 2 3
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TOPOLOGICAL RELIABILITY
Example 2
In an aircraft electronics system consisting of
a sensor subsystem,
guidance subsystem,
computer subsystem and
fire control subsystem
the system can only operate successfully if these four subsystems operate
NOTE: The figure only depicts the functional relationship required for system
operation and does not necessarily mean that these subsystems are electrically
wired together in series.
Sensor Guidance Computer Fire Control
Examples where components are not physically connected:
The set of legs on a 3-legged stool. The set of tyres on a car.
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SERIES SYSTEMS For the series structure the requirement that all
components must function implies that an algebraic form for the structure function is:
n
Φ(x) = ∏xi i=1
Only the functioning of all components results in system function
49
1 2 3
Examples x1= x2 = 1, x3 = 0 results in Φ(x) = 0 x1= x2 = x3 = 0 results in Φ(x) = 0 x1= x2 = x3 = 1 results in Φ(x) = 1
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PARALLEL SYSTEMS Definition
A parallel system is one in which any one component must function properly in order for the system to function properly.
Reliability block diagram of a series system Conceptual analogue Parallel electrical circuit
50
1
2
3
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PARALLEL SYSTEMS
51
1
2
3
Similar to the series the structure function for
the parallel system may be expressed as: n
Φ(x) = 1- ∏ (1- xi) i=1
Examples
x1= x2 = 1, x3 = 0 results in Φ(x) = 1 x1= 1, x2 = x3 = 0 results in Φ(x) = 1 x1= x2 = x3 = 0 results in Φ(x) = 0
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PARALLEL SYSTEMS Parallel systems are often referred to as Redundancy Often, but not always, the parallel components are identical There are actually several ways in which the redundancy may be implemented This diversity can lead to different reliability under different environmental conditions A distinction is made between redundancy obtained using a parallel structure in which all components function simultaneously (ACTIVE REDUNDANCY) and that obtained using parallel components of which one functions and the other or others wait as standby units (STANDBY REDUNDANCY).
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k-out-of-n SYSTEMS Definition
A k-out-of-n system is one in which any k of the n components that comprise the system must function properly in order for the system to function properly.
53
1
2
3
4
k-out-of-n
Example cases for a 3-out-4 system x1= x2 = x3 = 1, x4 = 0 results in Φ(x) = 1 x1= x2 = 1, x3 = x4 = 0 results in Φ(x) = 0 x1= x2 = x3 = 0, x4 = 1 results in Φ(x) = 0
Φ(x)={ 1 if i=1
∑n
xi ≥ k
0 otherwise
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TOPOLOGICAL RELIABILITY
Example 3
In a computer system with a computer, a controller, and three
memory units suppose that the system can only satisfy its
operational requirements if at least two of the three memory units
are operable and both the computer and the controller are operable.
The 4 branches represent the 4 possible
ways we can obtain system
operation.
Controller
Unit 1 Unit 2
Unit 1 Unit 3
Unit 2 Unit 3
Unit 1 Unit 2 Unit 3
Computer
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1
2
2
3
4 5
Equivalent Computer Network
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Communication System diagram
At least 1 of the two Antenna Receiver Converters must work
At least 1 of the two Teleprinters must work
The Pulse shaper must work
Pulse
Shaping
Unit
Antenna
Receiver
Converter
Antenna
Receiver
Converter
Teleprinter
Teleprinter
TOPOLOGICAL RELIABILITY
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In general suppose the topological or network representation
of a system consists of n nodes and define
R(N1,……Nm) = probability that nodes number N1,……, Nm are
operating and the other n-m nodes are not operating
Then the probability that exactly m nodes are simultaneously
operating is given by
Rm = 1
.....N Nm
R(N1, …, Nm)
Where the sum is taken over all positive integers N1, …, Nm
such that n N1 > N2 >….>Nm 1
Thus the probability that at least k nodes are operating is
given by
n
kmRm
TOPOLOGICAL RELIABILITY
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System of m elements in series with individual reliabilities
R1, R2, , Ri, Rm respectively.
