0:14

This lesson is about process capability analysis.

So what you're gonna 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.

That's going to be based on some expectations of customers that you get

based on market research, based on talking to customers.

We're making a comparison between customer expectations and the capability

of the process, how is the process performing given the current conditions.

0:48

Let's see how we can do that.

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 assume a 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.

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.

That becomes a 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 in

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.

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.

2:44

What is a CP Ratio?

It's the ratio of what is the customer tolerance

of whatever measurement you're 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.

You're getting the range of the tolerance for

that particular measurement that the customer is giving you.

For example, the customer maybe telling you,

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

That gives you a range of five 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.

That gives you a one ounce range for your tolerance.

And that goes into the numerator of this particular ratio.

3:37

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.

The numerator is 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.

The higher this ratio, the better it is

in terms of serving customer expectations in terms of keeping customers happy.

4:29

All right, so

where does this idea of six standard deviations in the denominator come from?

So why do we have upper minus lower specification limit,

divide by six standard deviations?

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.

You have plus and minus three so

you have a total of six standard deviations of range that you are getting.

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.

Let's take a look at the voice of the customer here first.

And what you have is the customer is telling you their tolerance range.

They're telling you their tolerance range.

7:05

The process capability index incorporates some more information than what we saw

in the process capability ratio.

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 x double bar minus the 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 the 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.

You're doing these two calculations and you're taking the minimum of these two.

We'll take the minimum of these two and

we'll compare it with that same standard that we had earlier.

Is we wanted to be 1 or greater than 1.

1 at the minimum, greater than 1 is gonna be better,

lower than 1 means it's not going to fit into what the customer is expecting.

8:28

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 3 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.

9:28

So what is this telling us?

That this process is located, is centered too much to the left.

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

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

So in that sense what you're gonna get 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 1.

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 intuition that you have behind the process capability index.

Now let's take a look at an example to see how this plays out.

10:38

Market research has determined that the customers that come in there,

they are mainly people who are working in the offices on Michigan Avenue and

in nearby offices or they are tourists who are walking in there to get a quick meal.

They expect their orders to take between 2 and 16 minutes.

So, what is our customer expectations?

The lower specification limit, or LSL, for customer expectation is two minutes.

The upper specification limit is 16 minutes, right?

They're expecting that because of the customization.

It can't be 0, so it's gonna take at least 2 minutes for it to get done, but

they're expecting it to be done in a maximum of 16 minutes.

That's their expectation.

When you go and look at the actual process,

when this restaurant assessed their actual process,

they found the average turn around time, from order to arrival, to be 12 minutes.

So this is coming from the process.

This is coming from data collected about the process, and

they find an average of 12 minutes and the standard deviation of 2 minutes.

So the question is,

is this process going to be capable of conforming to customer expectations?

Now, remember that we are assuming that this process is in statistical control,

that the 2 and 12 represent the inherent capability of the process.

So in that sense, we are quite confident of the 2 and

12 when we're comparing it with the 2 and 16, right?

So with standard deviation of 2 and mean of 12,

we're quite confident about that when we are comparing it

with the specification limits given to us by the customer.

12:16

All right, so let's do some of the calculations and see what we can find.

So what we're gonna calculate is the CP and

the CPK, process capability ratio and the process capability the index.

Both of these have to be calculated at all times.

You can't do one without the other.

So let's take a look at the process capability ratio first.

Upper specification limit of 16, lower specification limit of two.

We subtract 16-2 and we divide that by 6 times the standard deviation.

Where did the 6 come from?

That's part of the formula.

That came from having plus or minus 3 standard deviations, so

we used that property of the normal distribution, and

the 2 is the standard deviation in the denominator.

13:29

Now if you notice here before we get to the process capability index,

I said the process has the potential of being capable.

Because remember what we saw in the picture earlier,

that you can have a range that falls within the customer's specifications.

You can have a process range that falls within the customer range.

However, it might be located in terms of centering of that process.

It might be too much to the left or the right.

