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This lesson is about process capability analysis.

So, what you're going to see is how you can

compare based on some measurements that you get from the process,

how you can compare how the process is doing with what the customer is expecting.

So, that's going to be based on

some expectations of customers that you get based on market research,

based on talking to customers, right?

So, we're making a comparison between

customer expectations and the capability of the process.

How is the process performing,

given the current conditions, right?

So, let's see how we can do that.

So, process capability analysis,

this type of analysis can be used,

first of all, only for measurement data.

So, we're using this for continuous kind of

data where you're talking about time to serve the customer,

weight of a particular item,

those kinds of data.

We're assuming a normal distribution of data as we

do with a lot of things in quality management.

To keep things simple,

we use assuming normal distribution.

So, we're assuming a normal distribution for this kind of analysis.

And, the most important thing here to keep in mind is that,

we will be doing process capability analysis

with the assumption that the process is under statistical control.

So, what this means is, when you're doing this in practice,

you want to make sure that statistical control has been established,

that you know the inherent capability of the process

based on doing some kind of statistical process control analysis.

So, that becomes the first step before you go into doing a process capability analysis.

From an intuitive perspective, that should make sense.

It should make sense because what you're doing is

you're going and talking to a customer and promising something.

You're saying, "Are we going to be able to give you what you're expecting?"

In order to do that,

you better be sure about how your process is performing.

So from an intuitive perspective,

it should make sense that you establish the capability of your process before

you check for process capability based on customer expectations, right?

So, let's take a look at some of the calculations that we do here.

Basically, we'll look at two different ratios.

The first of which is called the process capability ratio or CP, in short, right?

So, what is the CP ratio?

It's the ratio of what is

the customer tolerance of whatever measurement you are talking about.

How do we get the tolerance?

You get it by taking

the upper specification limit that the customer is

giving you subtracting the lower specification limit, right?

So, you're getting the range of the tolerance

for that particular measurement that the customer is giving you.

So for example, the customer may be telling you,

I expect this to be delivered between 20 and 25 days.

So, that gives you a range of 5 based on 25 minus 20.

Or the customer might tell you,

I expect the weight of this to be between 15.5 to 16.5 ounces.

So, that gives you a one ounce range for your tolerance and that goes

into the numerator of this particular ratio, right?

What you have in the denominator of this ratio is six times the standard deviation.

So, S stands for standard deviation and that's what you get from your process, right?

So, the numerators coming from the customer and

the denominator is coming from what you measure in your process,

what you find out from your process,

how your process is currently doing.

How do you interpret what you get from this ratio?

You are looking for essentially a ratio that's greater than one.

Less than one is going to indicate that it's not

capable of delivering to customer specifications.

Greater than one, one is going to say that it's just

capable and greater than one is going to say that it's better than being capable, right?

So, the higher this ratio,

the better it is in terms of serving customer expectations,

in terms of keeping customers happy.

Alright, so, where does this idea

of six standard deviations in the denominator come from?

So, why do we have upper minus lower specification limit

divided by six standard deviation?

So, the idea comes from the standard normal distribution.

We rely on the fact that 99.7% of the observations are going to be

between plus and minus three standard deviations

or the other words plus and minus three standard deviations, right?

So, you have plus and minus three. So, you have a total of

six standard deviations of range that you're getting.

So, that's what's going into the denominator of this particular ratio.

Now, let's take a look at the intuition behind

this particular ratio and see what we're getting here.

So, let's take a look at the the voice of the customer here first.

And what you have is the customer is telling you their tolerance range, right?

They're telling you their tolerance range.

And we can call that the voice of the customer, right?

It's whatever the customer is telling you.

And what you're saying is that this range,

if you look at the width of this particular line segment,

what you're saying is that that should be greater than the voice of the process, right?

So, what you're getting in terms of the variation in

your process is being depicted in the denominator as six standard deviations.

And that's your process range,

which is being depicted by six times standard deviation.

So, when we're saying that we want this ratio to be one or greater than one.

A ratio of one would mean that this voice of the process and

this voice of the process and voice of the customer are equal.

If these are equal,

that saying that it's the ratio of one, right?

And if the voice of the process is

smaller and the voice of the customer has a greater range,

then you're saying that the ratio is going to be greater than one.

So, that's the intuition behind looking for a ratio that

is at least one and the higher it is than one,

the better it is going to be in terms of serving the customer, right?

So, let's take a look at the next ratio that is part of

this process capability analysis and that's called a CPK or the process capability index.

So, the process capability index incorporates

some more information than what we saw in the process capability ratio.

So what you have here is, you have,

if you look at the ratio that's given to us the calculation,

it's the minimum of the X double bar,

it's called double bar because it's the mean of means.

So, it's the double bar minus lower specification limit.

X double bar coming to you from the process

lower specification limit coming to you from the customer,

divide that by three times a standard deviation.

And as this next calculation,

you have the upper specification minus X double bar.

There should be an X double bar divided by three times the standard deviation.

So, you're doing these two calculations

and you're taking the minimum of these two, right?

We'll take the minimum of these two and we'll compare it with that same standard that we

had earlier is we want it to be one or greater than one.

One at a minimum. Greater than one is going to be better.

Lower than one means it's not going to fit into what the customer is expecting.

So, here we have the voice of the customer, right?

What we had earlier, when we looked at the process capability ratio.

And the voice of the customer is given to us,

based on market research,

there's a tolerance range that's given to us.

Now, here, these specific numbers matter. Why do they matter?

Because we're not just comparing this range with the other range.

This range with the process range.

We're comparing this with where the process is located.

So, if you noticed earlier,

I just looked at whether that range of the voice of

the customer was greater than the range of the voice of the process.

But here, I'm not only looking at whether it's greater,

but where it is situated in relation to each other.

So, if this is the voice of the process, right?

This is based on there being some kind of mean over here,

which we refer typically as X double bar,

and this is going to be based on your plus or minus three standard deviations, right?

So, in this particular example you're seeing,

just on the basis of this picture,

that there will be output from this process

that's going to go beyond the voice of the customer.

So, what is it telling us?

That this process is located,

is centered too much to the left.

Now, if you look at the range that we had in this process,

this range is smaller than the range of the tolerance of the customer.

So in that sense, what you're going to get if this was,

if we were to put numbers on this,

you're going to get a process capability ratio that's going to be okay.

That's going to be greater than one.

However, because the mean is too low,

even though the range is compatible,

it's falling within what the customer is expecting.

It's located too far to the left, and therefore,

you're going to get output from this process that's

going to fall outside of the customer's tolerance range.

So, that's the intuition that you have behind the process capability index.