Attribute Data Control Chart Examples!! How to select/create the P, NP, C and U Charts

hey guys andy robertson here at cqe academy and in today's video i want to teach you and share with you all about attribute data control charts whether you're implementing a control chart for the first time or whether you're preparing for an exam like the cqe exam the green belt exam or maybe the black belt exam this is all stuff you're gonna need to know on exam day or in your job to be successful all right let's head over the computer get started all right let's check out today's agenda so the first topic we're gonna touch on is this really interesting distinction that we make between defects and defectives this might feel like we're splitting hairs here but this is a really important distinction because it affects which control charts that we should be using within our process so we're going to start by talking about the differences between defects and defectives and then we're going to use that in the second slide where we talk about choosing the right control chart so depending on whether you're using defects or defectives and how your sample size might either change or stay constant that affects which control chart you should or should not be using and then we're gonna walk through the four most common control charts the mp chart the p chart the c chart and the u chart all right let's go ahead and get into this okay so defects versus defectives so a defective unit is an entire unit that fails to meet specifications now include this picture of this light bulb because there are a number of different things about this light bulb that might make it a defective unit the filament might be broken the glass might be cracked the electrical connections might be damaged whatever it is this single unit if it were to be inspected could be considered a defective unit if there was anything wrong with it now a defect is an undesirable condition within a unit so i want to use this classic example of like let's say a car door so let's say we've building cars we have a car door and we're inspecting our car door and we find six different defects so we find three scratches two runs and one bubble now on this single unit we have six different defects okay now this entire car door is considered a defective unit so if a unit has a defect on it it is a defective unit and a single defective unit can have multiple defects the reason this distinction is important is because it it changes the way we select our control charts so let's talk about that now so there are two variables that that we have to consider when choosing the right control chart the first is what type of data we're counting and collecting if we're counting defectives that would be a different control chart than if we were counting defects and then for the sample size again whether your sample size is constant or variable again changes the type of control chart you would use so the first type of control chart we're going to talk about is is the most basic it's the np chart and what we're doing here is we're trending a count of defective units with a constant sample size so if we're if we're trending defective units with a constant sample size you want to use an mp chart if you're trending defective units with a variable sample size you want to use a p chart and then the c chart if you change gears here and you're talking about defects instead of defectives and you have a constant sample size we can use the c chart and then if you are trending defects with a variable sample size you want to use the u chart now the reason we make this distinction between defective units and defects is because it changes the probability distribution that underlines or that forms the foundation of our control limits so when we're talking about defective units and every single unit that is inspected can only be counted as bad one time we're using the binomial distribution if we're counting up defects and a single unit could be inspected and contain multiple defects we have to use the poisson distribution and that's why it's really important to understand whether you're trending defects or defectives because it changes that underlying probability distribution and it changes the way our control limits are calculated all right so now let's start with the mp chart so remember we're using the mp chart when we're training defective items with a constant sample size now there's two variables here that we have to calculate in order to complete our control chart the first is the center of our process we call this np this is the average number of defective items per subgroup we're going to do an example in a minute here where i show you how to calculate this and what it means or what it looks like on the control chart the second variable that we have to calculate is p bar this is the percent defectives per subgroup and again i'll show you in the example how to calculate this once we have those two parameters we can then calculate the control limits for our control chart you can see it here the upper control limit is np that's the average or the center of our process plus three times the square root of np times one minus p and again the lower control limit is just minus instead of plus all right let's look at some data now to help you understand both how to do these calculations and then we'll look at a chart so you can kind of visualize what this all means so we have 15 different subgroups or lots and then within each lot we have a subgroup size of 120 units per subgroup by the way this here says lot size that's incorrect this 120 units is actually a subgroup it's a sample from a larger population or a larger lot size so that actually is incorrect that should say subgroup size and in total across these 15 subgroups we've sampled 1800 units now basically what our inspectors do is as they take these 120 pieces they simply just count up how many defective units they find 12 20 20 6 14 6. and on and on and down we go and then what we're going to do is we're going to use this data to create our control limits and the first variable we need to calculate is np this is the center of our process and the way we do this is we calculate the sum of np this is the sum of defective units so in total across these 15 different subgroups we had a total of 199 