In a discreet sense, I am going to describe
a quantity called ‘robustness’, and then the connection between quality and robustness
will be explained. What does the word ‘robustness’ mean? Usually people, be it learned or not learned
or engineers or scientists have a habit of using these words: quality, robustness, reliability
and durability synonymously. As a matter of fact, we will see that durability
is a subset of quality, and reliability is also a subset of quality in one sense. What do you think robustness is? Your opinion, your thoughts about it… Student 1: Strength of a product. Student 2: Maybe, how the product is performing
under different environmental conditions. Student 3: Efficiency. It can be any of these three answers or it could
be a combination of that, but the answer product performance under different environmental
conditions is very close to the actual perspective of what robustness is but then you have to
change the words to make it more precise. What robustness says is; irrespective of variations
in the input, the output can vary only within allowed specification or tolerance. There are ‘n’ number of variables that
are going to vary, we observed that they could be aleatoric uncertainties, which means there
is inherent randomness or the uncertainty could be epistemic which means you might be
able to control it. But there is uncertainty, which is going to
propagate through the model which in turn affects the performance. Irrespective of the variability in your input
my output variability should be minimal or it should be within the limits that I prescribed. So, this goes back to our example; that if
I am a two-wheeler seller. I sell a bike to you, a motorbike. And then I promise ‘x’ kilometers per
liter. You drive it and then you figure out that
it is x minus 15 kilometers per liter. What will you say when you come for the first
service? You are going to say that you have cheated
me, because it is heavily deviating from what we promised. Then I ask you where did you drive it? You said, “Oh, I actually drove it in Bangalore.” Then if I say, “No, no. This engine was designed to operate in Chennai. So, you can only drive it in the roads of
Adyar or Velachery, if you drive elsewhere we cannot promise this.” Is that an acceptable statement? It is not an acceptable statement. For whatever reason I just gave the example
of Bangalore, it could be anywhere else, it can be Kashmir. So, irrespective of the temperature, irrespective
of what kind of a rider you are, irrespective of what roads you have driven, irrespective
of where you went and pumped your petrol, irrespective of any input condition that would
influence the efficiency or the mileage of my vehicle. Your vehicle is expected to give minimal variation,
plus or minus of what I promised. I promised x kilometer per liter I understand
plus or minus few kilometer is acceptable. If I give like 50 kilometers per liter and
my engine is giving you only 35 kilometers per liter you are going to be a heavily disappointed
person. So, that is the key idea of robustness, this
is more from a conceptual perspective, but how do you achieve it? Irrespective of the variability in the input
my variability in the output should be minimal or within the specification that I state that’s
one part of it. The second part is you don’t touch the cause
for variation, you still live with the cause for variation, but you minimize the variation
in the output. That is the important part. For instance the dealer understood the variation
in the mileage was because of the roads in which you drove. So, Can he say? Sir, you cannot drive the vehicle in the gullies,
you can only ride the vehicle in the highways. He cannot say that, he should tune the engine
to an extent that irrespective of whatever road you drive, it should still give you close
to 50 kilometers per liter. So, you cannot get rid of the source of variation,
you have to live with the source of variation, but still make sure your output does not vary
more than the specified limit. Figure 1. Brick Kiln
We will discuss an example here, which will drive this point home. So, here is a Kiln (Fig. 1), Kiln which means
a furnace. It is being used to make tiles. There is a burner and this is the wall of
the Kiln and these are the the tiles that are being produced. You know how the bricks are usually done. There is some molten mixture, cut into cakes
and it is placed and then it is burnt. This furnace is a bit advanced. So, to make the problem little spicy, what
I have done is; I say that this machine was bought out of Germany or some other country. Don’t worry about where it was bought out
of. And you cannot make any changes to the furnace,
because the moment you make changes to the design the furnace the warranty is void. There was a problem when people started using
this furnace, what happened was; the output tiles that came out were of irregular size. If you see the tiles that we usually have,
they are 1x1 (one foot by one foot) right? So, imagine I give you 10 tiles to lay. One is 1x1.2, the other one is 1x0.8 and the
other one is 0.8x1. So, I give you tiles of different sizes, you
think you can lay it? You cannot. So, this is something that we might not have
really realized all these days. If you get down to the floor and then you
look at them they are all in a very straight line. Actually, if we observe them very closely
there will be small deviations. Very small deviations will be there, that’s
