Article Revised: May 14, 2019
The slides presented in this webinar are now available, click here.
This is a pretty typical slide that you see when people start talking about the different kind of charts that are available. The two in particular that we’re going to talk about is the IMR and the X bar R. As you can see they both require continuous data and really the difference is the subgroup size. So the IMR chart uses a subgroup size of 1 and the X bar R uses typically 2 to 9 for a subgroup size. So the individual chart is control chart for variable data, it’s for continuous data, monitors the process over time and you’ll see through this I mentioned a couple times that we’re using time order data. It plots the measurements as a separate data point for each value. So each data point stands on its own group size of 1 and then the moving range chart uses a default value of 2, which means that we’re checking we’re looking at the range between the different points on the chart. You can change that typically people leave it at 2 though. So there will be one less data point on the moving range chart than there will be on the IMR chart on the eye chart.
This is just an example of an IMR chart taken from Minitab. You can see on this one where you have the points that are out of range above the control limits. You can see that there’s a big difference in those points and that is also reflected in the moving range chart at the bottom. So when you’ve got a dramatic change in the points on the individuals chart you’re going to see that change also on the moving range chart. That just shows you the different points that we’re talking about there
So now let’s talk about the X bar chart and what’s the difference. Well it’s a control chart for variable data once again and it monitors the process over time. But the distributions need to be approximately normal and it’s based on the average of a series of observations. We call that a subgroup. Monitors the variation between those observations. The larger the subgroup the more sensitive the chart will be, providing you have a rational subgroup. So the question is well what’s a rational subgroup.
Well a rational subgroup is these are items that are produced under essentially the same conditions. Typically they’re consecutive so you’re talking about a series of observations consecutively that each become a subgroup. So if you look at a stable distribution and this distribution is made up of individual readings. Those readings… as soon as this there we go so you can see you have one subgroup and it’s black. Those readings occur all over this distribution but they are occurring in a time ordered sequence so they’re occurring sequentially. But the readings can come from anywhere in the distribution. So that’s where rational subgroups come from. So here’s just an example of an x-bar R chart and we’re going to talk about these in a little more detail.
Question Larry. That x-bar R chart is that the same data that you use in the IMR chart you showed earlier? Let’s go back and say yeah I believe it is. No this is blood pressure. Yeah but I’ve got some I’ve got some further on that are the same data that will show that. Let me get back to where we were.
So when do you use an IMR chart when you have a limited number of individual measurements. Where I work we have very few opportunities to use an X bar because you just don’t have enough data. We’re collecting one data point a week or one data point a month it just doesn’t work. Now we do have one area where we can do that where we actually calculate the cost of a bill. We do millions of those. Now that’s a great opportunity to use X bar R or even the X bar s chart. But typically you don’t have that amount of data so that’s why the IMR chart is so useful so. But you do use the X bar R when you when you can have subgroups of two to ten if your subgroups are larger you use the X bar s which is a little more sensitive.
Larry? Yeah. Well we have a question from Burhan and I’m going to unmute him if you’re ready to take this question. Sure. Okay all right Burhan you’re on the air. Okay it’s like a radio talk show I guess. So Buran have unmuted your microphone and you can go ahead and ask for your question or otherwise you can type it into the window if we can’t get your audio to work. Was my name mentioned? oh yeah yeah hi I didn’t have a question I don’t know where that come from just listening oh okay I’m going to go ahead and meet you again go ahead very sorry Burhan didn’t shot yeah. Well I can always type a question and you can let me know what it is Tom. Yeah that works too folks. Okay.
So once again the data is time ordered the difference here between the IMR and the x-bar are individual measurements subgroup measurements. Pretty straightforward. So when you’re interpreting these you always start first with the R chart to interpret them. Whether it’s an IMR or the x-bar are you look at the our chart first and you’re going to look at the control limits and you’re going to see if the data is in control on the moving range chart. If it’s out of control then the control limits on the individual in the x-bar chart are going to be meaningless so you need to fix that first. So you need to look for any special cause as a variation. A couple of rules of thumb you should see more than five distinct values plotted on your moving range chart and no single value should appear more than 25 percent of the time. You might not have, you might not have enough detail or getting the level of detail you need on your readings if you’ve got a lot of the same values down there.
So here’s an example of an individual chart and you can see that there’s a big change in two values on this chart. Now the chart says it’s in control but the moving range chart shows a point out of control. What that’s telling us is that there’s too much change in my individual chart that to make that random. Okay the software is believing that this is not a random event because of the amount of change I had in my individual chart. Okay.
