Week 4 - Lecture 19 : Sensor Systems for Electronics PHM and Common Cause Failure
Watch on YouTubeVideo summary
The lecture focuses on Prognostics and Health Management (PHM) specifically applied to electronic systems, highlighting how this industry is actively adopting these technologies despite them currently being largely at a laboratory level. Unlike massive mechanical systems like diesel generators that require vast resources for monitoring, electronics offer a relatively manageable environment where PHM can be effectively implemented. The primary drivers of degradation in electronic components are environmental factors such as temperature and humidity, which induce thermal fatigue and other severe mechanisms. To counteract these effects and ensure system reliability, the lecture introduces two main classes of monitoring: life consumption monitoring based on physical models and data-driven health monitoring, often integrated with fusion techniques to reduce uncertainty in predicting remaining useful life.
A critical aspect discussed is the management of common cause failures within redundant systems, where environmental stressors like humidity or temperature can simultaneously affect multiple channels. To mitigate this risk, electronic safety-critical systems employ redundancy combined with diversity; for instance, using three sensors monitoring the same parameter ensures that a single failure does not compromise system integrity, while diverse systems operate on fundamentally different principles to prevent simultaneous failures from identical causes. Design strategies include physical separation of redundant modules in different locations or elevations to guard against flooding and fire, staggering maintenance schedules to avoid human error affecting all units simultaneously, and utilizing independent power sources for each channel. Additionally, rigorous quality assurance through military-grade specifications (Mil-Std) and continuous periodic testing are essential to detect faults even when safety systems are in passive modes.
The lecture concludes by detailing the specific precursor parameters monitored for various electronic components to track degradation mechanisms before failure occurs. For electrolytic capacitors, key indicators include equivalent series resistance increases, leakage current changes, and internal electrolyte levels measurable via X-rays or other methods. Power electronics rely heavily on derating strategies where units are operated below their maximum capacity to enhance safety, while monitoring parameters for Insulated Gate Bipolar Transistors (IGBTs) involve collector-emitter voltage thresholds and thermal resistance. Other components like ceramic chip capacitors and CMOS devices have unique failure signatures such as dissipation factor shifts, RF noise variations, and logic level deviations. Finally, the presentation outlines a Markov model approach to mathematically analyze system reliability by defining states for healthy operation, compromised margins with one failed channel, and total system failure due to either multiple individual failures or common cause events, ultimately aiming to meet strict safety targets like a failure probability of less than 10^-5 per year.
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So uh we are in the fourth lecture of uh
this week uh that is fourth week and now
we are talking about a special
application area that is sensor. system
uh for uh phm phm of electronics. In
fact um
um the electronic industry has caught up
with this development though not at a uh
advanced rate but it is still initiated
actually use of uh as I mentioned uh PHM
still is at the laboratory level and uh
electronics industry is one of the
active u uh industry which is trying to
use it. uh you know um one more one more
reason for electronics is it is u
uh comparatively easier to go for phm of
electronics u because uh compared to the
mega system like uh diesel generators uh
uh you know or any uh generating station
generator
u there are there are huge systems so
there resources also are required but In
electronics can be managed uh relatively
easily though they have at material
level they also have a lot of complexity
understanding of upgradation mechanism u
you know so but then uh our fourth
lecture um uh will be on phm of
electronics in fact I am uh I am
planning to have a phm of electronics
and phm of u mechanical engineering so
mechanical engineering when we have a
separate week for that we'll discuss uh
and phm of electronics an overview I'll
be give you this in lecture many case
studies will be covered in our later uh
lectures you know so
um as I mentioned um environment
in fact environment is even for mega
structure it is there actually why
because suppose if we have a uh you know
humidity and uh Uh and then there there
is a structure at the coastal line you
know and uh then we have uh along with
the humidity the CO2 concentration you
know then uh carbide
you know the carbon formation at the
layer and that is degrading the uh the
structure uh strength to the mm level or
millimeter level you know uh deep into
the concrete um that affect the strength
of the but we uh as far as electronics
is concerned the temperature, humidity
uh apart from quality they are the major
contributor to uh electronics and of
course thermal fatigue these are the
some parameter thermal fatigue is a
operation mechanism. Okay. But then
environment is a one of the these two
parameters that is temperature and
humidity they are one of the uh severe
degradation mechanism are they
electronics are susceptible to these two
mechanisms uh maybe more but these two
are so uh that we talk about the uh
electronics uh often there are two
classes uh of monitoring um it is one is
life consumption monitoring and then
second one is datadriven health
monitoring of Of course, there is third
one also that is integrated uh fusion
technique where we we we integrate uh
fusion uh technology with a datadriven
uh method.