why they use the white color bonding material or whatever the tile color is, corresponding
bonding material will be used so that you will not be able to see the difference. But there will be this minor difference which
when you stand and see with the naked eyes you will not find. You will have to lie parallel to the tile
and then you should be able to see. Figure 2. Central Tiles (highlighted) in Brick Kiln
So this irregularity in tiles that we are talking about here is much larger than that,
0.8x1 is visually apparent, you can see the difference with the naked eyes. But I know the cause for the irregularity
in tile sizes. The cause is that the tiles in the central
part are exposed to a lower temperature compared to the ones on the outside which means there
is a temperature gradient, there is no uniform temperature. There is a burner and the way in which it
functions is, there is a gradient of temperature. As a result, the tiles when they come out
they are of different sizes. What do you think can be done to address this
problem? You cannot change the Kiln because it is very
expensive and you have bought it from Germany. You cannot go and change any part of the Kiln,
because the moment you make changes to it, its warranty is void, these are the constraints. Yeah? It’s better to not put the tiles in the
middle where the temperature gradient is low… Ok so given the assumption that you know the
gradient of the temperature, what he says is; let’s remove the central one so that
the bricks that are exposed to the low temperature are not, you know they are not exposed at
all, I mean they are not there. Yes, it is a potential solution, but also
remember that this is only a representative figure. I will make the problem slightly challenging. Imagine there are about 9 columns instead
of three, and then 9 columns from a projection and 9 columns deep also. So, it is about a 9 by 9 so you have about
81 and the central 3 represent the center. So, you are talking about 3 times 9, 27. So, let’s say about 10 brick height or tiles
high is what the each column is, then you are talking about 270 to 300 tiles, less in
productivity each time that you are you will have to open the furnace and close it, which
is why you have gone to Germany and bought this, it is very expensive, but it also gives
you a very good productivity, ok, but that answer is acceptable. But what I am saying is you still want the
full productivity right. So, you do not want to remove this one, what
else? Suppose you alter the rows that are burnt
with Oh no, no, that you cannot do, see basically
this is like baking, ok. You open the oven, you put the dough inside
and you close it. You open and then you take the made out bread. You cannot just open it in-between and put
some cherries and then close. Once done put it then take it once it is done. So, I otherwise also it is not that easy to
handle the hot brick, ok, and yeah then? It is symmetric so you can check one kind
of property, can choose that rows or columns or something
And do what? We can like, usually predict the results. No, I know the results, I know that meaning;
that is when I can do what he told right I know the temperature gradient; if you have
noticed clearly I use the word assuming that we know the temperature gradient. I know that this is going to come out with
0.8. I know that will come at 1 that I know. Before coming out you know that this is going
to be 0.8, this is going to be 1, this is going to be 1.2 that I know, but how do you
deal with the problem. Because I want all of them to be of the same
size more or less. Can the bed be moving type? The burner… Yes and yes and no, but what I am saying is
let us say it is yes, it is already there and with that you feel this problem, ok. So, if it is no. Fine, it’s no. With that you find this problem; meaning you
cannot change it now, if it is static it is static you cannot say let us go and rotate. No you cannot touch the furnace. Increase the temperature. Oh the other one will become even smaller,
from 0.8 it will become 0.5, you won’t know whether it is a tile or it is a stone. You understand what I am saying right? When you increase there is a gradient, the
gradient will go like this, the gradient will only translate. Increase the time. Time? Temperature will be uniform. No it will not, that is what I am saying the
gradient, it will maintain the gradient for whatever reason. We can insulate the tiles… um… We can design it the way that positive part
are on the outside of the same size; so, we can use multiple designs and accommodate… That is one way of looking at it. So, what he is saying is; since we know what
is going to be the output size why cut them all to the same size, why will you cut all
of them to 0.8 by 0.8. If you think that this guy is going to be
larger than what you expect, 1.2, then you cut it smaller so that when he instead of
being 1.2 he will become 1. Similarly, the ones who which go in the center,
you cut it of a larger size and then he will come to 1, ok. That is an acceptable solution, but still
you have to do some kind of a pre processing you need to understand you need to correlate
and then you need to, but that is an accepted solution, what else? Yeah, see in this whole thing the solution
that you give is fine. But I also want you to understand an important
underlying idea about robustness, ok, that is, that is; coming in terms of the constraint. In another couple of minutes you will understand