The system will only survive if every element survives , if
one element fails the system fails.
Assume The reliability of each element is independent
of the reliability of the other elements
The probability that the system survives is the probability
that element 1 survives and the probability that element 2
survives and the probability that element 3 survives etc.
The system reliability is the product of the element
reliabilities.
Rsyst = R1R2R3 Ri Rm
Reliability of Systems 1 Series systems
R1 R2 R3 R4 Ri Rm
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If we assume a constant failure rate for the elements
then since
Ri = e-t
Rsyst = e-1 t e
-2 t ….
e-I t
….e
-mt
So if syst is the overall system failure rate
Rsyst = e-syst t =
e
-(1 + 2 + ….+ I t
…. +m) t
syst = 1 + 2+…. +i+…. +m
Failure rate of a series network is the sum of the
individual element failure rates so it is important to
keep the number of elements to a minimum and so the
reliability will be maximum.
Reliability of Systems 1 Series systems
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Reliability of Systems 1 Series systems
Unreliability of Series System with Small Failure ratesProtective systems have element and system UNRELIABILITIES F
that are very small. The corresponding system reliabilities are
therefore very close to 1, for example 0.9999 may be typical. Then the
calculation of Rsyst = R1R2R3 Ri Rm may be arithmetically unwieldy
and the alternative equation involving unreliabilities may be more
useful since
Rsyst = 1 - Fsyst and Ri = 1- FI
We have 1 - Fsyst= (1- F1 ) (1- F2 )… (1- FI )… (1- Fm )
= 1 – (F1 + F2 +…+ FI + … +Fm )
+ terms involving products of F’s
If the individual Fi are small i.e. Fi << 1 the terms involving products
of Fs can be neglected giving the approximate equation
Fsyst F1 + F2 +…+ FI + … +Fm
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Reliability of Systems Parallel Systems
An overall system consisting of n individual
Elements or systems in parallel with
Individual unreliabilities F1, F2, …, Fj, …Fn
Only one individual element is necessary
to meet the functional requirements of the
overall system
The remaining elements increase the
reliability of the system
THIS IS CALLED REDUNDANCY.
Failure only if ALL the elements fail
The unreliability of a parallel system
Fsyst = F1F2…Fj…Fn
F1
F2
Fj
Fn
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Majority voting systems are used to protect
hazardous plant and processes and have
applications in the chemical, nuclear and aerospace
industries. Diagram shows a typical system with 2
out of 4 voting with initiators A, B, C, D.
Reliability of Systems Voting Systems
Trip setting
Process
parameter inputs
A
B
C
D
2oo4 voting
element
Shut down
system
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Reliability of Systems Voting Systems
Suppose R and F are the reliability and unreliability of
the individual initiators.
The overall initiation system fails to protect the plant if
either all 4 initiators fail
or any 3 initiators fail
If 2 or less initiators fail there are still sufficient left to
trip the plant
Since the F’s are normally small then the rare events
approximation is valid and the overall system
unreliability is the sum of the following probabilities
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Reliability of Systems Voting Systems
FINIT = Probability that A and B and C and D fail
+
Probability that A and B and C fail
+
Probability that B and C and D fail
+
Probability that A and C and D fail
+
Probability that A and B and D fail
Each of the terms is the product of individual
unreliabilities and reliabilities.
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Reliability of Systems Voting Systems
FINIT = F4 + F3R + F3R + F3R + F3R = F4 + 4F3R
= F3(F + 4R)
This result can be obtained from the binomial
expansion of (F + R)4
(F + R)4 = F4 + 4F3R + 6F2R2 + 4FR3 + R4
The first term F4 represents the probability of all 4
initiators failing and the second the total probability
of 3 failing. If R 1 and F 1 Then FINIT 4F3
The unreliability of the complete protective system is
FSYST FINIT + FVOTING + FSHUT-DOWN
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Reliability of Systems Majority Voting Systems
In a majority voting system there are n trip channels
and the plant is tripped if m (n m) indicate that the
plant should be tripped.