defective units and we found those defective units across 15 subgroups you can see that here that's the variable k and what we do is when we normalize the defective units per subgroup we find that on average we had 13.27 defective units per subgroup and that makes sense if you just kind of scroll your eyes down this list here 13 seems like a pretty rough average number of all of these defective units that we found now the second variable we have to calculate is p bar this is the percent defective that we found in our inspection now the way we calculate this is slightly different we still start with the the count of defective items in our numerator so we start with 199 units and we found those 199 defective units when we sampled 1800 samples so the sum of n is simply just right here in those 15 subgroups we inspected 1800 units and that comes out to about an 11 percent defect rate now that we have mp mp bar we can calculate the upper and lower control limits as 23.58 and 2.96 you can see how i just kind of plugged in those variables here now i want to help you visualize this so the first thing i've done is i've put those major factors down here on the on the bottom those major parameters the center lines 13.27 upper and lower control limits here's the np chart you can see the center line here in green this is the center of our process on average we get about 13 defective units per subgroup you can also see i've got our upper and lower control limits on here and then all we're doing is we're asking our team to basically plot out the the count of defective units uh per subgroup you can see this here 12 20 26 14. and in general this process looks like it's stable and in control all right now let's talk about the p chart so we were on the mp chart here with a constant sample size let's talk about how the the equations change and how the analysis changes when we have a variable sample size so remember we use the p chart when we're training defective items of the variable sample size there are two parameters here or two variables that we have to calculate p bar which is the exact same calculation as it was with the mp chart and then this new variable is called nbar a bar basically just means average so n bar means the average of n or the average sample size and let's do an example here to show you what that looks like by the way here's how we're going to calculate the upper and lower control limits when using the the p chart by the way if you want all of these equations i've got a great free cheat sheet go to cq academy dot com slash free cheat sheet it's got all of the equations you'll need on the cqe exam go over there sign up and you get a free cheat sheet and that's going to be super helpful on exam day it's going to save you a ton of time in the exam instead of having to look up equations they're all right there for you okay so let's do this example so we've got all of our equations here on the left and let's look at a data set here to talk about how we would calculate these control limits so again this should be subgroup size and you can see the subgroup size changes 200 220 180 240. every time we take a different sample the size is slightly different and so we need to account for that in the way we the way we calculate our control limits now we're still counting up the number of defective units so we're going to give these samples to our inspector or operator and they're going to do the inspection and count up the number of defective items but because we have a variable sample size we have to add a new calculation this is the percentage of defective items now this calculation is simply just 8 divided by 200 and that's 4 percent similarly right if we did 11 divided by 240 that would come out to 4.6 percent now we can use this data to calculate those variables so p bar is the average percent defective and so what we do here is we take the sum total of all defective units that's the sum of np that's 140 we had 140 defective items divided by the sum of n in total we inspected 3060 samples and we found 140 defective units meaning that our defective rate is four point five eight percent that is p bar now for n bar this is the average sample size on average how many samples did we take and what we do is we essentially sum this up right we take the sum total of n which is 3060 and we divide by the number of subgroup sizes k to get 204 sample sizes that makes sense right if you kind of scan this column you'll notice that on average we have about 200 samples per subgroup now we can take these two parameters p bar and n bar and plug them in to calculate our upper and lower control limits 8.969 0.19 percent and now we can talk about what this looks like graphically so again i've i've left those major parameters here on bottom and here's what the chart looks like so you can see our lower control limit upper control limit you can see the center of our process here in green that's p bar that's that four point five percent and then what you actually see on the chart here in blue is the process this is the trend line for the process and what we're doing is we're plotting these individual percent defectives four percent 3.2 2.8 3.8 5.5 6.7 and you can see here the y-axis is actually in percent defective and for each subgroup we essentially just plot another data point for percent defective now there's something unique about the p-chart in that the control limits can actually be recalculated using the individual subgroup sizes so here in these calculations for upper lower control limit instead of using n bar and calculating just one generic control limit you can actually calculate control limits for each individual subgroup if you wanted to do that and you can see how the control limits change as the sample size fluctuates okay now we're done talking about control charts for defectives now let's talk about defects and the first one to talk about is the c chart this is probably the the easiest there's only one parameter that we need to calculate when we talk about the c chart and that is c bar this is the average number of defects per subgroup and then once we once we calculate c bar we can then plug that in to the upper and lower control limits so let's look at our data here and talk about how we calculate c bar so again we have 20 subgroups you can see that