ENGG ZC242-L6
Content
MAINTENANCE & SAFETY
Anil Jindal
BITS Pilani
Pilani Campus
Mechanical Engg Department
BITS Pilani, Pilani Campus
BITS Pilani
Pilani Campus
Reliability – Centered Maintenance
(RCM)
Chapter – 4:Part-1
Reliability
• Reliability refers to the consistency of a measure. A test is
considered reliable if we get the same result repeatedly.
• For example, if a test is designed to measure a trait, then
each time the test is administered to a subject, the results
should be approximately the same.
• Unfortunately, it is impossible to calculate reliability exactly,
but it can be estimated in a number of different ways.
• the probability that no (system) failure will occur in a given
time interval
• A reliable system is one that meets the specifications.
BITS Pilani, Pilani Campus
Various aspects of
centered maintenance
reliability
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
Step 1: Educate from Top to Bottom on ReliabilityCentered Maintenance
• Shatter the old myths
• Presentation to the staff the better way
• Use multiple formats
• Make the employees understand the importance of
their benefit in following the new techniques
• Planting lots of small seeds
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
Step2: Benchchmarking the Present position
• Companies will realize that once they are bench-marked,
they will realize that how far they are behind. The realities
will provide the necessary attitude adjustment.
• For safety, the International Standards Organization has
defined to calculate lost time incident rate (LTIR) and
recordable incident rate (RIR).
• It is understood that an RIR of 0.5 and LTIR of 0.05 are
considered to be high. Similar norms are not available for
reliability centred maintenance
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
Step4: Building up of a Business Case
Some examples of improvement are given below:
A 5 percent increase in availability = 5 percent increase in
revenue for a continuous process plant that can sell all that it
makes.
For example, a plant that produces Rs. 1,000 crore per year
generates another Rs. 50 crore in revenue. Reducing
overtime from 20 to 10 percent moves 10 percent of labour
from overtime rates to straight time rates. If the overtime
multiplier is 1.5 and a plant has a Rs. 10 crore labour budget
towards overtime Rs. 1 crore is saved.
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
Step5: Conducting a Pilot Program
• It may be necessary to conduct a pilot programme so
as to get the real feel of the benefits of following an
organized maintenance scheme.
• The pilot serves the following critical functions:
• Reduce initial investment.
• The pilot may cost only 10 percent of the full
programme, so the budget approvals are likely to be
fast.
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
BITS Pilani, Pilani Campus
System Reliability
“Reliability of the product (made up of a number of components) is
determined by the reliability of each component and also by the
configuration of the system consisting of these components”
–Product design, manufacture, maintenance influence reliability, but
design has a major role
–One common approach for increasing the reliability of the system is
through “redundancy in design”, which is usually achieved by placing
components in parallel.
–As long as one component operates, the system operates
Systems with components in series
–For the system to operate, each component must operate
–It is assumed that the components operate independently of each other
(Failure
of one component has no influence on the failure of any other component)
A
B
C
Systems with components in
series – contd..
– If there are ‘n’ components in series, then system reliability is given by
Rs = R1 x
R2 x - - - - - - Rn
– System reliability decreases as the number of components in series
increases
– Manufacturing capability and resource limitations restrict the maximum
reliability of any given component
– Product redesign that reduces the no. of components in series is the
viable alternative
– Use of the Exponential Model
• If the system is in chance failure phase, a constant failure rate
could be justified based on which we can calculate failure rate,
mean time to failure and system reliability
Systems with components in
series – contd..
– Use of the Exponential Model
• Suppose the system has ‘n’ components in series
• Each component has exponentially distributed time-to-failure
with failure rates given by
1, 2 n
• The system reliability is given by
R s e 1t X e 2 t X e 3 t X e n t
e
n
i
i1
t
• Thus if each component that fails is replaced immediately
with another that has the same failure rate, the mean time to
1
failure for the system is given by
MTTF n
i
i1
•When all components have same failure rate, If
then
M T TF
1
n
System with components in parallel
– System reliability can be improved by placing components in parallel as system
will operate as long as at least one of the components operates.
– The only time the system fails is when all the parallel components fail
– All components are assumed to operate simultaneously.
