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

They're mainly people who are working in the offices on Michigan Avenue and

near by offices.

Or they are tourists who are walking in there together, quick meal.

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

So, what is our customer expectation?

The lower specification limit or the LSL for

customer expectation is 2 minutes, the upper specification is 16 minutes, right?

They're expecting that, because of the customization, it can't be 0,

so it's going to 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 turnaround 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 a 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 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.

So the standard deviation of 2 and the mean of 12,

we are quite confident about that when we are comparing it with

the specifications limits given to us by the customer.

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

So what we are going to calculate is the CP and the CPK,

process capability ratio and the process capability index.

Both of these have to be calculated at all times; you can't do one without the other.

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

Upper specification limit of 16, lower specification limit of 2.

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 + or- 3 standard deviations.

So we used that property of the normal distribution, and

the 2 is the standard deviation in the denominator.

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In the numerator, you have the upper and

lower specification limits coming from the customer.

Ratio works out to greater than 1.

You can see that the numerator is greater than the denominator.

So it fits into,

the range of the process fits into the range of the customer in this case, right?

Let's look at the next thing and that's going to be your process capability index.

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 off their 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 of 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.

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So we're going to take the minimum of these two ratios.

And when you calculate these through, you get 1.6 and 0.67.

So, what is this telling us?

It's telling us that there's going to be a problem, right?

We find a ration 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 I gave as a 0.67, and

you'll see that it was on the upper side.

When you did 16- 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 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 + 7, 9.

7 + 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.

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All right, so this gives us a quick indication that this process is not going

to be capable of serving these types of customers.

They are going to 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 9.

By getting it to 9, it's going to have a process that will look capable

of serving the customer expectation.

Or you can reduce the standard deviation.

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

have the standard deviation of their process reduced, let's say from 2 to 1.

Right now the standard deviation is 2, if they can

have that standard deviation to 1, that would also make the process capable.

Now which one this restaurant is able to do?

That's going to need more information, right?

I mean, whether they 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.

And if that can be reduced,

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

You'll get a ratio that is going to be greater than 1.

Both in the case of CP and CPK.

All right, so in summary what we're saying is that

the process is capable when you have a process capability ratio,

as well as a process capability index, both being 1 or greater.

1 is a minimum, greater than 1, better.

The higher the better.