All right, so let's take a look at the process capability index.

The calculations are going to be based on,

we need to do two calculations based on incorporating the mean off the process.

So, here we're actually going to use that average service time

of 12 minutes in our calculations.

If you noticed in the CP calculation, we had nothing to do with the 12 minutes.

We simply relied on the 2 minutes of standard deviation.

So we're gonna take the minimum of these two ratios and

when you calculate these through, you get 1.67 and 0.67.

So what is this telling us?

It's telling us that there's going to be a problem.

We find a ratio that's less than 1,

it's telling us that this process is not capable of serving this customer.

In fact, it's telling us that the mean is too far to the right.

Now, how do we know that?

Two ways, you can look at which of those two ratios gave us a 0.67 and

you'll see that it was on the upper side when you did 16 minus 12.

That's where you got the number that was less than 1.

So that's telling us that it is going to be on the upper side.

You can also simply take a look at the upper and lower specification limits and

compare with

15:15

the center of the process that you have from the process average, right?

So if you look at the center of the upper and

lower specification limits of the customer, it's between 16 and 2.

So that's going to be at 9, right?

So you have 2 plus 7, 9.

7 plus 9, 16.

So 9 is the center.

And then you can see the average service time of 12 minutes is higher than 9.

So it's too much to the right, too far to the right, and

that's why you have times that are going to be higher than the upper

specification limit coming out of this process, right.

So this gives us a quick indication that this process is not going to be capable of

serving these types of customers.

They're gonna be unhappy customers.

So overall interpretation, the variability seems to be okay.

It's low enough for us to fulfill customer expectations, for

the restaurant to fulfill customer expectations, but the average is too high.

What can this restaurant do?

it can do two things.

It can reduce the average, get it to nine.

By getting it to nine it's going to have a process that will look capable

off serving the customer expectation.

Or you can reduce the standard deviation.

So if the restaurant were to make their process more predictable.

Have their standard deviation of the process reduced.

Lets say from two to one, right now the standard deviation is two if they can

have that standard deviation to one that would also make the process typical.

Now which one this restaurant is able to do, that's going to need more information.

Right, I mean whether they can can actually reduce the time that it takes,

it may not be able to reduce the average time.

Based on the kinds of orders that it gets, and

the kinds of things it needs to do to produce those orders.

Can it reduce the standard deviation?

Maybe, based on different training of different

people who are working in the kitchen, and

different training of different people who are serving and taking orders outside.

There might be some things that can be done to reduce the variation,

to reduce the standard deviation of the process.

If that can be reduced,

then the process will become capable of serving these kinds of customers.

You get a ratio that is going to be greater than one.

Both in the case of CP and CPK, all right?

So, in summary, what we're saying is the process is capable

when you have a process capability ratio as well as a process capability index.

Both being one or greater.

One is the minimum, greater than one better.

The higher the better, right?

So, let's take a look at this whole idea in terms of pictures.

What are we saying here.

So, if a process is capable, this is how it will look, right?

You have the center value of 9.

We can call that the nominal value that the customer has given us.

We have a lower specification limit of 2 minutes.

Upper specification limit of 16 minutes.

The 9 minutes is a nominal value.

That's a center value.

That's the ideal value that the customer is expecting.

What we are saying with a process that is capable is we are saying that the process

distribution falls within the lower and upper specification limits.

18:35

Picture this with a process that is not capable

of serving these kinds of customers.

So we're saying that we found the process to be centered too far to the right.

It was centered the mean was 12 minutes.

So if you look at 12 minutes and

the standard deviation going from 12 minutes toward the higher side.

It was falling too much to outside of the upper specification limits.

So you needed to either shift the mean or reduce the standard deviation.

Get this distribution to be tighter for

that red graph to fall within two and 16.

More importantly more than 2 and 16, right?

So that's an interpretation that you can see, in terms of pictures.

19:20

All right, so let's take this and try to apply it in terms of different scenarios.