– A system having ‘n’ components in parallel, with the reliability of the ith component
denoted by Ri, i=1, 2, ----- n.
– Also assume that the components operate randomly and independently of each
other.
– The probability of failure of each component is given by
Fi = 1-Ri.
–System fails only if all the components fail and hence the probability of system
n
failure is
Fs 1 R1 1 R2 1 Rn (1 Ri )
i1
Systems with components in
parallel – contd..
– Reliability of the system is the complement of Fs and
is given by Rs = 1-Fs
– Use of Exponential model
– If the time to failure of each component can be modelled by the exponential distribution,
each with a constant failure rate λi, then the system reliability, assuming independence of
component operation is
– Time to failure of the system is not exponentially distributed
– In the special case, where all the components have the same failure rate
the system reliability is Rs = 1- (1-e- t)n
– Mean time to failure for a system of n components in parallel is given by
1
1 1
MTTF 1/ 1
n
2 3
Reliability block diagrams
Once the reliability of the subsystems is determined, the overall
system can be effectively modeled from the reliability perspective.
Once modeled, the weak links usually become evident and can be
addressed with reliability growth measures to eliminate the
deficiencies. Figure illustrates block-diagrammed examples of simple
serial, parallel and combination systems.
BITS Pilani, Pilani Campus
Reliability while active and
standby
BITS Pilani, Pilani Campus
Reliability centered maintenance
Economic optimization of machine reliability relative to organization goal is the primary
objective of RCM.
RCM helps to insure that if we spend on improving reliability, we are getting the full
money back, plus some acceptable return on investment.
BITS Pilani, Pilani Campus
Law of diminishing marginal
returns
• The implementation of RCM follows the law of
diminishing marginal returns.
• The money invested in reliability improvement tends to
yield a higher return on investment than any money
subsequently invested.
• The objective is to reach the point of optimization at
which the benefits of reliability expresses as total
operating cost, are maximized through cost reduction.
BITS Pilani, Pilani Campus
Law of diminishing marginal
returns
BITS Pilani, Pilani Campus
Plot between time & condition
• The warning time in advance of a functional failure that a monitoring
technique provides is called the P-F interval.
• P refers to the time at which the potential failure occurs.
• F refers to the time at which actual failure occurs.
• Longer the P-F interval, more time one has to make a good decision
and plan action.
BITS Pilani, Pilani Campus
Basic guidelines for RCM
• Function oriented: seeks to preserve the system function not just
operability.
• System focused: more concerned about system then components.
• Reliability centered: seeks to define the probability that the system
perform its intended function for a specific operating time interval.
• Accepts design limitations
• Towards safety and economics
• Address failure: failure is defined as loss of function
• Uses logic tree: consistent approach to maintenance
• Needs effective tasks: technically sound and effective
• It should be applicable: must reduce the number and impact of
failure.
BITS Pilani, Pilani Campus
Failure Modes Effects and
Criticality Analysis (FMECA)
• Valuable tool to identify primary functional failure, their related
failure modes, the effect of failure modes on the operation of
system and associated criticality of the failure modes as a function
of impact and criticality.
• Used in advanced maintenance techniques, redesign or
redundancy.
• Example:
Safety engineering
Maintainability engineering
Design engineering
23
BITS Pilani, Pilani Campus
Root Cause Failure Analysis (RCFA)
•
To find the root cause for event.
•
Used to find the recurrence, cost to control and control
methods.
26
BITS Pilani, Pilani Campus
Criticality Analysis/Criticality Matrix.
It’s to rank failure modes found from FMEA, according to severity
classification and it’s probability of occurrence.
The failure mode criticality number of for each failure mode is calculated
as:
Cm = βα*(λp) t
Where:
Cm = failure mode criticality number
β = conditional probability of failure effect
α = failure mode ratio
λp = part failure rate per million hours
t = duration of relevant mission phase (operation in hours)
25
BITS Pilani, Pilani Campus
Criticality Analysis/Criticality Matrix
The next step is to divide the criticality scale into number of sections
according to probability of occurrence.
