0:14

This lesson is about Variable Data Control Charts.

Â Specifically, about one type of variable data control chart.

Â Before we get to that particular type of chart, generally speaking,

Â when we think of variable control chart, we are talking about measurement data.

Â Something that can be measured.

Â So, we are talking about characteristics of a product, or

Â a process such as a weight of a product, the height, the length,

Â the viscosity of a particular liquid, the density, those kinds of things.

Â So, it's something that can be measured.

Â 0:49

To put it in simpler terms, it's where decimal points have a meaning.

Â So, if we talk about 22.8 degrees or we talk about at 34.8 inches.

Â It has meaning, rather than when you're talking about discrete distributions

Â where there are no decimal points, so

Â we're talking about continuous distributions here.

Â We're talking about measuring data.

Â 1:11

The difference with between attribute control charts and

Â variable control charts is that variable control charts, they are used in pairs.

Â So, you're always looking at the variability in some

Â kind of a measurement of range, or measurement of standard deviation.

Â In addition to, looking at the variation in the mean.

Â So, they're always going to be in pairs.

Â So, that's why we call this the X-bar, R chart that we are going to look at next.

Â We don't used the X-bar chart without the R chart or

Â the R chart without the X-bar chart.

Â They always go in pairs.

Â 1:52

They study process averages, and they study the process variability.

Â And that variability can be measured.

Â In our case, we'll be looking at range.

Â It can be measured as standard deviation.

Â So, there may be different types of control charts using different aspects

Â of variability that they're measuring.

Â 2:12

Now, let's take an example here, and

Â work through it to get a sense of the Xbar-R Chart.

Â So, we have Holly, who's a barista at a coffee house and

Â she is known for her Cold Americanos that she sells.

Â These are White Americanos, these are with cream and

Â milk in them and she prides herself on making these.

Â She builds each drink with a very elaborate process that involves

Â making the espresso in stainless steal cups that have been pre-cooled,

Â transferring them in to a glass cut,

Â adding the cold milk, which is maintained, in a refrigerator set

Â at a certain temperature at 34 degrees Fahrenheit, 0 degrees Celsius.

Â 2:59

Now, Holly wants to assess the consistency of temperature

Â that she gets from making these Americanos.

Â So, she wants to see whether this works out to be within a certain range.

Â So, she wants to see how good this is in terms of, in

Â terms of the variability that is in the process.

Â So, what she has done is she has collected data over the last five days,

Â using samples of the first four Americanos.

Â So, each of those five days, she's taken the first four Americanos that

Â were made between the 12 noon to 1 p.m hour each day.

Â 3:35

So, what you have on this slide is the data that she has.

Â In the rows, we have each of those samples, that's day one,

Â day two, day three, day four, day five.

Â And then, what you have in terms of the temperature for each Americanos,

Â four Americanos that are taken on each of those five days.

Â So, what is the sample size here?

Â The sample size is four, and

Â the number of samples that she has taken is five, five samples of size four.

Â This is going to have some meaning when we do some calculations, so it's

Â worthwhile for you to make a note of that, that there are five samples of size four.

Â Right, so let's get into some basic calculations of this.

Â So, what can we see, in terms of the basic averages and

Â the ranges that we can get from this.

Â So, we're moving towards a X bar R chart, a mean and range chart, so the first thing

Â that we need to do is take each sample, take each row and calculate it's average.

Â You add them up you divide by four, your get an average, right?

Â And then, for the range for each of those rows, you want to calculate,

Â take the maximum subtract from that the minimum and you get a range.

Â So, if you do that for all five samples, you can get the ranges and

Â the averages for all samples, and

Â what you have in the last row is the average of averages.

Â So, it's a mean of means.

Â So, the 35.08 is representing the mean of means for all of the samples.

Â And then, you have a range average of .074, right?

Â So, that's what we get from simply looking at the averages and the ranges.

Â And what you're also seeing over here is these averages are going to be used as

Â center lines for both of those charts.

Â So, you've already go the center line for

Â the rain chart as well as the average chart.

Â 5:31

All right.

Â Now, let's look at the computations for the upper and lower control limits.

Â Now, if you're not comfortable with Greek symbols,

Â you might be intimidated by these but what these are basically saying is that,

Â the upper control limit for the arranged control chart

Â is going to be based on the average range that you already got, so

Â what you're looking at sigma R divided by K is simply the average of all the ranges.

Â You take the average range, and you multiply with something called a D4.