So um so as I said the PF model and
datadriven model they they in principle
uh tend to reduce the uncertainty in
prediction of uh remaining useful life.
So that's how it is and for common cause
failure uh dedicated sensors are
required because even uh humidity can
induce um a common cause failure um into
into the uh electronics redundant
channels redundant and diverse channels
you know diverse channels have less
probability compared to redundant
channel. Uh similarly increase in
temperature the electronics uh uh
cubicles uh where it is like if we
cannot maintain a good um ground benign
condition that is uh 22° centigrade
temperature and 50% humidity uh the
performance of the electronics will uh
degrade uh and that will affect our
target functions adversely actually and
u uh that's why um That's why there is a
due consideration uh in the reliability
and safety for safety in the design of
electronic system. If I have to like we
have one sensor and one channel uh to
increase the reliability of the complete
monitoring signal there will be three
sensors. Okay. And though right from
sensor to data equation and actu
actuation function these three channels
will be monitoring the same parameter.
If it is temperature, it is only
monitoring the same parameter. So u so
why? Because if one sensor fails, it
should not affect the uh you know uh
system adversely. Of course, capacity
will come down. Earlier three sensors is
monitoring now two sensors are
monitoring uh but then uh reliability or
safety is not affected but if two sensor
fail uh then yes the system should go to
the safe mode. Okay. So that's why they
they are called having and then if there
is a common cause failure then all the
three or at least two will go to fail
failure mode. So um uh that's why for
common cause failure in the panel itself
there will be temperature monitoring uh
and humidity moni monitoring systems are
there. In fact air flow monitoring
systems are also there. There should not
be uh reduction in air flow. So uh and
that is again a process parameter. So
that is a kind of uh built-in uh uh
safety reliability is uh there in the
system especially for a complex system
because the uh because the consequences
uh um of safety and reliability uh
especially safety being the overriding
factor uh it is a no no for uh any uh
electronic system because our subject is
electronic system as of now.
So uh what are the potential precursors
uh in um in electronic system uh that we
have uh see and the component so let's
say for our uh electrolytic capacitor I
would say um particularly for aluminum
electrolytic capacitor let us say let us
choose this component and uh then if
this is a component what are the
precursor that we need to monitor to
track the degradation
So one is that capacitors alone you know
uh reduction in capacitors is an
indication that capacitor uh uh so
capability is coming down equivalent
series resistance you know of the
capacitor if that that increases uh that
is another parameter. So and it has been
demonstrated demonstrated uh you know
that if you monitor these parameters you
can track the degradation mechanism and
that in turn the remaining useful life
of the cap leakage current and
electrolyte level. In fact these two are
also extensively being used. uh in fact
I had a very good experience on
measuring the level of electrolyte uh
through X-rays or whatever or any uh
internal buildup uh of you know uh
inside the capacitor that also and that
reflect in terms of uh uh leakage
current or electro uh equivalent series
resistance. Okay. Now we have insulator
get bipolar transistor IGBT. This is
very important component. uh in fact I
have listed out only those component
which are which are uh relatively
having more failure rate compared
especially if you talk about the power
electronics you know um power
electronics is little tricky game micro
electronics we have still lot of
built-in quality reliability and all but
same thing is not true with the power
electronics power electronics if you
want to have a safe mode derating is the
only mode if If you require a unit of 20
kilowatt, you go for 40 kowatt or 50
kowatt so that the components are less
stressed. So that is called the derating
to increase the reliability or safety of
the system. So IGBT collector emitter on
voltage get threshold voltage uh
transductance collector leakage current
uh chip thermal uh the resistance. Uh so
these are the things for IGBT and they
are very important device um for power
electronics as as well as micro
electronics
ceramic chip capacitor leakage current
resistance dissipation factor and RF
noise
um and and the increase in these
parameters we'll know that our ceramic
chip capacitor is a giving problem thing
though both are capacitor but both have
other than the uh uh you can Say leakage
current there is no other parameter
maybe we can say equivalent series
resistance is common here it is
resistance here we call equivalent
series resist across the capacitor then
uh complimentary metal oxide cos uh
devices um supply leakage current um
supply current variation operating
signature and then current noise and
then logical level variation uh because
all simos devices they have logical
operations on the through the
transistors on board and these kind of
things gets reflected here at logic
level variation and then RF noise radio
frequency noise and then RF power supply
um there are something but somehow I
have not given anything because I was
not getting pretty confident about those
kind of precursor failure but maybe in
future classes when I do more research
probably for RF power supply we'll I'll
give you something Uh then solder joints
delamination thermal fatigue these are
the two major modes and uh they sometime
appear as a crack or you know and the
they are monitored by either voltage or
current v variation in the circuit at
appropriate location
cable connector cable and connector
change in impedance leakage current
insulation embritment loss of fitment.