Such a system is referred to as ‘m out of n’ or m oo n
The binomial distribution can be used to calculate
overall failure probabilities.
Consider the jth term in the binomial expansion of
(F +R)n where F and R are the single channel
reliability and unreliability and n is the total number
of channels.
This is nCjFjRn-j and is the probability that
j channels fail i.e. (n-j) channels survive.
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Reliability of Systems Fail-Safe & Fail-Danger
Fail-Danger failure
Any system or component failure that prevents, or
tends to prevent, the plant being tripped when a
potentially hazardous fault condition occurs.
Example A pressure switch failed to open when the
pressure exceeded the trip pressure
Fail-Safe failure
Any system or component failure that produces a
plant trip when a plant trip is not required.
Example A pressure switch opened when the
pressure was below the trip pressure
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Reliability of Systems Fail-Safe & Fail-Danger
A fail-danger failure is a very serious occurrence
Fail-safe failures are less serious but cause loss of
production and confidence in the trip system
Fail-danger and Fail-safe failures will generally
have different failure rates and so different failure
probabilities
Detailed information on the failure rates associated
with all possible modes of failure of trip equipment
is not always available
We may have to assume both rates are equal to the
average failure rate
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Reliability of Systems Fail-Safe & Fail-Danger
Supposing we wish to calculate overall fail-danger
and fail-safe for a system with ‘two out of three’
voting i.e. 2 oo 3 where m = 2 and n = 3 . These
probabilities can be calculated from the binomial
expansion of (R + F) 3, where F and R are the single
channel reliability and unreliability respectively.
So we have (F + R)3 = F3 + 3F2R + 3FR2 + R3
where F3 represents the probability that all 3
channels fail, 3F2R the probability that 2 channels
fail, 3FR2 the probability that 1 channel fails and R3
the probability that no channel fails
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Reliability of Systems Fail-Safe & Fail-Danger
Looking at fail-danger first
if either 2 or 3 channels fail dangerously then
there are correspondingly only 1 or zero channels
left working.
This is insufficient to trip the plant with 2 oo 3
voting and an overall fail danger situation has
occurred.
If FD is the single channel fail-danger probability
then the overall fail danger probability is
PD = FD3 + 3R FD
2 = FD2(3R + FD)
In a protective system R 1 and FD 1 giving
PD 3FD2
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71
Reliability of Systems Fail-Safe & Fail-Danger
Looking at fail-safe
A fail-safe failure of no channels or only one
channel will not cause a plant trip with 2 oo 3 voting.
A fail-safe failure of two channels will cause an
unnecessary plant trip.
The failure of a third channel is irrelevant because
the plant is tripped by only 2 channels.
The overall fail-safe probability is therefore
PS = 3RFS2 3FS
2
where FS is the single channel fail-safe probability
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72
Reliability of Systems Fail-Safe & Fail-Danger
Overall fail-danger probability
PD = nCrF
r
D
where r = n-m+1 and nCr = n! {r!(n-r)!}
FD
MAX = 1- e
-DT DT (if DT 1
Overall fail-safe probability
PS = nCmF
m
S
where nCm= n! {m!(n-m)!}
FS
MAX = 1- e
-ST ST (if ST 1
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Reliability of Systems Fail-Safe & Fail-Danger
FRACTIONAL DEAD TIME FDT
Is related to fail-danger probability
Is the mean proportion of the testing interval T that
the trip system is incapable of protecting the plant
FDT = {1 T} 0TFD(t)dt
FDT is a similar concept to unavailability
FDT = {1 (r+1)} nCrF
r
D
Majority voting can be implemented with
combinatorial logic.
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FAULT TREE , EVENT TREE and
FMECA ANALYSIS
To check for fault propagation one technique is
Failure
Modes
Event
Criticality
Analysis
A full FMECA is hard and expensive. Take every
component, wire, connector and think of every possible
fault. Consider the effects of all of these - are they single
point failures? Can they propogate? Document the
results.
