0:14

This lesson is about process capability analysis.

Â So what you're gonna see is how you can compare based on some measurements that

Â you get from the process,

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

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

Â based on market research, based on talking to customers.

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

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

Â 0:48

Let's see how we can do that.

Â Process capability analysis, this type of analysis, can be used,

Â first of all only for measurement data.

Â So we're using this for continuous kind of data, where you're talking about

Â time to serve the customer, weight of a particular item, those kinds of data.

Â We're assuming a normal distribution of data,

Â as we do with a lot of things in quality management.

Â To keep things simple, we use assume a normal distribution, so

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

Â And the most important thing here to keep in mind is that we will be

Â doing process capability analysis with

Â the assumption that the process is under statistical control.

Â What this means is, when you're doing this in practice.

Â You want to make sure that statistical control has been established.

Â That you know the inherent capability of the process

Â based on doing some kind of statistical process control analysis.

Â That becomes a first step before you go into doing a process capability analysis.

Â From an intuitive perspective that should make sense.

Â It should make sense because what you're doing is you're going in

Â talking to a customer and promising something.

Â You're saying, are we going to be able to give you what you're expecting?

Â In order to do that, you better be sure about how your process is performing.

Â From an intuitive perspective, it should make sense that you establish

Â the capability of your process before you check for

Â process capability based on customer expectations.

Â 2:44

What is a CP Ratio?

Â It's the ratio of what is the customer tolerance

Â of whatever measurement you're talking about.

Â How do we get the tolerance?

Â You get it by taking the upper specification limit

Â that the customer is giving you subtracting the lower specification limit.

Â You're getting the range of the tolerance for

Â that particular measurement that the customer is giving you.

Â For example, the customer maybe telling you,

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

Â That gives you a range of five based on 25 minus 20.

Â Or the customer might tell you,

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

Â That gives you a one ounce range for your tolerance.

Â And that goes into the numerator of this particular ratio.

Â 3:37

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

Â So s stands for standard deviation.

Â And that's what you get from your process.

Â The numerator is coming from the customer, and

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

Â what you find out from your process, how your process is currently doing.

Â How do you interpret what you get from this ratio?

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

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

Â of delivering to customer specifications.

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

Â greater than one is going to say that it's better than being capable.

Â The higher this ratio, the better it is

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

Â 4:29

All right, so

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

Â So why do we have upper minus lower specification limit,

Â divide by six standard deviations?

Â The idea comes from the standard normal distribution.

Â We rely on the fact that 99.7% of the observations

Â are going to be between plus and minus three standard deviations,

Â or the other words, plus and minus three standard deviations.

Â You have plus and minus three so

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

Â That's what's going into the denominator of this particular ratio.

Â Now let's take a look at the intuition behind this particular ratio and

Â see what we're getting here.

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

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

Â They're telling you their tolerance range.

Â 7:05

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

Â in the process capability ratio.

Â What you have here is you have, if you look at the ratio that's given to us,

Â the calculation, it's the minimum of the x double bar.

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

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

Â x double bar coming to you from the process,

Â lower specification limit coming to you from the customer.

Â Divide that by three times the standard deviation.

Â And as this next calculation you have the upper specification minus x double bar.

Â There should be an x double bar.

Â Divided by three times the standard deviation.

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

Â We'll take the minimum of these two and

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

Â Is we wanted to be 1 or greater than 1.

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

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

Â 8:28

Now here, these specific numbers matter.

Â Why do they matter?

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

Â this range with the process range.

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

Â So if you noticed earlier, I just looked at whether that range of

Â the voice of the customer was greater than the range of the voice of the process, but

Â here I'm not only looking at whether it's greater but

Â where it is situated in relation to each other.

Â So if this is the voice of the process Right?

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

Â which we refer typically as x double bar, and

Â this is going to be based on your plus or minus 3 standard deviations, right.

Â So in this particular example you're seeing just on the basis of this picture

Â that there will be output from this process that's going to go beyond

Â the voice of the customer.

Â 9:28

So what is this telling us?

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

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

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

Â So in that sense what you're gonna get if we were to put numbers on this,

Â you're going to get a process capability ratio.

Â That's going to be okay, that's going to be greater than 1.

Â However, because the mean is too low, even though the range

Â is compatible, it's falling within what the customer is expecting,

Â it's located too far to the left and therefore you're going to get output

Â from this process that's going to fall outside of the customer's tolerance range.