what I am talking about, ok, but I want you to appreciate that while you are trying to
give the solution. Anything else? Any other solution that you can think of? Ok. So, these are fair enough solutions that you
have given from a data perspective because that is all I have told you right? But you can also go into the physics of the
problem a little bit which I don’t expect, but it is a trivial thing if you look at it. You know how these bricks are made? What are the major components of the bricks? And, why temperature is going to influence
the size? Do you know? Because what I am saying is that’s all right. What is the problem here? It says no uniform temperature, why should
the uniform temperature or no uniform temperature influence the size of your tile? What plays the role here? The temperature plays a role, what will happen
if I am going to heat something; if I am going to heat something what will happen? They will contract? and if you heat something
they will contract, is it? Depends on the material. Depends on the material right, but in this
material what will happen? Whether it expands or contracts there is a
property of the material that will play a role, what is that material; no sorry what
is the property, you told just now. Thermal expansion. It is a coefficient of. Thermal. Thermal expansion, ok, there is some material
that might expand this much, there is some material that might only expand this much. How do I describe that? Using the coefficient of thermal expansion. That plays a role here. What it is saying is; there is a material,
this is the coefficient of thermal expansion, but what is happening is; there is a ?? that
??? is what the term is right? The ?? is large in the ones that are in the
corner compared to the ones in the center. Hence, they will expand more compared to the
ones in the center. One way to deal with that would be to check
out what is the size and then do it, the other one will be to look at the material itself
because the material that goes into it is your input it is not part of the furnace. If you know the physics of it, basically lime
and clay are the material that go into it. What I will do is; I will play around with
the composition (because there are two materials) such that the coefficient of thermal expansion
matches the gradient. So, it will have a large coefficient of thermal
expansion at the center and it will have a less coefficient of thermal expansion towards
the end in such a gradient that it will match the temperature gradient. So, you can go ahead and do that, but this
is also pre processing only, you should know you should do some experiments to understand
how to do that. This is just an example to drive home the
point on robustness. Now let me ask you the question, what was
the source of randomness in this or source of uncertainty in this? Source of the error in this? Temperature. Sorry? Temperature gradient. The temperature? Gradient. The temperature, the non-uniform temperature
right. Did you go and change the non-uniform temperature? Because I told you that you cannot touch the
furnace otherwise the first thing that you would have told is, “Sir, let us go and
fix the burner”. You cannot fix that I told you that you cannot
touch that. So, irrespective of the variation in the input,
I expect my tile which is my output variation should be very less. I say 1x1, but I will accept 0.98 to 1.2. I will accept that, sorry not 1.2, 1.02 I
will accept. I cannot accept 0.8 and 1.2, I can accept
0.98 and 1.02. The variation in the input temperature, I
have not addressed that at all it is still, with whatever solution that you gave and the
one that I showed just now, the uniform temperature, the non-uniform temperature is still there
I have not addressed that problem, but still I am getting an output of my tiles which are
1 by 1. That is the idea behind robustness. You should minimize the effect of the cause,
you cannot touch the cause, we did not go and change the non uniform temperature, but
what you have done is, what is the effect of the non-uniform temperature? It is, it created or it resulted in tiles
that are of, that did not adhere to a 1x1 size. However, I have minimized the effect of the
non uniform temperature which is the cause, without controlling the cause itself, in this
case it will be the Kiln design. I have not touched that. This is the robust design principle. You have to live with the uncertainties or
you have to live with the cause of the variation, but still you should be able to achieve your
output, which in our case is a specified variation or within the specification and this is also
sometimes called as parameter design or p-design. Usually if you see there will be a block,
and they will have some factors that come into it. The factors are nothing but the parameter
so, p stands for the parameter hence it is called the p-design. This is the underlying idea on robustness. Now what I am trying to show you is a small
pictorial depiction of the Kiln example itself, ok. So, there are… the first one is this initial
distribution here. You see this guy, what it means is there is
a mean, ok, average that we are talking about, ok. So, this average that I am talking about is
probably the 1 cross 1 that I am talking, ok, the area square meter or sorry square
feet let us say, 1 by 1 square feet, ok. What I am saying is; if I were to draw this
here let us say, this is your tile dimension. Okay, and then I am taking the first tile
and then I am measuring what it was, it was this much, ok, it’s it’s somewhere here,