An FMECA is a development from an FMEA - (Failure
Modes Event Analysis)
FMEA and FMECA are bottom-up analyses. The alternative
approach is a fault tree analysis.
propagate?
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FMECA ANALYSIS
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FMECA ANALYSIS
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78
FAULT TREE , EVENT TREE and
FMECA ANALYSIS
Encountered frequently in the analysis of
events including human activities that can
lead to disasters or undesirable events
Sometimes called Cause - Consequence
analysis
Used more frequently in Safety studies
Event trees are
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EVENT TREE
Consider the following example of a fire alarm system.
Ideally if there is a fire then
The alarm goes off.
A sprinkler system extinguishes the fire.
In each case there is a human standby
If either the alarm or the sprinkler system fails
Human operator can operate either or both
This can be represented by the event tree in the figure
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Fire
starts
Alarm
functions
Operator notices
malfunction
Operator notices
malfunction
Sprinkler
system
functions
YES
510-4
YES
YES
YES
YES
YES
YES
NO
NO
NO
NO NO
NO NO 0.999
10-3
0.9995
10-2
210-3 10-3
210-3
0.99
0.998
0.9
0.999
0.998
0.1
Fire Suppressed 9.910-10
Fire Spreads 510-9
NO FIRE 0.9995
Fire Spreads 9.910-13
Fire Spreads 9.9910-8
Fire Suppressed 4.910-7
Fire Suppressed 8.9910-7
Fire Suppressed 4.9810-4
EVENT TREE
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EVENT TREE
Notice that of all the possible outcomes only three are that the fire
spreads
The possible sequence of events that that can lead to this undesireable
event can now be identified from these outcomes.
The alarm fails to function and the operator fails to notice and
take action in time
The alarm functions but the sprinkler fails to function and the
operator fails to notice and take action in time
The alarm fails to function, and the operator notices, but the
sprinkler fails to function, and the operator fails to notice
If sufficient data exists to estimate probabilities the likelihood of the
various outcomes can be obtained
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FAULT TREE
An Example of a Deductive approach.
“What can cause this?”
Used to identify the causal relationships leading to a
specific system failure mode.
The system failure mode is the TOP event and the
FAULT TREE is developed in branches below this
event showing its causes.
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a
f f
T6
T4
T5
T1
T3
T2 T
b
a
e
b
d
a
c
Fault Tree From Logic Expression T = (abc + f)[(a + d)f](a +be)
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Simplifying the expression:
T = (abc + f)[(a + d)f](a +be)
= (abc +f)(af + df)(a + be)
= abcf + af + abcdf + adf + abcef + abef + abcdef + bdef
Using XX = X
= abcf(1+d+e+de) + af (1+d+be) + bdef
= abcf + af + bdef Using (1 + X) = 1
= af (bc + 1) + bdef
= af + bdef
= f(a +bde)
Fault Tree from Logic Expression
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TESTING ACTIVITIES
Design testing refers to
laboratory tests
on computerand / or
prototype models
to prove that the design is capable of
meeting the quality specification
QUALITY DESIGN AND QUALIFICATION
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QUALITY DESIGN AND QUALIFICATION
Qualification testing refers to
field testing of
pre-production models and
production models involving
all performance characteristics
over the full range of relevantenvironmental variables
to further verify that the specification canbe met.
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DESIGN FOR RELIABILITY
Objective
To design a given product or system which
meets the target failure rate T
under the environmental conditionsspecified.
It is assumed that
all components and elements are operatingin the useful life region where failure rate isconstant with time.
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DESIGN FOR RELIABILITY
General principles to be observed.a) Element / component selection
Only elements / components with wellestablished failure rate data / models should beused
Some technologies are inherently more reliable thanothers.e.g.
Solid state switching devices are more reliablethan electromechanical reed relays
Inductive displacement transducers are morereliable than the resistive potentiometer type.
