CONTROL CHART BASICS and the X-BAR AND R CHART +++++ EXAMPLE

hey there andy robertson here with cqe academy and in today's video i want to go through some of the fundamental concepts and control charts and then talk about one of the most popular control charts out there the x bar on our chart all right let's head over the computer and dive in all right let's go ahead and get into it what i'm showing here is kind of the agenda for today's lecture so i'm going to start with talking about the two types of variation so the beauty of a control chart is that it helps us distinguish between special and common cause variation that's exactly why we use them so i want to talk about what those things are and then we're briefly going to talk about the key elements of control chart these are those unique features of a control chart that help us distinguish between normal and special cause variation and then there's a really important topic in control charts called rational subgrouping so i want to talk about that and then we're going to go through both the equations associated with our control chart so we're going to talk about the x bar and r chart and we're going to talk about the equations we use to calculate the center line and the upper and lower control limit of both the x bar and the r chart and then we're going to talk through some constants so being able to work those equations requires that you use some constants so i'm going to show you how to look those up and use those in your x bar and r chart calculations and then we're going to do an example so i'm going to show you exactly how to create an x bar in our chart by the way i've added timestamps to each of these different slides so if you already understand types of variation or the key elements of a control chart or maybe rational subgrouping you can kind of jump ahead to that particular timestamp all right let's go and get into it okay so the two types of variation every process no matter what we're talking about has two types of variation the first is common cause variation this is the inherent normal random variation associated with your process that every process experiences when it's in control and i'm talking about every type of process a manufacturing process an administrative process maybe it's a healthcare process it doesn't matter what it is every process has some random normal common variation associated with it now special cause variation is different and are things that are not unique to the process so maybe you have a piece of equipment that's starting to wear out over time or maybe a vendor ships you some non-conforming material or maybe you have an operator that's new and is operating the machine differently that's special cause variation and as quality engineers or continuous improvement experts we want to make sure we're monitoring our process and making sure that our processes are only experiencing common cause variation because if we're experiencing special class variation we should do an investigation we should uncover the root causes of those special cause variations and we should work to eliminate special cause variation now the way we identify special cause variation versus common cause variation is by using a control chart and so what you'll see here is every control chart has these upper and lower control limits these control limits create the boundaries you can see it here between common cause variation and special cause variation so we've got our upper and lower control limits here in red and we've got we're plotting our data here and everything that falls between the upper and lower control limits is generally considered normal process variation now what happens is as we're plotting our data if we run into a data point like this that should be a sign that perhaps we're experiencing some special cause variation and this is exactly how control charts work we have control limits and when we're outside of those control limits we're likely experiencing special causation now there are some other rules you can apply to control charts to identify special cause variation but as a just a general rule we do use those control limits to identify a special cause from common cause all right so rational subgrouping this is a really important concept in controlled charts so a rational subgroup is defined as a collection of units that are all produced under the same conditions now let me tell you why that's important so the upper and lower control limits for the x bar chart includes the average range okay so let me show you what i'm talking about here let's say we have an x bar chart and we have a subgroup sample size of five so every time we take a sub group we take five measurements and within each measurement within each subgroup we're calculating a range value okay we're calculating a range value now this range value is eventually used to calculate the upper control limit for x bar and so let's imagine we're taking this subgroup here and let's say we take the first three data points and then we do like a tooling change or we we change vendor lots and we take the next two data points okay that would be an example of poor rational subgrouping because we've made an inherent change okay so when we're creating our control limits we should make sure to collect data that's all produced under the same conditions because if the range associated with our subgroup is large the control limit for our x bar chart is also going to be large and if we have wide control limits then we're not going to be as sensitive to changes in the variation so the key here is that when we're picking our rational subgroup we should only include normal inherent process variation in that rational subgroup that's how we distinguish between common cause variation and special cause variation because we're only including common cause variation in this r bar value okay and then the x bar in our chart equations so as you probably know the x-bar chart monitors the mean or the average value of your process and here are those equations for calculating the center line and the control limit of the x bar chart so the center line of your process is simply just called x double bar this is the grand average and it's really just the average of all of our average values now the upper control limit of x bar so that's how you read this upper control limit of x bar is that grand average that x double bar