So these are the things in fact um uh
cable and connectors they uh when when
we talk of couple of years of operation
because they are not because of
degradation because they are plugged in
plugged out uh uh comparatively more
frequently they are the cause of uh
electronics module uh failure. So
sometimes it is replacing certain
isolation component or sometimes you
have to go for large maintenance
replacing the card itself you know and
then switch mode power supply uh which
is so common then all the computers and
all output current and voltage and
ripple and efficiency these three
similarly field effect transistor also
uh I I'm still trying to work on what
are the degradation mechanism probably
in the uh maybe next lecture uh next
lecture mean next week I'll cover when
we talk about the realtime application
of electronics PHM
then criteria for PHM sensor like here
we saw for mechanical also but we here
we have measurement temperature humidity
dust and is for uh mostly they are for
environmental monitoring then output is
voltage current and uh capacitors these
are the things so input output uh we
have seen uh and the measurement quality
matrix is accuracy again on of
sensitivity, precision u because they
are miniature components. So precision
is very important for them and uh ranges
and resolution. These are the things
sensor electrical parameters power uh
power consumption uh this particular
thing that is power consumption uh to
have a solution for this. Now the modern
sensors they are having a onboard uh
power management that there will be
external supply but still onboard itself
there will be in autonomous mode they
will have the power management system uh
you know uh to to continue the ability
of the uh sensors uh to perform its
intended function. Now operating
environment uh requirement ground benign
industrial so depending on which
environment we are operating our
robustness should be built accordingly.
uh if uh I'm having a control room my
instrumentation should room should have
uh the ground ban condition if it is a
factory the class component and then the
component quality itself matters
actually if I have military grade
component then I can expect a huge good
performance you know u but if an
industrial setup we have to have those
kind of specification otherwise the
reliability will not be the same
actually in industrial
environment. So online sensor monitoring
as as I mentioned for common cause
failure uh is uh should be there
actually typical configuration of
electronic channels in a complex safety
critical system. Now we have come to a
very specific requirement unless until
you are able to imagine what is a
complex engineering system. So simply I
have given the definition of complex
engineering system earlier. Um it is
safety critical system. Earlier the
safety is overriding factor. Then there
are uh number of component they are
interacting with each other. Uh they are
rel much higher compared to a normal
system. Human interaction is a is a uh
there is a lot of inter human machine
interaction uh that that uh helps some
decision making and all. So it is there
and then there there are redund because
it is a complex system single component
or single channel failure should not
affect my operation the redundancy
diversity uh you know and fail safe
criteria they should be built. So that's
how visualizing a uh not only number of
component it's interconnection okay and
its operation uh and they are not linear
in all uh uh domain uh like a simple
component they will have a linear
relationship but they they don't have a
linear relationship so we have to have
that kind of diagnostic mechanism
electronic system so redundancy in
monitoring and production by so this is
one of the characteristic of K out of N
that means at
least k number of channels or components
are required out of n uh for for having
a noble operation. Okay. So, so success
criteria if failure criteria if two
component fails out of n component that
there then the system fails that is so
it depends how you define the
configuration in failure domain or in
success domain then diversity uh
diversity uh uh diverse system diversity
form part of the uh thing diversity
means redundancy is one thing similar
line at three but diversity means you
are having components or channels or
system operating on fundamentally two
different principle.
Okay. So that is called diversity. That
means the cause for failure here and
here it will not be uh the same
phenomena will not be it is thing you
know at plant level if I have built two
system and another one is diverse system
that means it's a operation of mechanism
totally totally different from the first
principle. Let's say a redundant system
is operating by fall of safety devices.
A diverse system will be operating not
by fall. It will be injection of certain
uh certain uh fluid into the system to
bring the state of the system to the
safe state. So this is called diverse
system operating entirely on different
principle.