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89
DESIGN FOR RELIABILITY
b) De-rating
Stress (x) was defined as variable which when appliedto an element or component tends to increase failurerate.e.g.
mechanical stress
voltage
Strength (y) was defined as any property of theelement or component which resists the appliedstresse.g.
elastic limit
rated voltage
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DESIGN FOR RELIABILITY
To reduce failure rate
strength should exceed stress by anadequate
Safety Margin
In a mechanical element SM > 5.0
In an electronic circuit the voltageStress Ratio SR should be kept below0.7
Stress Ratio
( y - x )
(x2 +
y
2)
x
y
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DESIGN FOR RELIABILITY
c)Environment
Component / element failure rate critically dependent on environment.
Environment correction factor E
OBS = E B
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DESIGN FOR RELIABILITY
d) Minimum complexity
For a series system the system failure rate is the sum of the individual component / element failure rates
thus The number of components / elements in the system should be the minimum required for the system to perform its function
In electronic systems reliability can be improved by using integrated circuits which replace hundreds or thousands of basic devices.
The failure rate of the integrated circuit is generally less than the sum of the failure rates of the devices it replaces.
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DESIGN FOR RELIABILITY
e) Redundancy
The use of several identical elements /systems connected in parallel increases thereliability of the overall system.
Redundancy should be considered in situationswhere either the complete system or certainelements of the system have too high a failurerate.
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DESIGN FOR RELIABILITY
f) Diversity
The problem of common mode failure was discussed
Here a fault can occur that causes more than one element in a system to fail simultaneously e.g.
Electronic system where several of the circuits share a common power supply
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DESIGN FOR RELIABILITY
If the probability of common mode failure limitsthe reliability of the overall system
equipment diversity should be considered
Here a common function is carried by twosystems in parallel
but
Each element is made up of
different elementswith
different operating principlese.g. A temperature measurement device made up oftwo subsystems in parallel
one electronic
one pneumatic
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DESIGN FOR RELIABILITY
g) Calculation of system reliability
Once the components / elements have been chosen and their configuration in the system/product decided
then
The overall system / product reliability can be calculated.
The Reliability / Failure rate calculated for the overall product should be then compared with the target value
If the target value is not met then the design should be adjusted until the target figure is reached.
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The system designer may consider component
redundancy
ADVANTAGES of redundancy
The quickest solution if time is of prime importance
The easiest solution, if the component is already
designed
The cheapest solution, If the component is
economical in comparison with the cost of redesign
The only solution, if the reliability requirement is
beyond the state of the art
High Reliability Design
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DISADVANTAGES of redundancy
Too expensive, if the components are costly
Exceed the limitations on size and weight,
particularly in satellites
Exceed the power limitations, particularly in active
redundancy
Attenuate the input signal, requiring additional
amplifiers which increase complexity
Require sensing and switching circuitry so complex
as to offset the advantage of redundancy
High Reliability Design
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Exercises
1) Discuss, giving examples, the methods including procurement and testing procedures,
used by manufactures to ensure the reliability of a product.
2) Discuss the differences in reliability required in systems such as consumer products,
trains, aeroplanes, satellites. What value would you assign to the overall failure rate of
each of these systems.
3) What do you understand by the reliability of a system? Discuss some practical ways to
assign a quantitative value to the reliability of a system.
4) Draw a fault tree for the lighting system in a car and hence derive a logic equation for
the failure of the headlights.
5) Discuss the concepts of fail-safe and fail-danger. Why is the single unit probability for
fail-safe and fail-danger often assumed to be the same. Explain why in spite of this
assumption the overall fail-safe probability of a complex system will be different from the
overall fail-safe probability.
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0
Problems
1) )The figure shows a protective system, based on temperature measurement. The system is to have a
maximum fail-danger probability not exceeding 810-3 and a maximum fail-safe probability not exceeding
510-2. The system is tested and proved to be working correctly at three-week intervals. Annual fail-safe
and fail-danger failure rates for each component are:
Thermocouple S = D = 0.5
Thermocouple input trip amplifier/comparator S = D = 0.1
m out of n voting element S = D = 0.05
Logic operated switch S = D = 0.1
Solenoid valve S = D = 0.1
Trip valve S = D = 0.1
Calculate the maximum fail-safe and fail-danger probability PS and PD for:
a) The high integrity voting equipment, HIVE.
b) The high integrity trip initiator, HITI.
c) The high integrity shutdown system, HISS.
