0:13

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

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

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

Or for you to use this control chart

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

So, you have calibrated it.

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

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

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

I'm going to take five samples every day.

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

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

could be ten, whatever that you've chosen.

0:59

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

And then, you go and

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

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

points that are outside of the control limits.

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

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

beyond its inherent capability.

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

it's gone beyond its inherent capability.

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

What do I mean by that?

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

that it's a negative thing that happened.

Especially when you're looking at something like proportion of

defects, right?

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

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

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

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

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

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

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

2:15

And then finally, when you go see,

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

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

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

You want to improve the process so

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

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

So if you're finding too many points outside,

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

that you need to recalibrate your control limit.

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

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

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

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

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

3:10

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

the center line and the lower control limit.

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

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

deviations above and three standard deviations below the process average.

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

You will take the samples from that process and

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

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

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

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

3:58

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

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

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

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

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

So the first one that you see over here is,

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

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

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

Towards the upper control limit or the lower control limit.

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

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

If there is a cycling of points, right,

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

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

then they're towards the upper control limit.

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

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

So in this particular example,

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

You might want to think about separating out the data for

those two different distributions.

This might be the idea that there are two different

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

this is showing you that they're performing differently.

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

coming up with two different control charts for them, or

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

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

6:11

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

you have an upper control limit and lower control limit.

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

what it's probably telling you is that,

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

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

So it's time to recalibrate the control limits and

use a new process control chart with new control limits.

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

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

6:51

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

Now some of you may already by familiar with this.

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

the standard normal distribution.

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

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

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

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

That under normal circumstances, and that's quote,

unquote normal circumstances.

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

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

7:39

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

types of control charts that can be used.

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

What are attributes?

Attributes are things that you can count.

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

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

So attribute control charts are going to be based on

discrete kind of distribution data.

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

8:20

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

charts, you can have many different types of charts.

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

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

So the p stands for proportion.

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

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

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

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

And the c chart is used for defects.

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

products, you would use a c chart.

And the c there stands for count and

there are several other types of attributes control charts.

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

these are based on continuous distributions, so

distributions where the decimal points have meaning, right?

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

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

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

or looking at whether a product is defective or not.

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

product or process and actually measuring it.

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

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

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

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

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

And then to use it further for

looking at whether the process is a statistical control.

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

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

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

are constructed and used.

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

select from.