Then provision of defense against
perceivable and postulated common cause
failure. So on one hand we say that
common cause failure is uh is is a
serious thing and it should be looked
into it but that doesn't mean there are
provisions are not there in the plant
there are provisions made like uh
separate separation between two
redundant module so that uh if any fire
or flooding is there both the modules
will not get affected so there is a
physical separation I'll I'll I'll show
you in some way or the other how we
implement this independent source source
of power. Suppose if the all the
redundant component they are being fed
from the same source then common cost
failure is the moment that particular
source fail. So uh in redundant system
the similar items they operate from
different source of power actually or
different location of power you know. So
then shoulding maintenance to reduce the
human error. In fact maintenance is
staggered maintenance or the philosophy
maintenance philosophy they they are
such that they say simple in one day all
the three redundant system will not be
maintained or maintenance activity will
be carried out because mistake happening
at one can happen at two and three also.
So after if you do it in a staggered
manner in the sense that uh on one
equipment you do it today next next
month or next 15 days third one for so
same common cause will not affect or
same crew or same tools or same thinking
process will not affect all the three
redundant system location module to
guard flooding fire I mean if you if I
want to safeguard against common pass
I'll be locating
equipment in different location not only
different location but different
elevations also because let's say
flooding is there in the lowest location
if I have one redundant unit at the
other loc top location that that will
not fail at least that will work
actually and fire there should be
separation you know so these are the
things and this is how safety
philosophies are implemented in complex
engineering system imagine we we we had
one parameter
that is uh CP1 uh primary system. Okay,
let us say um first is we are monitoring
the environment but because it is
electronics and then uh the these are
the uh sensors here this is a sensor. So
it is a channel A, channel B, channel C.
So same parameter is being monitored
by three channels. Okay. So then we have
a like usual sensor after sensor we have
data equation system channel A channel B
channel C.
So here we are having three channels
monitoring the same parameter. So we can
say there is a redundancy
the this channel is also doing the same
job. This channel is also doing the same
job and this channel is also doing the
same job. advantage is one channel
failure doesn't affect my operation
because my logic is two out of three
control protection logic that means as
long as two channels are operating it
doesn't get second advantage is I'm able
to do maintenance also on one channel
without affecting my plant operation so
and then safety of course u one one
channel failure will not affect our
system because two channels are in
majority voting two are working properly
out of three. So my system output will
go and it will not get affected because
the moment this channel is B the output
will be generated from these two
channels. Okay. But we said all the
three channels are uh uh same that means
they might get affected by a single
cause. Let us say um so what what I
should do I should have separation
between these channels. So this is a
physical separation to reduce the
chances of common cause failure and this
is done in realtime plant also these
channels either they are located at
different location uh different rooms so
that there is a isolation okay so now
imagine uh if suppose there is increase
in humidity in this uh room let us say
this before this partition up uh then
only this channel will be affected but
if this separation is not there then it
will be affect all the channels so that
will lead to a common cause. So we are
trying to uh to separate out common
cause failure. Okay. So this is between
among these three channel but the same
function
uh it is a primary we have a diverse
function because
suppose if this because of some common
cause reason this channel fails. So I I
as I mentioned the second safety system
is built upon the diverse mode different
totally different uh uh you know
fundamental principle. Okay. So this is
there. So with this common cause this
will not be get affected. If there is a
common cause here but this is primary.
So if there there is a failure here
automatic signal will go to take care or
it is online always. So these two
diverse system monitoring the same
parameter are these two system uh the if
this fails then this will actuate my
control output will go. So there is a
red redundancy and there is a diversity
for this system and this is how uh
systems are built uh for complex
engineering system. you you won't find
this in uh normal systems or I would say
the systems which are not um uh safety
oriented or you know u where the safety
is the overriding factor you know so
this is the kind of caution being design
provisions are made uh dur uh in fact uh
in many plants you'll find not only
three four channels also okay because if
one channel fails we totally depending
on two two channels. So um so um it is
something like you are trying to have
more resilience against uh failure. So
uh three out of four. Now it depends how
you get the your reliability get
saturated whether in two out of three or
two out of one uh but reliability or
safety is the prime importance you know.
Now let us do some uh common cost
failure mapping. Uh you know uh before
that let us understand electronic system
quality ensured through specification
like American military standard. Okay.
