0:13

Once you've come up with the upper and lower control limits,

Â once you've calibrated the control chart, the next step is for you

Â as a manager to give it to somebody in the front line, and them being able to use it.

Â Or for you to use this control chart

Â to keep an eye on the future performance of your process, right.

Â So, you have calibrated it.

Â Now you've locked in the upper and lower control limits.

Â And now you take daily samples from your process and you plot them, right?

Â So you take them at predetermined intervals, you might say,

Â I'm going to take five samples every day.

Â Or you might say, I'm going to take a sample every hour every day.

Â And each sample is going to be of size x, could be five,

Â could be ten, whatever that you've chosen.

Â 0:59

So you do that, you collect the data, and you plot it on the control chart.

Â And then, you go and

Â see if there is a point that's outside of the control limits, right?

Â So you plot the points and as you plot the points, you look for

Â points that are outside of the control limits.

Â If you find a point that's outside the control limits, what is that telling you?

Â It's telling you something happened that made this process go

Â beyond its inherent capability.

Â Now, you would think that that's necessarily a bad thing,

Â it's gone beyond its inherent capability.

Â Yes, it may be a bad thing, or it may be something good that happened.

Â What do I mean by that?

Â It's not necessarily that when there's something outside of the control limits

Â that it's a negative thing that happened.

Â Especially when you're looking at something like proportion of

Â defects, right?

Â So if you think about a control chart for proportion of defects,

Â if there's a point outside the control limit on the lower side,

Â that's telling you your proportion of defects was lower than you

Â anticipate in the normal course of events, which might be a good thing.

Â So, what all we can say when there is a point outside of control limits is,

Â there's something that has happened that's worth going and looking at.

Â So go see is what a point outside the control limit tells us.

Â 2:15

And then finally, when you go see,

Â you may be able to take action based on what you find there.

Â But finally, what you want to do is, if you do find a lot of points going

Â outside the control limit, you want to do something about it, right?

Â You want to improve the process so

Â that there are not points outside the control limit, but also, more importantly,

Â what's that also telling you is to recalibrate your control limits.

Â So if you're finding too many points outside,

Â it's saying that maybe there's something that's changed in the process

Â that you need to recalibrate your control limit.

Â And on the other extreme, we can look at patterns that will tell you

Â something even when there is a point that's not outside the control limits,

Â even when there is not a single point outside the control limits.

Â So we'll look at those kind of patterns later, but before that,

Â let's just get a sense of the general structure of control charts.

Â 3:10

So any control chart will have these three lines called the upper control limit,

Â the center line and the lower control limit.

Â The center line is going to be some sort of a process average.

Â The upper and lower control limits are going to be based on three standard

Â deviations above and three standard deviations below the process average.

Â And once you've calibrated this kind of a control chart, you will plot the samples.

Â You will take the samples from that process and

Â you will plot them in chronological order, going left to right.

Â The idea being that you're looking for points outside of the control limits.

Â But you're also looking for any kind of pattern that you might see in

Â this control chart even if there is not a single point outside of the control limit.

Â 3:58

So to put some specifics on the kinds of patterns that might be worth going and

Â looking into, now this is not something that has a statistical

Â principle behind it, it's going to be more context specific.

Â So based on what your context is, and what that process control chart is all about,

Â you might find something that might be worth looking into or not.

Â So the first one that you see over here is,

Â if there's a sudden shift in the point clusters, right?

Â You had all the points in random fashion within the control limits all this time.

Â And there seems to be a sudden shift either upward or downward.

Â Towards the upper control limit or the lower control limit.

Â And there seems to be a concentration going one side of the other

Â that could be a sign that's telling you something.

Â If there is a cycling of points, right,

Â if the points are all below the center line towards the lower control limit.

Â And then subsequently, they are all above the center line and

Â then they're towards the upper control limit.

Â Next again, they're down towards the lower control limit, lower than the center line.

Â And this cycle keeps on continuing, that may be telling you something.

Â So in this particular example,

Â it might be telling you that there are two different distributions here, right.

Â You might want to think about separating out the data for

Â those two different distributions.

Â This might be the idea that there are two different

Â operators that are working on this task at two different times, and

Â this is showing you that they're performing differently.

Â So that might be information that might be useful in terms of either

Â coming up with two different control charts for them, or

Â saying that, well, one of them is doing a good job, one is not.

Â So let's do something about this and try to get this to be the same.

Â 6:11

If you find all the points are concentrated at the center line,

Â you have an upper control limit and lower control limit.

Â And you find that the points are all very close to the center line all the time,

Â what it's probably telling you is that,

Â there's less variability than you expect in this process.

Â That the process has actually become much more predictable, right.

Â So it's time to recalibrate the control limits and

Â use a new process control chart with new control limits.

Â So these are some of the things that you might want to look at

Â in addition to looking for points outside of the control limits in a control chart.

Â 6:51

Where does this whole idea of plus or minus 3 standard deviations come from?

Â Now some of you may already by familiar with this.

Â The idea is coming from what we know as the bell curve,

Â the standard normal distribution.

Â And it's the idea that 99.7% of the observations

Â are going to be within plus or minus 3 standard deviations.

Â So that's the idea that we're using,

Â that's the idea that's being used in statistical process control.

Â That under normal circumstances, and that's quote,

Â unquote normal circumstances.

Â A process reflects what is seen as the normal distribution plus or

Â minus 3 standard deviations will cover, 99.7% of observations.

Â 7:39

So, what you have here is a schematic that showing you a different

Â types of control charts that can be used.

Â Broadly speaking, we can take measurements based on attributes and variables.

Â What are attributes?

Â Attributes are things that you can count.

Â Attributes are things that you can see in terms of something being good or bad.

Â In statistical terms, you're talking about discrete distributions there.

Â So attribute control charts are going to be based on

Â discrete kind of distribution data.

Â So like I said, there are many types of control charts that you can use.

Â 8:20

And within the attribute control charts, within the attribute type of control

Â charts, you can have many different types of charts.

Â What I have described over here, what you're seeing over here is that

Â the p chart is the one for, if you're looking at proportion defector.

Â So the p stands for proportion.

Â And if you're looking at the number of defectives in a process,

Â you're simply interested in looking at whether a product is defective or

Â nondefective, you would use what is called a p chart.

Â The other kind of attribute chart that is commonly used is called a cchart.

Â And the c chart is used for defects.

Â So if you're interested in the number of defects in a particular sample of

Â products, you would use a c chart.

Â And the c there stands for count and

Â there are several other types of attributes control charts.

Â On the other side, you have the variable type of control charts,

Â these are based on continuous distributions, so

Â distributions where the decimal points have meaning, right?

Â You're talking about length, weight, you're talking about viscosity

Â off of liquid, those are the kind of things that you can actually measure.

Â So this is going beyond say, I'm counting the defects,

Â or looking at whether a product is defective or not.

Â A variable control chart is actually looking at a particular aspect of that

Â product or process and actually measuring it.

Â So here, what we've depicted or what you're seeing is the XR

Â chart the X stands for mean and the R stands for range.

Â So the XR chart, or the X-R chart as how it is known,

Â is one that's looking at the mean and the range, and

Â using those to come up with inherent capability of the process.

Â And then to use it further for

Â looking at whether the process is a statistical control.

Â So in this lesson, what we'll do is, we'll look at

Â these three different types of charts, the p chart and the c chart and the X-R chart.

Â And we'll go through the mechanics of each one of these as in terms of how these

Â are constructed and used.

Â Knowing that there are many other types of charts out there that you can go and

Â select from.

Â