So then average charts become more sensitive to process changes as a subgroup size increases. Well what does that really mean? Okay so let’s take a look at… this is the same data and the chart on the left shows glucose readings with a subgroup size of three and the chart on the right shows the same data with a subgroup size of nine. Now you can see at the bottom I put the range in there for the upper and lower control limits on both of those. You can see that the control limits on the subgroup three chart are narrower than the control limits on the subgroup of nine charts. So that means that there’s better discrimination on the subgroup of nine chart. You can see also there’s one out of control point on the subgroup size of three chart on the top for the X bar. I would call that an unfortunate choice of subgroup size. Then you change when you make these subgroups then the upper and lower control limits are going to be tighter than from the individual chart. So in this case this one just popped above the line.
So then interpreting the individual chart. So now we want we’re going to look at the top chart we’ve got the bottom chart in control and now we want to look at the top chart. So you want to look at it relative to the control limits and the run tests. What are run tests? The run tests are… some people call them run tests some people call them the Western Electric rules. I’ve got those on here let’s see like to bring that up. That going to drop to that if that could took a while when we rehearse this to Larry. Oh actually, okay. Ah we’re waiting for the art. Oh we were waiting for the art. Okay so I’ll just go ahead and finish this slide and then I’ll get to the run test. So what you want to do is look for out of control points and the point here is that if you’re using an x-bar r chart it cannot be compared to the requirements. So what do I mean by that?
We’ll go to the next slide. Come on, next slide. It seems to be getting slow over time. Yeah. Okay there we are.
All right so the this is once again the same data. This is glucose readings. You can see on the individual chart on the left and the subgroup size of nine on the right. Once again we want to look at the control limits but now we’re looking at the top chart control limits. You can see that the control limits for the IMR chart are much wider than the control limits for the x-bar chart. So if I’ve got individual readings up near the control limit on the IMR chart of 131 and I set my requirements at 109, which is what the x-bar r chart says, then I’m going to have things that are out of control show up and my customer is not going to be satisfied. So that’s the whole point of you can’t use the x-bar r chart when you build your requirements or when you set your customer specification.
Comment. Another thing is that the customer feels the individual experience they don’t really feel the average. So yep. You know the average is something that we can use for process control and to detect changes and special costs in the process, but from the customers point of view there are individual experiences what counts and that’s what shows up on the I chart.
Good so it’s really easy to construct the IMR chart I mean you just have to figure out what am I going to collect data about. Then the purpose of the chart that you set up your data collection points and like I said we have rarely do we have opportunities where we have an update aware we could even use the X bar R. Determine if you need any special measurement method or criteria and then drop it into Minitab or some other charting tool, it’s pretty simple.
Then this chart, this was the run test and these are the special conditions that have been identified over the years as being something that is other than random. So I just included these because these a lot of people don’t know what all of these are.
Comment. Yes go ahead. So these the run rules are designed so that any given run rule as about the same probability of occurring in random data as a point being outside of the control limits. While they’re very handy to use for offline analysis, I never apply them in real time and I use them in team situations just to really look for patterns that might help us put things on the cause and effect diagram or might help us find ctq’s that we can use for experimental design. Yeah where we use these is when we’re trying to determine if a process change occurs. So that’s been very helpful because then it points then it highlights it in red and you can point that out to management. One of the problems with using them for real-time troubleshooting is that so you take the 15 consecutive observations within the standard deviation, whatever change happened occurred 15 observations ago and the time lag makes it very difficult to identify those causes. So you don’t really want to stop the process while you look for something that’s going to be so hard to find.