Uh if you don't have national standard
mil grade component mostly quality is
assured through buying a component which
is milgrade. So I'm in some sense I'm
I'm reducing the chances of common cause
failure because procurement has to be
done to build a system but if I buy
quality system the chances of uh failure
or affecting the u reliability of the
system is less then testing as part of
procurement is also measured. Now uh
like you saw pre previous system uh you
know uh where yeah u there is one more
uh thing which is there systems they are
tested by system alone automatic signals
are sent and uh they are when there so
uh that means there is a continuous
testing which goes on into the safety
system especially electronic system you
will generate a signal at this this end
and you send it here and response will
come back here. So this complete channel
will be monitored that this channel is
functioning. This is especially true if
this channel channel channel is doing a
function of safety in safety uh system
they they are in passive mode till the
demand comes. So for safety system
monitoring of the uh let's say if I give
one small impulse and test it the in
between component or modules I obtain
the desired output and then I'll say it
is healthy. If the desired output
doesn't come uh this is called periodic
testing module here also periodic
testing module. So you send a small
impulse and test the complete channel.
You you have found a beautiful way of
checking the availability of the safety
channels also when they are not active.
Okay. So that's how the safety is
ensured uh even for passive mode uh
especially safety system because process
process system they are on always if any
deviation is there you will come to know
but in safety system you will not come
to know because they are not having
active channel of course arrangements
are made in the design that some uh some
active uh phenomena is happening around
here but testing periodically and this
periodicity is it is not something like
uh minutes or hours or days. It is frau
some second one second one pulse will
go. So perpetually uh we are monitoring
the health of the system in continuous
mode actually you know if any any fault
is there it will get displayed on the
control room or the panel itself. So, so
here we are trying to say is that
testing the system uh in in institute in
the location. Okay. Failure mode effect
analysis. This is one more thing there
should not be any failure mode left out
which did not form part of our coverage.
Reliability analysis at the plant level
and meeting reliability at risk level.
So for all these systems it is very much
required in complex engine system that
reliability target and safety target
should be met. So at system level at the
plant level also individual production
uh system unavailability uh should be so
it's just a quantitive figure for some
standard I would have got it so 1 into
10^ - 5 if it is a single channel the
failure probability you can imagine
should be less than or equal to 1 into
10^ minus 5 per demand it can be around
also but it should not deviate too much
similar similarly for a complex uh Let's
say uh uh nuclear plant the s the
failure of this thing should be 10 - 5
per year one. uh now you can com if you
compare with other systems probably
you'll you'll find that the uh kind of
safe uh inbuilt safety uh into the
system is so high that we get this
probability you know and they all make
up from from component to system like
electronic system from system to plant
and that's how it is reflected here per
year 10 to minus 5 even though the plant
design ensures resilience please note
all of against the common cause failure
through various defense mechanisms uh
like uh redundancy, diversity,
independence, power supply separation,
human factors uh consideration, software
reliability.
Uh in many safety critical systems uh
the digital uh production uh is used
along with some redundancy or diversity.
Why? Because a software failure uh can
disable because imagine if the same
software on a digital three digital
channels are operating any combination
of input fault and some some uh failure
occurs it will be a common cause failure
for all the three. So always one has to
guard and you provide additional
arrangement either through analog or
maybe even other another digital system
built on different principles
altogether.
So that is the thing one has to ensure
that when electronics or this thing. So
now let us say we are talking about
plant we carried out a uh risk
assessment of the plant and so many
common cause u uh list was there with
us. Common cost failure list was there
which has come up on top you know
importance very high or high rather uh
though it is rare but relatively high um
so human affect which group this group
this group and this group they are
called common cause component group so I
have just written here I'm not giving
the specific details here and group one
to group n these are the so many things
and for some temperature is they are
giving so see here here I'm saying it is
not getting affected by temperature some
common cause group let us say hardware
component they will they will don't get
affected by temperature but if it is
electronic system yes temperature also
will will play a role in some group and
then humidity again temperature and
humidity high sensitivity for
electronics actually flooding so I have
not given the complete the this thing I
can map it here and what will happen if
I map
I have a physics of failure approach. I
can work on see common cause failure uh
is a phenomena defense against that is
again a phenomena we have reduced the
possibility but at the end of the day I
to understand all the common cause
failures and through physics of failure
approach so that this thing become
irrelevant
irrelevant I will through robustness
through some production at that level or
through some separation at that level I
will reduce the whatever PF model or
root cause analysis model says. So what
an elegant mechanism we have here only
uh probabistic mode we got this
information. Now this input we give it
to physics of failure uh consideration
or root cause analysis and we find this