Â The lower control limit for the range chart is based on a D3

Â number multiplied by the D average range, and then when you look at the upper and

Â lower control limit formulas for the means chart, you're looking at the mean of

Â means, and that's why you have the double bar on top of the X, it's saying that it's

Â the average of the five averages that you have taken, plus the A2 times R bar.

Â 6:50

Where they come from is this chart that we can use to pick out these values.

Â So, what is this chart?

Â This chart is taking the different sample sizes that you might use, and giving

Â you the different A2, D3 and D4 values that you would plug in, to those formulas.

Â Now, where are these numbers coming from?

Â They're basically representing the idea of 3 standard deviations, so,

Â because we have a very small sample size,

Â it's not appropriate for us to use standard deviations, we are using

Â the idea of three standard deviations, by substituting with these multipliers.

Â So, the A2, D3, and D4 are multipliers that help us replicate the idea of plus or

Â minus three standard deviations.

Â So, the one that we are going to use here is based on our sample size of,

Â now you may recall that I said earlier, we have five samples of size four.

Â So, we go to the row that says sample size of four.

Â And it tells us 0.729 is the A2 value that we need to use,

Â and then 0 and 2.282 are the D3 and D4 values.

Â So, we're simply gonna take these and plug it into the formulas.

Â The center line for the range chart is based on the mean of the ranges,

Â we already got that earlier as 0.074 from that table that we had,

Â the upper control limit is going to take that .074 multiplied by 2.28 to multiplier

Â that you saw on the chart on the previous slide.

Â So, upper control limit is 0.1689,

Â lower control limit based on a multiplier of 0 is going to be 0.

Â 8:39

Right. So, we get the upper and

Â lower control limits for the R chart.

Â Similar calculations for the X chart, the X bar chart.

Â Center line is based on mean of means.

Â Upper control limit is mean of means plus the multiplier 0.73.

Â The multiplier in this case is A2 value.

Â And for the lower control limit, you are using the same multiplier.

Â But you are subtracting, in this case.

Â So, you have mean minus 0.73 times the range.

Â 9:09

Now, what you've noticed over here.

Â Here or what you should have noticed here is that between these two charts,

Â between the range chart and the X chart in the X bar chart.

Â In the R bar chart and the X bar chart we are using the range

Â to come up with the upper and lower control limits for the X bar chart.

Â Right? So, this seems kinda strange,

Â that we're using something from a different chart to compute the upper and

Â lower control limits.

Â But the reason I bring this up, is because it's important for the range to be

Â in statistical control, if you are going to use that range to compute the X chart.

Â In other words, you need both of them to be in statistical control,

Â to call a process as being in statistical control or

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

Â You need both of them to be within the statistical control limits.

Â Right?

Â All right, so let's take a look at the interpretations

Â of the chart by plotting the points on each of these charts.

Â So, once again, like you had earlier for

Â the other kinds of charts here, for the X bar R chart,

Â you have the points plotted on the chart of upper and lower control limits.

Â 10:31

Right, now once again, we've used, as we talked about

Â in the case of the proportion chart and the count chart that we looked at earlier,

Â we've used a very small number of samples to come up with these values.

Â So, if you were to do this problem in reality, you would want to get a larger

Â sample and use that, what I'm talking about is the number of samples.

Â Your sample size may remain small but you definitely want a larger number of samples

Â to come up with a upper and lower control limit.

Â Five samples are not going to be enough.

Â 11:04

All right, taking those results for

Â what they are, let's take a look at what this implies.

Â Well, this is showing us that Holly's process is pretty consistent, right?

Â She's giving a pretty consistent temperature,

Â the maximum that it varies is 0.1688 degrees Fahrenheit.

Â The maximum of that range chart was a 1.68 degrees Fahrenheit, which is pretty good.

Â The range is pretty small, it's between 0 and 0.1688, the temperatures for

Â the actual icy cold Milky Americanos is between 35.0356 and

Â 35.1434 degrees Fahrenheit.

Â So again,

Â a very small range of temperatures that you're getting from this.

Â So, it seems to be a pretty tightly controlled process.

Â She's able to achieve that consistency

Â in the coffee that she's serving her customers.

Â Now, the question that you have not addressed by looking at

Â whether the process is a statistical process control, and even focusing

Â on the inherent capability of the process, is, what is the customers expectation?

Â We don't know how this temperature compares to what the customer expects.

Â Whether the customer is gonna be happy with this particular temperature or

Â not, that's something that you don't know

Â from doing a statistical process control analysis.

Â So, keep a note of that.

Â