and then I went to the second one it was here it was here, it was here and then what does
the height of this one mean? It means there are multiple numbers at that
level. So, if I did about 1000 tiles, ok. It is likely that this number of tiles might
be about 500 or 600 in this level. And there might be some here like about 200,
this might be about 200 this might be like that, ok and this is usually called the histogram,
ok. It is basically a frequency plot. How many times or how many tiles out of the
total tiles measured about 1 by 1. How many of them measured 0.8 by 1, how many
of them measured 1.2 by 1, ok. Then you can kind of I mean it is not straightforward,
but you can kind of come up with this, that is what we have plotted here, ok. So, what it means is there is a larger variation;
I have not given you any dimensions here, the dimensions was just to motivate the example,
ok. So, what it means is this ‘m’ is what
your target is this is 1 by 1 for instance is what the ‘m’ is, this is what is the
promised target but there was a deviation in the tile dimension before the solution. After implementing the solution, again, it
is not that it is going to be a straight line still there will be variation, but the variation
is… smaller. This is how you measure the variation. How thin or how fat that is not the correct
word, but for us to discuss here to enable the discussion, ok, this distribution is thinner
compared to this distribution which is fatter. A fatter distribution means; there is lot
of deviation from what is promised or what is expected, ok. Whereas in this there is only a smaller deviation
from what is expected, ok, which again means that there is more samples that is why this
is a taller distribution when it is a thinner it is also a taller distribution, ok, but
let us say that you have a magic machine, which lets you produce tiles of 1 by 1 dimension. How will this plot look like? It is just this straight line, ok, if you
had thousand products it will be 1000 by 1000. It’s 1, that’s all. Otherwise I am saying there are about 800,
in here there are about 800 tiles, where here there are about 100 tiles in this area and
there are about 100 tiles in this area and there are about 10 tiles here and there are
about 10 tiles here, ok. They will come as close as possible to your
promise, but still there will be some variation. So, the requirement in any manufacturing or
product, ok, so these are two different things when I say manufacturing is manufacturing
of a product, but manufacturing ends by the time the user goes to the shop and gets it,
until then is what the manufacturer has control, the dealer has control. After that it is the performance that is why
I said either in manufacturing or product, when I say product it is performance when
I say manufacturing when it is with the dealer. And this is also one of the subtle difference
that people point out is until I sell it to you it is called quality. The moment you bought it from me it is going
to be how well it performed to your expectations or to my promise then that is called reliability. How well it performs with you is called reliability
and how well did I meet the specifications, ok, until I sold it to you is called quality. That is that is a small distinction that people
make, it is a subtle distinction, ok. Okay, so, from… are you fine with this explanation? like, so, usually you can draw it from a histogram
you can get these distributions if at all we are talking about that, ok. So, another part what becomes interesting
is; when you want to measure the quality during design, ok. So, all this time we were only talking about
the geometry or the manufacturing tolerance and all that right. So, that is what is given here in terms of
parameter versus performance, ok. Now you need to talk about both performance
as well as adhering to the specifications in terms of the geometric conditions, right? So, that is what is the parameter and then
the performance is what the reliability that we talk about. And… what are all the parameters that you
need to worry about, ok, in this one for instance in this particular example that we are talking
about there might be other parameters also that will play a role. You can you can do further research to understand
why there was a variation in this. Didn’t I make sure? like after 5 days after 10 days you might
get a better understanding of the composition, and you might be able to drive it even further,
ok, or let’s say that I relax one of the constraints like you can touch it you can
touch the burners a little bit. Then you might be able to bring down the variation
even better, ok. So, you need to understand what the parameters
are which parameters play a role that becomes a very important stuff. And in order to do that you need to have efficient
experiments this exp stands for experiments; to find a dependable information on the parameters. There are different ways or mathematical techniques
or statistical techniques to do that, if you have a bunch of data today you can find out
causal relationships, you can use something called the principal component analysis, support
vector, singular value decompositions and things like that. These are all comes under something called
factor analysis, they will tell you out of these factors, out of the 10 factors that
you thought only these 2 factors are very important, then you can do the study representing
only those 2 factors.