plus a2 times r bar now in the next slide i'll talk about a2 how to find that a2 factor and then the lower control limit is that same grand average simply minus the a2 factor times r bar and then the range chart so the range chart in the x bar and r chart monitors the variation within your process so special cause variation can either change the mean value of your process or it can change the variation of your process and we want to monitor both of those things to be able to detect special cause variation now here the equations associated with the r chart so the r bar or the average range value is simply just the average value of our measured ranges and then the upper control limit of the range chart is the d4 factor times r bar and the lower control limit is the d3 factor times r bar now i've thrown a lot of constants at you so let's talk about that next these are the x bar and r chart constants so here are those equations we just talked about and here's a table showing you all of the constants for the x bar on our chart now let's walk through these so remember for the upper and lower control limits of x bar we use the a2 factor so here's that a2 factor and the way we find the right value is we look up the subgroup sample size so in our example today our subgroup sample size is going to be 3 and our a2 factor is going to be 1.023 but if in each of your rational subgroups you're taking 5 or 7 or 9 or 10 you just select a different a2 value and then for your range chart these are your two range factors d3 and d4 so again in today's example when our subgroup sample size is 3 our d3 value is going to be 0 and our d4 value is 2.575 and again the way to look this up is just to come over here to your subgroup sample size and then move across and find the right factor and then the last thing to talk about is estimating the population standard deviation so we'll actually talk about this when we talk about process capability but we can take this r bar value from our range chart and convert it into an estimate of the population standard deviation and we use that using this d2 factor here this d2 factor so again we look this up the same way we find our subgroup sample size we come across we find that conversion factor to convert our r bar value into an estimate of the population standard deviation all right so now let's work an example so in this example we're going to have 10 subgroups and each subgroup is going to have three samples so our subgroup sample size is three and what we do is we take our first subgroup data and we have sample values of seven four and four and then what we do is we take that subgroup data and we calculate the average value and the range so seven plus 4 plus 4 is 15 divided by 3 is 5 so that's our average value and the range is simply just the max minus the min so 7 minus 4 is 3. we can do that for all of our subgroups so here our average value is 5.7 and our range is 5. here it's 10.3 and 3. here it's 6.3 and 4 and we can go on and on all the way down the list for all of our 10 subgroups now once we have all of this data we can calculate the grand average which is x double bar and that's simply just the average value of all of these subgroup averages and it happens to be 7.7 and then what we can do is we can take that data and we can graph the beginnings of our x bar in our chart so here in green you can see the center line of our process this is our grand average that's a 7.7 and then each of these data points is simply just the average value of the subgroups so it's 5.0 5.7 10.3 6.396 and on and on and on we can do the same thing for the range chart so we can find our r bar the range center line which is simply just the average value of all of our ranges so if we find the average value here it's 3.7 and we can use that to create the beginnings of our range chart so again the center line of our range chart is 3.7 and then you can just see we're plotting the data so three five three four five three three and on and on down the list here you can see how we've just simply plotted those range values on the r chart and now it's time to calculate our control limits so here are those equations for the upper and lower control limit so we've got x bar here and the range chart here and we can look up those constants that we just talked about to calculate the final control limits so our subgroup sample size is three right we're taking three samples per subgroup and we know our a2 factor our d3 factor zero you can see our d4 and our d2 factor now all we got to do is plug these in the upper control limits 11.5 lower control limit is 3.9 now remember these are both for the x bar chart and then for the range chart we plug in those d3 and d4 factors the upper control limit is 9.3 and the lower control limit is 0. now what we can do is we can take those control limits and overlay them on the data so you can see here we've added the upper control limit and the lower control limit and it looks like our process is is in control right we don't have any data outside the control limits same thing for the range chart so we take that previous data where we had plotted each of our range points and we can overlay the control limits so 9.3 and 0. and again it looks like our range values are within the control limits alright that is it that is how you create an x bar and r chart using the equations and the constants alright that's it for me i hope you enjoyed it if you did hit that like button so other people just like you can find this exact same content and if you loved it and you want to take this journey to become a cqe hit that subscribe button so as i publish new material it gets sent to you and you get to grow with me on this journey to become a cqe alright that's it i'll see you in the next video bye [Music]

Channel: CQE Academy

Views: 10,266

Rating: 4.9423633 out of 5

Keywords: Control Chart, Control Chart Example, Control Charts, Statistical Process Control, SPC, Variation, 2 Types of Variation, Special Cause Variation, Common Cause Variation, Rational Subgrouping, Control Limits, X-Bar Chart, R Chart, X-Bar Control Limits, R Chart Control Limits, Equations for the X-bar Chart, Equations for the Range Chart, Range Chart, Constants for the X-bar and R Chart, Upper control limit for the X-bar Chart, Lower Control Limit for the X-bar Chart

Id: Aj7lJLR-7b4

Length: 12min 16sec (736 seconds)

Published: Wed Feb 03 2021