• LevelA: Frequent. overall probability of failure =>0.2
• Level B: Reasonable. 0.1< overall probability of failure<0.2
• Level C: Occasional. 0.01< overall probability of failure<0.1
• Level D: Remote. 0.001< overall probability of failure<0.0.
• Level E: Unlikely. 0.001> overall probability of failure
26
BITS Pilani, Pilani Campus
Criticality Analysis/Criticality Matrix.
Severity Classification:
• Category I:Catastrophic - death, weapon system loss, eg
aircraft, tank, missile etc.
• Category II: Critical – severe injury, property damage, mission
loss
• Category III: Marginal – Minor injury, minor property damage,
delay of mission
• Category IV: Minor – unscheduled maintenance or repairs
27
BITS Pilani, Pilani Campus
Criticality Analysis/Criticality Matrix.
• Benefits of Criticality Analysis
• Quickly identifies risk and high exposure.
• Ranks functional areas and equipment based levels on exposure.
• Sums exposure levels for user defined areas and entire facility.
• Reduces red zone exposure with engineering follow up and action plans.
• Prioritize programs, initiatives and maintenance on critical ranking.
• Establish guidelines for determining maintenance work order priorities.
RCM vs RCA (Root Cause Analysis)
RCM:
• To find the root cause of event.
• Use criticality matrix.
• Driven by preventive maintenance strategy.
• Can find symptoms of the event.
ENGG ZC242, Maintenance & Safety,
02/009/14, Lecture-7
29
BITS Pilani, Pilani Campus
RCM vs RCA
RCA:
•
To find the underlying reason and to find necessary step to eliminate that event
•
Use logic tree method
•
Driven by maintenance prevention strategy
•
To find and correct the cause
30
BITS Pilani, Pilani Campus
Reliability prediction model
The following diagram show that how field reliability of a system is predicted
and factors associated with it.
31
BITS Pilani, Pilani Campus
Software in RCM
Computerized RCM tool is depicted below in the figure
32
BITS Pilani, Pilani Campus
Example
An amplifier has an exponential time to failure distribution
with a failure rate of 8% per 1000h. What is the reliability
of the amplifier at 5000 h? Find the mean time to failure.
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
What is the highest failure rate for a product if it is to have a
probability of survival (that is, successful operation) of
95% at 4000h? Assume that the time to failure follows an
exponential distribution.
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
A module of a satellite monitoring system has 500
components in series. The reliability of each component
IS 0.999. Find the reliability of the module. If the number
of components in series is reduced to 200. What is the
reliability of the module?
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
The automatic focus unit of a television camera has 10
components in series. Each component has an
exponential time –to-failure distribution with z constant
failure rate of 0.05per 4000h. What is the reliability of
each component after 200h of operation? Find the
reliability of the automation focus unit for 200h operation.
What is it mean time-to-failure?
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
In continuation with previous example, the automatic focus
unit of television camera, which has 10 similar
components in series. It desired for the focus unit to
have a reliability of 0.95 after 2000h of operation. What
would be the mean time to failure of individual
components?
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
Find the reliability of the system shown in Fig
below with three components (A,B and C) in
parallel. The reliability of A,B and C are
0.95,0.92 and 0.90, respectively.
A
B
C
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
For the system shown in fig, determine the system reliability for
2000 h of operation, and find the mean time to failure. Assume
that all three components have an identical time-to failure
distribution that is exponential, with a constant failure rate of
0.0005/h. what is the mean time to failure of each component?
If it desired for the system to have a mean time to failure of
4000h, what should the mean time to failure be for each
component?
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
Find the reliability of the eight component system shown in
fig below some components are in series and some are
in parallel. The reliabilities of the components are as
follows: RA1=0.92, RA2=0.90 RA3=0.88 RA4=0.96
RB1=0.95 RB2=0.90 RB3=0.92 and RC1=0.93.
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
Find the system failure rate and the mean time to failure for
the eight-component system shown in fig the failure rate
( number of units per hour ) for the components are as
follows:
λA1=0.0006,
λA2=0.0045,
λA3=0.0035,
λA4=0.0016, λB1=0.0060, λB2=0.0060, λB3=0.0060,
λC1=0.0050
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Anil Jindal
BITS Pilani
Pilani Campus
Mechanical Engg Department
BITS Pilani, Pilani Campus
BITS Pilani
Pilani Campus
Reliability – Centered Maintenance
(RCM)
Chapter – 4:Part-1
Reliability
• Reliability refers to the consistency of a measure. A test is
considered reliable if we get the same result repeatedly.
