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 kind of chart, generally speaking,

Â when we think about variable control charts,

Â we're talking about measurement data, something that can be measured,

Â so we're talking about characteristics of a product or

Â a process such as the 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

Â we talk about 34.8 inches it has meaning, rather than when you're

Â talking about discreet distributions where there are no decimal points.

Â So, we're talking about continuous distributions here, right?

Â We're talking about measurement data.

Â The difference between attribute control charts and

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

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

Â 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 so

Â that's why we call this the Xbar-R chart that we're going to look at next.

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 is a barista at a coffee house, and

Â she is known for the cold Americanos that she sells.

Â These are White americanos, these are whipped cream and

Â milk in them, and she prides herself in making these, right?

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

Â making the espresso in stainless steel cups that have been precooled,

Â transferring them into a glass cup, adding the cold

Â milk which is maintained in a refrigerator at a certain temperature.

Â Set at 34 degrees Fahrenheit, 0 degrees Celsius.

Â 3:35

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

Â So in the rows, we have each of those samples.

Â So that's day 1, day 2, day 3, day 4, day 5.

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

Â each Americano, 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 the number of samples that she's taken is five.

Â Five samples of size four.

Â This is going to have some meaning when we do some calculations.

Â So it's worthwhile for you to make a note that there are five samples of size four.

Â 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 Xbar-R chart, a mean and range chart.

Â So the first thing we need to do is take each sample, take each role and

Â calculate its average.

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

Â And then for the range for each of those rows, you wanna 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.

Â And 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 0.074.

Â Right?

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

Â the ranges, and what you're also seeing over here

Â is these averages are going to be used as a central line for both of those charts.

Â So, you've already got the central line for

Â the range chart as well as the average chart.

Â 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 symbols,

Â with the Greek symbols, you might be intimidated by these.

Â But what these are basically saying is that, the upper control limit for

Â the range control chart is going to be based on the average range

Â that you already got, so what you're looking at,

Â sigma R divided by K, is simply the average of all the ranges.

Â So you take the average range and you multiply with something called the D4.

Â The lower control limit for the rain chart is based on a D3 number.

Â Multiply that by the 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.

Â It's saying that it's the average of the five averages that you had taken

Â plus the A2 times R bar.

Â 6:33

Lower control limit is x double bar minus A2 times R bar.

Â Now the question that you should be asking or

Â what you should be wondering about at this point is, what is this D3, D4, and A2?

Â What are these things and where do they come from?

Â So, 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 you

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

Â Now where are the numbers coming from?

Â They're basically representing the idea of three standard deviations.

Â So because we have a very small sample size,

Â its not appropriate for us to use standard deviations.

Â We are using the idea of three standard deviations by

Â substituting with these multipliers.

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

Â minus 3 standard deviations.

Â So, that 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 and

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

Â 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 0.074, multiply it by

Â the 2.282 mutliplier that you saw on the chart on the previous slide.

Â So upper control is 0.1689.

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

Â Right?

Â So we get the upper and lower control limits for the R charts,

Â similar calculations for the x chart, the x bar chart.

Â Center line is based on means.

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

Â Multiplier in this case is the A2 value and for the lower control limit,

Â you're using the same multiplier but you're subtracting in this case.

Â So you have mean minus 0.73 times the range.

Â 9:09

Now, what you've noticed over what you should have noticed over here,

Â is that between these two charts, between the range chart and the x chart,

Â in the x bar chart, between the r bar chart and the x bar chart, we are using

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

Â Right? So this seems kinda strange that we're

Â using something from a different chart to control the upper and

Â lower control limits.

Â 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, 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 Xbar-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,

Â as we talked about in the case of the proportion chart and

Â 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

Â you would want to get a larger sample and use that.

Â 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 an upper and lower control limit.

Â Five samples is not going to be enough.

Â 11:04

All right, taking these results for

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

Â What this is showing us that Holly's process is pretty consistent.

Â Right? She's

Â giving a pretty consistent temperature.

Â The maximum that it varies is 0.1688 degrees Fahrenheit.

Â The maximum of that range chart was 8.1688 degrees Fahrenheit.

Â Which is pretty good.

Â The range is pretty small.

Â It's between 0 and 0.1688, right?

Â The temperatures for the actual IC called Milky Americanos

Â is between 35.0356 and 35.1434 degrees Fahrenheit.

Â Again a very small range of temperature that you are getting from this so,

Â it seems to be a pretty tightly controlled process, she's able to achieve

Â that consistency in the coffee that she is 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 on

Â the inherent capability of the process, is what is the customer's expectation, right?

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

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

Â not, that's something that you don't know from doing a statistical process control

Â analysis.

Â So, keep a note of that.

Â