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 nine;

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

We have a lower specification limit of two minutes,

upper specification limit of 16 minutes;

the nine minutes is a nominal value.

That's the center value;

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

What we're saying with a process that is capable,

is we are saying that the process distribution

falls within the lower and upper specification limits.

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 towards 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 that you had to fall within 2 and 16,

more importantly at less than 16, right.

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

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

So what you see in the next slide,

is you'll see four different situations based on

customer specifications and process distribution being depicted.

And what I would like you to do is 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 pictures and being able to say 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.

So what can we see from here?

We can see that when you look at the scenario A,

the customer specification is much wider than the process distribution, right?

So the process capability ratio is definitely going to be greater than one;

it's going to be quite larger than one,

simply because the denominator of

that ratio is going to be much smaller than the numerator;

the customer specification is what goes into the numerator.

The process capability index is also going to be greater than one,

simply because the process is centered exactly at

where the customer specification is, right?

So that's scenario A for you.

For scenario B, what can you say?

You can say that each of those,

that 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 three standard deviations

makes up exactly the customer specification range.

So if you look at upper minus lower specifications,

and you compare that to six times standard deviation;

this is telling you that it's going to be exactly equal,

so the ratio will be one and the index will also be one in

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

Let's take a look at C, what can you expect there?

C is clearly going to be a case where

your process capability ratio is going to be less than one;

process distribution is much wider than customer specification.

So right off the bat you can say that you're going to have a lot of

output from the process that's falling above and below customer specification.

The CP or the process capability ratio is going to be less than one;

the process capability index is also going to be less than one,

simply 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,

the CPK because then the CPA is also going to be less than 1.

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 CP value that's less than 1,

the CPK value is either going to be equal to that or less than that,

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

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 going to get a lot of output or you're going to get output

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

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

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 the time that it took at a restaurant in the previous example,

and there may be situations where you say,

look 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;

your 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 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 a 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 a standard deviation or S of 0.5 minutes.

Is the process capable of conforming to customer expectations?

Right. So since we don't have a lower specification limit here,

the calculations are going to be slightly different.

So let's take a look at these calculations.

So when you don't have

a lower specification limit or the lower specification limit is zero,

you basically do not even need to look at the process capability ratio;

It's going to be meaningless, right?

Because it's bounded on the left side.

So you don't really have a meaning of comparing the range of

what the customer is expecting to the range of what your process is doing.

In calculating the CPK,

you're only going to care about one side.

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 a one sided CPK,

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

So in general or 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 specifications limit.

So you're 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,

an index of one;

a minimum of one, tells you that it's going to fall within specification limits or not.

It gives you the ability to compare this particular metric across different processes.

If you have different suppliers who you're considering or you're comparing,

you want the CP and CPK to be higher for the suppliers that you choose,

so you can do that.

It helps you think about

the cost calculations for supplies that you're getting from particular suppliers;

the higher the CP and the CPK numbers of suppliers,

the lower the chances of you getting defective raw material,

the lower the chances of you having

to work with defective raw material and get defective product at your end.

So that gives you a sense of calculating costs from different suppliers.

It becomes an effective tool in terms of giving specifications to

suppliers: You can use this ratio and index to tell

suppliers what you expect in terms of

the process capability ratio or

the process capability overall for particular items that you're dealing with.

4-2.6c Process Capability

Operations Management

Meet the Instructors