• For example, if a test is designed to measure a trait, then
each time the test is administered to a subject, the results
should be approximately the same.
• Unfortunately, it is impossible to calculate reliability exactly,
but it can be estimated in a number of different ways.
• the probability that no (system) failure will occur in a given
time interval
• A reliable system is one that meets the specifications.
BITS Pilani, Pilani Campus
Various aspects of
centered maintenance
reliability
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
Step 1: Educate from Top to Bottom on ReliabilityCentered Maintenance
• Shatter the old myths
• Presentation to the staff the better way
• Use multiple formats
• Make the employees understand the importance of
their benefit in following the new techniques
• Planting lots of small seeds
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
Step2: Benchchmarking the Present position
• Companies will realize that once they are bench-marked,
they will realize that how far they are behind. The realities
will provide the necessary attitude adjustment.
• For safety, the International Standards Organization has
defined to calculate lost time incident rate (LTIR) and
recordable incident rate (RIR).
• It is understood that an RIR of 0.5 and LTIR of 0.05 are
considered to be high. Similar norms are not available for
reliability centred maintenance
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
Step4: Building up of a Business Case
Some examples of improvement are given below:
A 5 percent increase in availability = 5 percent increase in
revenue for a continuous process plant that can sell all that it
makes.
For example, a plant that produces Rs. 1,000 crore per year
generates another Rs. 50 crore in revenue. Reducing
overtime from 20 to 10 percent moves 10 percent of labour
from overtime rates to straight time rates. If the overtime
multiplier is 1.5 and a plant has a Rs. 10 crore labour budget
towards overtime Rs. 1 crore is saved.
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
Step5: Conducting a Pilot Program
• It may be necessary to conduct a pilot programme so
as to get the real feel of the benefits of following an
organized maintenance scheme.
• The pilot serves the following critical functions:
• Reduce initial investment.
• The pilot may cost only 10 percent of the full
programme, so the budget approvals are likely to be
fast.
BITS Pilani, Pilani Campus
Practical steps towards achieving
reliability–centered maintenance
BITS Pilani, Pilani Campus
System Reliability
“Reliability of the product (made up of a number of components) is
determined by the reliability of each component and also by the
configuration of the system consisting of these components”
–Product design, manufacture, maintenance influence reliability, but
design has a major role
–One common approach for increasing the reliability of the system is
through “redundancy in design”, which is usually achieved by placing
components in parallel.
–As long as one component operates, the system operates
Systems with components in series
–For the system to operate, each component must operate
–It is assumed that the components operate independently of each other
(Failure
of one component has no influence on the failure of any other component)
A
B
C
Systems with components in
series – contd..
– If there are ‘n’ components in series, then system reliability is given by
Rs = R1 x
R2 x - - - - - - Rn
– System reliability decreases as the number of components in series
increases
– Manufacturing capability and resource limitations restrict the maximum
reliability of any given component
– Product redesign that reduces the no. of components in series is the
viable alternative
– Use of the Exponential Model
• If the system is in chance failure phase, a constant failure rate
could be justified based on which we can calculate failure rate,
mean time to failure and system reliability
Systems with components in
series – contd..
– Use of the Exponential Model
• Suppose the system has ‘n’ components in series
• Each component has exponentially distributed time-to-failure
with failure rates given by
1, 2 n
• The system reliability is given by
R s e 1t X e 2 t X e 3 t X e n t
e
n
i
i1
t
• Thus if each component that fails is replaced immediately
with another that has the same failure rate, the mean time to
1
failure for the system is given by
MTTF n
i
i1
•When all components have same failure rate, If
then
M T TF
1
n
System with components in parallel
– System reliability can be improved by placing components in parallel as system
will operate as long as at least one of the components operates.
– The only time the system fails is when all the parallel components fail
– All components are assumed to operate simultaneously.