So what you will see in the next slide, is you will see four different situations,

based on customer specifications and process distribution being depicted.

And what I would like you to do for each situation just think about what

it's telling you in terms of whether this process is going to be capable or

whether the process capability ratio and the process capability index will be

one or greater in each of these cases simply based on looking at these pictures.

No numbers here simply looking at pi whether each of those, whether

the ratio and the index are going to be one or greater in each of these cases.

So take a look at these pictures now.

20:55

For scenario B, what can you say?

You can say that each of those, the ratio and

the index, both of them are going to be exactly one, right?

The variability in the process, if you look at plus or

minus 3 standard deviations, makes up exactly the customer specification range.

So if you look at upper minus lower specifications,

then you compare that to 6 times the standard deviation.

This is telling you that it's going to be exactly equal.

So the ratio will be 1 and the index will also be 1 in

this case because it's centered exactly at the nominal value of the customer.

22:07

Simple because you have points that are outside of the upper and

lower specification limit of the customer.

So what you can actually infer from C is that if you have a process

capability ratio, if you have a CP value that so

a process capability ratio that is less than one,

there's no point of even calculating the index there, the CPK.

Because then the CPK is also going to be less than one.

In other words what you can generally say is that the CPK value is

always going to be either equal to or less than the CP value, right?

So if you've already calculated a CP value that's less than one,

the CPK value is either gonna be equal to that or less than that so

there's no point of even looking at the CPK value.

23:00

In terms of scenario D, what do you see there?

You see that the customer specification, the range that you get from that,

and the process distribution, are equal.

So the process capability ratio will be exactly one,

however the process is centered too much to the right.

The average of the process is too much on the higher side, so you're gonna

get output that's going to be beyond customer specifications on the right side.

So that's gonna be a case of CP being one and CPK being less than one.

23:37

So let's take an example now of a situation where you

don't really care about both sides of the ratio.

So we looked at at the time that it took at a restaurant in the previous example.

And there may be situations where you say look I,

I expect the time to be zero, right.

It should be instantaneous if I'm talking about a fast food restaurant.

Then it's curtailed at zero on the left side.

You're expectation of the customer is zero.

Another example that you can think of is when you're looking at something like

a roughness of cloth, well, customer expectation is going to be that

the roughness of cloth is not there, that it's perfect, that's it's smooth and

therefore you don't have anything towards the lower specification limit.

All you have is an upper specification limit that you can tolerate.

So let's take a look at an example of that and see the difference in calculations

there, and how you would go about looking at the process capability there.

So here's a fast food restaurant now,

and the customers expect orders to arrive in less than three minutes.

So, in other words, we're saying zero to three minutes, right?

So, it's lower specification of zero.

Current process is at a burger joint,

Leslie's Burgers, delivers orders in an average of one minute.

So x double bar is one minute, and the standard deviation or s of 0.5 minutes.

Is the process capable of conforming to customer expectations?

25:38

In calculating the Cpk, you're only going to care about one site.

You're not going to look at the minimum of both of them like you did in the previous

example, but you're only going to care on the upper side in this case, and

that calculation, in this case, works out to 1.33.

So it's telling us that the process is capable of

fulfilling customer expectations.

So, when you're dealing with a one sided specification limit

you would go about it in terms of simply calculating the CPK and the one sided CPK.

You're not even going to calculate both sides for the particular index.

26:20

So in general, what are the uses of the process capability?

So it gives a quick indicator of the chance that this process,

or what you're getting from the process, is going to fulfill customer requirements.

If you scrutinize the idea of process capability analysis and if you're

familiar with statistics in general, it's not giving you any new information.

Other than simply comparing the mean of the process and looking at

when you go plus or minus, three standard deviations from the mean of the process,

whether that falls within the range of upper and lower specification limit.

So you are not getting any new information more than that, but

it's giving you a quick indicator.

So thinking about it in terms of process capability, ratio, and index- a minimum of

one- tells you that it's going to fall within specification limits or not.