is the cause uh humidity affects these
three things. So what we should do? Do
we should we provide any barrier or we
should locate in the case or I mean
there the sky is open if we understood
the cause for failure. If it is a
quality related failure then we will
check the quality of the component at
the end before it goes into the uh
plant. If it is a maintenance related
issue like maintenance means either
human or some parts which have not gone
wrong and which is potential for common
cause failure and there's some
experience is there if it is there then
we take action institutional failure
electromagnetic electromagnetic is a
phenomena which can affect the system in
adverse manner and it doesn't have to
intro introduce the system and uh so one
has to um so in common cause failure the
in the
configuration management itself these
things are ruled out you know the the
signals if it is there it will get
attunated and the effect will be
negligible or known uh failure
so fault tolerant approach for electron
design and all so I'm just giving you
one example how common cause failures
are handled so marcom model so is a
popular approach and u and then I am
making this two out of three u failure
I'm do going that means handling the all
the channels in for you saw the three
channels they are operating and all that
so two out of three I consider when the
two channel out of three channel fail I
call it a failure so suppose if I have
three channels and then the assumption
is protection and control system
comprise of three redundant channel okay
the failure uh criteria is two out of
three two channel out of three channel
or only one repair station. Okay. And I
have assumed here one more thing that
the failure rates are say average
failure rate I am applying for you for
simplifying my model. So in marco there
are you'll understand when you see the
next slide actually the there are one P1
P2 P3 poor condition P1 condition means
all three out of three they are
operating and system is healthy. In P2
one out of three failed. So that means
we have two operating system it is
failed but compromised margins are
reduced and P3 is two out of three
channel failure system failure and three
out of three failure system. So that
means this three out of three failure
means there is something common cause.
So common cause and two out of three I
declare the system to be failed. Okay.
So
if I have to model this system how what
I do? So as I mentioned P1 is the
healthy state, P2 is the um P2 is the
compromised state. Uh okay uh and I have
so let us see P1 P2 are operating states
okay because even if one component
failure we have operating state and uh
there are three channels so there can be
three any of the channel can fail. So
three mode and then P2 one channel is
repaired we can only repair one channel.
So that's why one mu is one only. Uh P3
is a failed state. So I have convert
concentrated them into three state
module P1, P2 and P3 because common
cause also takes system to failed state
and two out of three also to takes to
the to the failed state. So the P3 is
called as a failed state. Exponential
distribution V used uh and all the
channels have same failure rate that is
average failure rate. MU is repair rate
and lambda C is common cause failure
rate. So this information and we saw how
the three channels they operate and what
is the failure rate two out of three. So
I'll write a state specific equation uh
probability of being in state one and if
rate of change of migrating from that
state to the other state. So dp 1 by dt
that is probability of change in
probability of this state is minus 3
lambda. So minus that mean it is
departing from this state. So minus 3
lambda plus mu returning to this state.
So this is the uh system we have. So
first equation of the system that is
they are called maron equation or state
space equations dp2 by dt. So dp2 by dt
for this state this is a outgoing state
state that is and this is again outgoing
and this is incoming. So 3 lambda will
be plus incoming state and minus 2
lambda minus mu minus uh 2 lambda minus
mu. So that will define uh rate of
change of state uh dp2 by uh dt and this
one and third one also dp3 by dt. So the
three state means here these two states
are joining it is called absorbing state
you know dp3 by d2 2 lambda plus 3
lambda c 2 lambda plus common cause
failure three lambda c
actually this should be uh lambda c only
there should not be three lambda c
because we are saying common cause
failure all the three channels have
failed okay so here this three will go
out please correct in your this thing
this equation can be solved for arriving
at probability of system failure rate. I
have written the differential equation.
You can use any method um algebraic
method or you can say uh you can these
are very simple equation you can say and
find out the probability of uh system
being in P1, P2 and P3. Our interest
will be failed state. This P3 state so
that we can find out. Okay.
You can use matrix method also you can
use algebraic methods also uh any method
you can use and solve it. Okay.
So week four electronics phm. We have
seen a interesting uh interesting uh
features of uh redundant system diverse
system. We have seen precursor parameter
how they are um for which the mode what
is the precursor parameter for for which
uh sensor what are the um uh degradation
attribute we should monitor role of
common cost failure in complex
engineering system sensor failure and
common cost failure. Why envir
environmental modeling and finally the
common uh a marco model uh to account
for failure repair and common cause
failure. So probably you would have
understood now by this time that it is
not only a electronic component but it
is basically a channel that means
starting from sensor to final actuations
you can monitor and their combination uh
and then common cause failure what
effect and human factor what effect it
has got probably it was pretty clear in
this now I'll touch upon this
electronics PM when I have dedicated
week for uh electronics prognostics and
health management because there are many
subtle aspect that we need to discuss uh
over there as part of the system. Thank
you.