– A system having ‘n’ components in parallel, with the reliability of the ith component
denoted by Ri, i=1, 2, ----- n.
– Also assume that the components operate randomly and independently of each
other.
– The probability of failure of each component is given by
Fi = 1-Ri.
–System fails only if all the components fail and hence the probability of system
n
failure is
Fs 1 R1 1 R2 1 Rn (1 Ri )
i1
Systems with components in
parallel – contd..
– Reliability of the system is the complement of Fs and
is given by Rs = 1-Fs
– Use of Exponential model
– If the time to failure of each component can be modelled by the exponential distribution,
each with a constant failure rate λi, then the system reliability, assuming independence of
component operation is
– Time to failure of the system is not exponentially distributed
– In the special case, where all the components have the same failure rate
the system reliability is Rs = 1- (1-e- t)n
– Mean time to failure for a system of n components in parallel is given by
1
1 1
MTTF 1/ 1
n
2 3
Reliability block diagrams
Once the reliability of the subsystems is determined, the overall
system can be effectively modeled from the reliability perspective.
Once modeled, the weak links usually become evident and can be
addressed with reliability growth measures to eliminate the
deficiencies. Figure illustrates block-diagrammed examples of simple
serial, parallel and combination systems.
BITS Pilani, Pilani Campus
Reliability while active and
standby
BITS Pilani, Pilani Campus
Reliability centered maintenance
Economic optimization of machine reliability relative to organization goal is the primary
objective of RCM.
RCM helps to insure that if we spend on improving reliability, we are getting the full
money back, plus some acceptable return on investment.
BITS Pilani, Pilani Campus
Law of diminishing marginal
returns
• The implementation of RCM follows the law of
diminishing marginal returns.
• The money invested in reliability improvement tends to
yield a higher return on investment than any money
subsequently invested.
• The objective is to reach the point of optimization at
which the benefits of reliability expresses as total
operating cost, are maximized through cost reduction.
BITS Pilani, Pilani Campus
Law of diminishing marginal
returns
BITS Pilani, Pilani Campus
Plot between time & condition
• The warning time in advance of a functional failure that a monitoring
technique provides is called the P-F interval.
• P refers to the time at which the potential failure occurs.
• F refers to the time at which actual failure occurs.
• Longer the P-F interval, more time one has to make a good decision
and plan action.
BITS Pilani, Pilani Campus
Basic guidelines for RCM
• Function oriented: seeks to preserve the system function not just
operability.
• System focused: more concerned about system then components.
• Reliability centered: seeks to define the probability that the system
perform its intended function for a specific operating time interval.
• Accepts design limitations
• Towards safety and economics
• Address failure: failure is defined as loss of function
• Uses logic tree: consistent approach to maintenance
• Needs effective tasks: technically sound and effective
• It should be applicable: must reduce the number and impact of
failure.
BITS Pilani, Pilani Campus
Failure Modes Effects and
Criticality Analysis (FMECA)
• Valuable tool to identify primary functional failure, their related
failure modes, the effect of failure modes on the operation of
system and associated criticality of the failure modes as a function
of impact and criticality.
• Used in advanced maintenance techniques, redesign or
redundancy.
• Example:
Safety engineering
Maintainability engineering
Design engineering
23
BITS Pilani, Pilani Campus
Root Cause Failure Analysis (RCFA)
•
To find the root cause for event.
•
Used to find the recurrence, cost to control and control
methods.
26
BITS Pilani, Pilani Campus
Criticality Analysis/Criticality Matrix.
It’s to rank failure modes found from FMEA, according to severity
classification and it’s probability of occurrence.
The failure mode criticality number of for each failure mode is calculated
as:
Cm = βα*(λp) t
Where:
Cm = failure mode criticality number
β = conditional probability of failure effect
α = failure mode ratio
λp = part failure rate per million hours
t = duration of relevant mission phase (operation in hours)
25
BITS Pilani, Pilani Campus
Criticality Analysis/Criticality Matrix
The next step is to divide the criticality scale into number of sections
according to probability of occurrence.
• LevelA: Frequent. overall probability of failure =>0.2
• Level B: Reasonable. 0.1< overall probability of failure<0.2
• Level C: Occasional. 0.01< overall probability of failure<0.1
• Level D: Remote. 0.001< overall probability of failure<0.0.