Any questions? Okay, let’s give a moment of silence and time to type in your question. Paul so you have a question, do you want to type it in or would you like to have the microphone? Ive unmuted Paul so go ahead. I was looking at that chart and I’m a little bit confused that’s the way if something would be wrong with that. I’m thinking I’m looking at that time saying oh this looks great you mean it takes a very long and it’s very tight around the center. So I understand what you’re saying it’s like well this is actually good and so why do we why do we call it out of control is that the question? Yes why do we have a problem with it? You want to take it Larry or you want to give me a shot. Yeah I’ll start. What that tells me is there’s a specific cost for that. That’s what this chart is trying to get you to understand is something specifically happens some special cause similar to when a data point is outside of the control limits there’s a special cause. You have anything to have Tom? Yeah a control chart not doesn’t tell you when something’s necessarily gone wrong it’ll also tell you if something spontaneously gotten better. So perhaps that’s what happened here is you know we had a process change that made the process better. For example maybe the control chart was based on several different suppliers providing input and somehow we got a single supplier and that made the process more stable. So that’s one thing that happened. So this pattern would tell you that you know take a look and see why your process got better and perhaps it’s something that you can lock in and do continuously. More often what I’ve seen is that it involves stratification of the data. So when I’ve seen this occur most often is if let’s say for example we have several different people involved in the process when we set up our control chart and we end up sampling from the same person all the time. That would create this kind of a pattern. Or if we set up our process control limits let’s say if we have a multiple station machine sampling from all of the different stations on the machine and then we have a sampling pattern that we don’t really want. So for example I saw a situation where there was a machine with 4 workstations and after the control chart went onto the process people start sampling one out of four. So they’re always sampling the same workstation and the this pattern occurred and it was really something that we needed to do to revise our control chart sampling procedure. Okay so what I’m supposed to take away from this if I’m understanding you is that the control charts are not necessarily looking for problems in the system but they’re looking more for changes in the system. That’s right. A control chart is the operational definition of a special cause of variation. All that will tell you is that there is a special cause and you you’ll want to find out what that cause is so that you can either lock it in if it made the process better or fix it if it made the process worst. Okay. So in the case that Tom mentioned first where you have multiple vendors and you go to a single vendor in that instance that’s a special cause. It’s a change in your process. I have seen this as Tom mentioned I have seen this when you are looking at individuals and you’re looking at the performance of individuals and sometimes you’ll see this. With that same logic some of that hold for the 14 consecutive observation alternate and open though. Well what that involves is a special cause in is called mixture. So what happens is that if you have that problem your two samples are correlated with one another and they’re telling you that there’s a pattern in your data. So one place I saw that occur was that we in the electronics industry they have parts that are called axial parts. So a resistor for example will have a wire coming out of each end and the process I saw was measuring the distance from the end of the left side of the wire to the resistor and then from the right side of the wire to the resistor. What happens is that if I make the left end shorter, the way that the ends are trimmed, if I move the resistor to the left then the left side will be shorter in the right side longer. If I move it to the right then the left side will be longer in the right side shorter. If you measure the two and put them on a control chart you’re going to get that alternating up and down pattern. Okay so this can happen in for example in a process where there a time index in. There yeah that’s right. It could also happen if you have if you’re sampling from two different workers and they have two different performance levels. So you know person a is higher person B is lower and it’s alternating up and down. So that would be a stratification problem there again. Right it’d be a problems of stratification and mixture. So you have two distributions together your sampling pattern is stratified and the process is a mixture of two cause systems. Okay great, okay thank you. Thanks. You bet, any other questions? Just go ahead and click the raise the hand button I’ll see it and then I’ll unmute your mic for you.
So I’d like to make a comment. Way back at the beginning of your presentation there you have a chart that I know came out of a Six Sigma handbook and showed how to select these how to select a control chart. I think it’s like you’re maybe your first or second slide. Challenging you, keep going. It’s that decision tree. That’s what I’m looking for. There we go.
So if you look at that decision tree it says that you have attribute data on the left and continuous data on the right. But we often use the individuals chart for attributes data. I just wanted to comment that you can do that. So if you’re plotting defects are defectives and you have… let’s say you’re looking, Larry’s in the insurance business, but saying you’re looking at errors on applications. You should or you know the correct quote unquote chart for that might be the C chart if you’re counting errors or the N P or P chart if you’re counting applications with errors. But you can actually plot that data on an IMR chart. It would work pretty well in most cases, in fact some places it’ll work better than the quote unquote correct chart. So if you have a lot of variation between samples and that variation is normal for your process, the attribute control charts would show you processes being out of control if you have large sample size. It would be perhaps an amount of variation that was of no practical importance and you should in those cases use the I chart to plot those data. Just because the I chart is only going to show you changes that that have some economic meaning. We have used this when we get we get a form called a healthcare 1500 form and accounting defects on forms. We’ve used it for that. Okay any other questions? Well if not I’m going to thank you all for attending and thank you Larry so much for presenting. At this point I’m going to end the meeting. I will be sending everyone a link. Oh I do have a question here Paul go ahead I’ve unmuted you. All right I am I think it’s maybe what you’re about to mention and I was just wondering if this presentation would be see if somewhere on the website. Yes I’m going to upload this presentation and I will post a link to it on Six Sigma training org and in the blog. So if you go up there and search for Swiss Army knife or webinar you’ll be able to see the link to the video up there. Great, okay thank you. So and I’ll also send a link to the presentation to each of you and I want to thank you all for attending and hopefully we’ll see you at future webinars. Thank you so much for presenting Larry, great job. You’re welcome, thank you.”