And hence
d) The total system fail-danger probability
e) The total system fail-safe probability
State whether the system meets the design criteria
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1
Problems
0.5 0.1
0.5 0.1
0.5 0.1
0.05
0.1 0.1 0.1
0.1 0.1 0.1
HIVE HITI HISS
Thermocouple Trip amp/comp
2 oo 3 voting Logic switch Solenoid valve Trip valve
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2
Problems
Solution
i HIVE Maximum FS = FD = 1- e-0.053/52
= 2.8 10-3
ii HITI single channel
Maximum FS = FD = 1- e-0.63/52
= 3.4 10-2
2 00 3 voting HITI;
PD= 3FD2 = 3 (3.4 10
-2)
2 3.4 10
-3
iii HISS single channel
Maximum FS = FD = 1- e-0.33/52
= 1.7 10-2
Two channels in parallel
PD= FD2 = (1.7 10
-2)
2 0.3 10
-3
PS= 2FS 2 1.7 10-2
= .3.44 10-2
iv Total System fail-danger probability = (PD)HITI + (PD)HIVE + (PD)HISS
= 3.4 10-3
+ 2.8 10-3
+ 0.3 10-3
= 6.5 10-3
v Total System fail-safe probability = (PS)HITI + (PS)HIVE + (PS)HISS
= 3.4 10-3
+ 2.8 10-3
+ 34.4 10-3
= 40.6 10-3
= 4.1 10-2
The system meets the design specification
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3
Problems
2) A taxi owner has 20 cars. Records show each car on average breaks down once every 2 years and that this is
reasonably constant. How many breakdown calls will he have per year?
What is the probability of 1 breakdown in a 3 month period?
Solution.
‘Statistical assumptions hold’
c = 1/2 (for 1 car)
F = Nc = 10
3 months = 1/4 year
F(t) = 1 - e-Ft
F(1/4) = 1 - e-10.1/4
= 0.92
OR
92% chance of at least one failure in 3 months.
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3) A basic guidance and navigation system for a proposed space probe consists of an Inertial Set, a
Canopus Sensor, a Sun Sensor, and a Computer. The reliability for each device is Rinertial set =
0.95; Rsun sensor = 0.90; Rcanopus sensor = 0.85; Rcomputer = 0.90. For the system to operate all four
subsystems must be operating. Due to design constraints the space probe can only contain one
Inertial set and one Computer. To increase the reliability of the system three Canopus Sensors
and two Sun Sensors are used in hot redundancy.
(i). Draw a reliability block diagram for the system without the redundancy
(ii). Draw a reliability block diagram for the system including the redundancy
Calculate the reliability of the system in each case.
Problems
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(4) In a distillation column a hazardous situation is created if the flow rate of steam to the reboiler goes high; this
causes a high flow rate of vapour up the column producing a high pressure which could cause the vessel to rupture.
The temperature control loop consists of a platinum resistance thermometer (PRT), a transmitter ( which converts
resistance change to a 4-20mA current signal), a controller, a current-to-pneumatic converter and a control valve.
The plant is protected by a pressure trip system consisting of a pressure switch and three-way solenoid valve
located in the air line between the converter and the control valve.
Failure mode and effect analysis of the system shows that:
1. A fail-danger situation F in which the Steam control valve moves fully open, occurs if either Pressure in valve
bonnet increases (F1) or Control valve fails open (F2).
2. F1 occurs if Pressure signal to control valve increases (F3) and Solenoid does not vent air (F4).
3. F3 occurs if PRT short circuit (F5) or Transmitter O/P fails low (F6) or Controller O/P fails high (F7) or I/P
Converter O/P fails high (F8).
4 F4 occurs if Pressure switch fails to open (F9) or Solenoid fails to vent (F10)
(i). Draw a fault tree diagram for the fail-danger failure
(ii). Write down the logic expression for the fail-danger failure F.
Problems
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