• Level E: Unlikely. 0.001> overall probability of failure
26
BITS Pilani, Pilani Campus
Criticality Analysis/Criticality Matrix.
Severity Classification:
• Category I:Catastrophic - death, weapon system loss, eg
aircraft, tank, missile etc.
• Category II: Critical – severe injury, property damage, mission
loss
• Category III: Marginal – Minor injury, minor property damage,
delay of mission
• Category IV: Minor – unscheduled maintenance or repairs
27
BITS Pilani, Pilani Campus
Criticality Analysis/Criticality Matrix.
• Benefits of Criticality Analysis
• Quickly identifies risk and high exposure.
• Ranks functional areas and equipment based levels on exposure.
• Sums exposure levels for user defined areas and entire facility.
• Reduces red zone exposure with engineering follow up and action plans.
• Prioritize programs, initiatives and maintenance on critical ranking.
• Establish guidelines for determining maintenance work order priorities.
RCM vs RCA (Root Cause Analysis)
RCM:
• To find the root cause of event.
• Use criticality matrix.
• Driven by preventive maintenance strategy.
• Can find symptoms of the event.
ENGG ZC242, Maintenance & Safety,
02/009/14, Lecture-7
29
BITS Pilani, Pilani Campus
RCM vs RCA
RCA:
•
To find the underlying reason and to find necessary step to eliminate that event
•
Use logic tree method
•
Driven by maintenance prevention strategy
•
To find and correct the cause
30
BITS Pilani, Pilani Campus
Reliability prediction model
The following diagram show that how field reliability of a system is predicted
and factors associated with it.
31
BITS Pilani, Pilani Campus
Software in RCM
Computerized RCM tool is depicted below in the figure
32
BITS Pilani, Pilani Campus
Example
An amplifier has an exponential time to failure distribution
with a failure rate of 8% per 1000h. What is the reliability
of the amplifier at 5000 h? Find the mean time to failure.
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
What is the highest failure rate for a product if it is to have a
probability of survival (that is, successful operation) of
95% at 4000h? Assume that the time to failure follows an
exponential distribution.
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
A module of a satellite monitoring system has 500
components in series. The reliability of each component
IS 0.999. Find the reliability of the module. If the number
of components in series is reduced to 200. What is the
reliability of the module?
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
The automatic focus unit of a television camera has 10
components in series. Each component has an
exponential time –to-failure distribution with z constant
failure rate of 0.05per 4000h. What is the reliability of
each component after 200h of operation? Find the
reliability of the automation focus unit for 200h operation.
What is it mean time-to-failure?
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
In continuation with previous example, the automatic focus
unit of television camera, which has 10 similar
components in series. It desired for the focus unit to
have a reliability of 0.95 after 2000h of operation. What
would be the mean time to failure of individual
components?
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
Find the reliability of the system shown in Fig
below with three components (A,B and C) in
parallel. The reliability of A,B and C are
0.95,0.92 and 0.90, respectively.
A
B
C
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
For the system shown in fig, determine the system reliability for
2000 h of operation, and find the mean time to failure. Assume
that all three components have an identical time-to failure
distribution that is exponential, with a constant failure rate of
0.0005/h. what is the mean time to failure of each component?
If it desired for the system to have a mean time to failure of
4000h, what should the mean time to failure be for each
component?
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
Find the reliability of the eight component system shown in
fig below some components are in series and some are
in parallel. The reliabilities of the components are as
follows: RA1=0.92, RA2=0.90 RA3=0.88 RA4=0.96
RB1=0.95 RB2=0.90 RB3=0.92 and RC1=0.93.
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
Example
Find the system failure rate and the mean time to failure for
the eight-component system shown in fig the failure rate
( number of units per hour ) for the components are as
follows:
λA1=0.0006,
λA2=0.0045,
λA3=0.0035,
λA4=0.0016, λB1=0.0060, λB2=0.0060, λB3=0.0060,
λC1=0.0050
BITS Pilani, Pilani Campus
Solution:
BITS Pilani, Pilani Campus