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

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

Â 10:38

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

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

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

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

Â So, what is our customer expectations?

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

Â The upper specification limit is 16 minutes, right?

Â They're expecting that because of the customization.

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

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

Â That's their expectation.

Â When you go and look at the actual process,

Â when this restaurant assessed their actual process,

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

Â So this is coming from the process.

Â This is coming from data collected about the process, and

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

Â So the question is,

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

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

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

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

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

Â So with standard deviation of 2 and mean of 12,

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

Â with the specification limits given to us by the customer.

Â 12:16

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

Â So what we're gonna calculate is the CP and

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

Â Both of these have to be calculated at all times.

Â You can't do one without the other.

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

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

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

Â Where did the 6 come from?

Â That's part of the formula.

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

Â we used that property of the normal distribution, and

Â the 2 is the standard deviation in the denominator.

Â 13:29

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

Â I said the process has the potential of being capable.

Â Because remember what we saw in the picture earlier,

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

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

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

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

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

Â The calculations are going to be based on,

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

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

Â of 12 minutes in our calculations.

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

Â We simply relied on the 2 minutes of standard deviation.

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

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

Â So what is this telling us?

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

Â We find a ratio that's less than 1,

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

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

Â Now, how do we know that?

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

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

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

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

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

Â compare with

Â 15:15

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

Â So if you look at the center of the upper and

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

Â So that's going to be at 9, right?

Â So you have 2 plus 7, 9.

Â 7 plus 9, 16.

Â So 9 is the center.

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

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

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

Â specification limit coming out of this process, right.

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

Â serving these types of customers.

Â They're gonna be unhappy customers.

Â So overall interpretation, the variability seems to be okay.

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

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

Â What can this restaurant do?

Â it can do two things.

Â It can reduce the average, get it to nine.

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

Â off serving the customer expectation.

Â Or you can reduce the standard deviation.

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

Â Have their standard deviation of the process reduced.

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

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

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

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

Â it may not be able to reduce the average time.

Â Based on the kinds of orders that it gets, and

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

Â Can it reduce the standard deviation?

Â Maybe, based on different training of different

Â people who are working in the kitchen, and

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

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

Â to reduce the standard deviation of the process.

Â If that can be reduced,

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

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

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

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

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

Â Both being one or greater.

Â One is the minimum, greater than one better.

Â The higher the better, right?

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

Â What are we saying here.

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

Â You have the center value of 9.

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

Â We have a lower specification limit of 2 minutes.

Â Upper specification limit of 16 minutes.

Â The 9 minutes is a nominal value.

Â That's a center value.

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

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

Â distribution falls within the lower and upper specification limits.

Â 18:35

Picture this with a process that is not capable

Â of serving these kinds of customers.

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

Â It was centered the mean was 12 minutes.

Â So if you look at 12 minutes and

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

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

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

Â Get this distribution to be tighter for

Â that red graph to fall within two and 16.

Â More importantly more than 2 and 16, right?

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

Â 19:20

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

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

Â based on customer specifications and process distribution being depicted.

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

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

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

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

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

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

Â So take a look at these pictures now.

Â 20:55

For scenario B, what can you say?

Â You can say that each of those, the ratio and

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

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

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

Â So if you look at upper minus lower specifications,

Â then you compare that to 6 times the standard deviation.

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

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

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

Â 22:07

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

Â lower specification limit of the customer.

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

Â capability ratio, if you have a CP value that so

Â a process capability ratio that is less than one,

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

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

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

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

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

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

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

Â 23:00

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

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

Â and the process distribution, are equal.

Â So the process capability ratio will be exactly one,

Â however the process is centered too much to the right.

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

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

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

Â 23:37

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

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

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

Â And there may be situations where you say look I,

Â I expect the time to be zero, right.

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

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

Â You're expectation of the customer is zero.

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

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

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

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

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

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

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

Â So here's a fast food restaurant now,

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

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

Â So, it's lower specification of zero.

Â Current process is at a burger joint,

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

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

Â Is the process capable of conforming to customer expectations?

Â 25:38

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

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

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

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

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

Â fulfilling customer expectations.

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

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

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

Â 26:20

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

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

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

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

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

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

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

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

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

Â it's giving you a quick indicator.

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

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

Â