here within each subgroup we sample 500 units and then what we have our team do or what we have our inspectors do is simply just count the number of defects they find in their inspection so in total we inspected 10 000 pieces and we found 95 defects so now let's talk about c bar c bar is the average number of defects per subgroup so what we do is we take those 95 defects we found we divide by the 20 subgroups that we found them in and we calculate that on average we find about 4.75 defects per subgroup and again that makes sense right if you kind of scan this data you'll find that yeah on average there's about four or five defects within each subgroup right within these subgroups and then we can take that value of 4.75 and simply just plug it in to calculate the upper and lower control limits 11.29 and minus 1.79 now if you ever get a negative number here for your lower control limit basically what you do is you round that up to zero because you can't have a negative number of defects in an inspection so the lower control limit is basically zero now graphically let's see what this looks like again you'll see our lower control limit here is at zero upper control limit 11.29 and essentially what we have our team do is they simply just plot the count of defects they call it a c chart we're simply just counting the number of defects that we find in the inspection that makes sense and then you can see here green this is the center line of our process right this is the average of our process and on average we have about 4.75 defects per subgroup all right let's keep going here with the u chart so again the u chart is used when we're trending defects and we have a variable sample size so let's let's take a look at what that what that looks like okay so when we talk about the u chart there's two parameters that we have to calculate to calculate our control charts u bar which is essentially the average percent defects per subgroup and n bar which is the average number of samples per subgroup and once we understand those two parameters u bar and n bar we can then calculate our upper and lower control limits so it's simply just u bar plus 3 times the square root of u bar divided by n bar that's the upper control and then of course for the lower control limit the only thing we change is we subtract that three standard deviations and then similar to the p chart the u chart is actually flexible enough where you can recalculate your control limits based on your actual sample size instead of your average sample size so again let's look at some data here we've got those equations on the left and then this first column here the the subgroup size you can see here that it changes right every time we take a different subgroup the quantity changes and then again what we have our team do is when they do their inspection just count up the number of defects that were observed within that subgroup so for example within subgroup 1 we inspected 100 pieces 100 samples we found 8 defects now we can use that data to calculate the percent defects within each subgroup so here we had 10 defects over 100 pieces that's a 10 defect rate and then to calculate u bar this is simply just the average percent defects so the way we calculate that is on the new in the numerator here we have the sum of c which is simply just a sum of how many defects that we counted so in total we had 117 defects you can see that here and we we found those defects after sampling 1560 total pieces which means on average our defect rate or the the percent defects per subgroup is 7.5 percent the other variable we have to calculate is n bar so we sampled 1560 pieces again you can see that here and we did that across 15 different subgroups which means on average we sampled 104 samples per subgroup that makes sense and again you can kind of scan this this column here and you can see that okay yeah on average we have about you know 100 pieces per uh per sub group and it comes out to 104 is the exact answer and then we can take those two variables and we can plug them into our upper and lower control limits you can see it here 7.5 percent 104 and our upper controller comes out to 15.56 lower control and again comes out to a negative number which we simply round up to zero and so again i'm i'm showing those major parameters here the center of our process the upper and lower control limit and here's what our control chart looks like again the the y-axis here is is in percent defects and i made a mistake here this lower control limit should actually be at zero percent right now it's showing as a as a negative percent which doesn't make any sense you can see the center of our process here at 7.5 percent defects and then all we're plotting in blue is simply just the percent defects within each subgroup so 8 8.3 11.3 4.3 10.0 you can see how this kind of jumps around 6.3 back to 10 8.3 but in general our process here appears to be stable and in control and then like i said similar to the p chart you can actually calculate unique control limits for every sample size so for example let's look at subgroup 11 here we only inspected 60 pieces so we could actually calculate specific control limits using 60 instead of n bar so remember we used n bar which was 104 to calculate our generic control limits if you wanted to you could use the actual subgroup size and and you could see your control limits change as your sample size fluctuates all right that was it for today's lecture i hope you really enjoyed it if you did hit that like button so that other people just like you can find this and if you want to subscribe and you want to stay on this journey to become a cqe hit that subscribe button and that bell icon that way as i publish new material you get notified and you can stay on this journey to become a cqe all right thanks so much have a great day bye

Channel: CQE Academy

Views: 2,934

Keywords: Attribute Data Control Charts, Control Charts, Defects v Defectives, The NP Chart, The P Chart, the C Chart, the U Chart, The NP Control Chart, the P Control Chart, the C Control Chart, the U Control Chart, how to choose the right attribute data control chart, control charts for attributes, control charts in quality control, control chart examples

Id: p-gvwkHePaU

Length: 18min 40sec (1120 seconds)

Published: Wed Jul 14 2021