Sample subgrouping is important for SPC and Cpk; but does it affect sampling frequencies?

Taking several samples to form one datapoint, called sample subgrouping, strongly affects the precision and predictive power of your measurement system. You might be tempted to reduce sampling frequency when using larger subgroups, but that relationship is not so simple.
Subgrouping choices as based on many factors, like cost, ease of analysis, process setup and quality of measurement. You could get away with a slightly lower sampling frequency, but that should not be the reason why you use subgroups, and most likely you won't want to reduce sampling frequency...
#continuousimprovement #sampling #spc

[@domenicoscarpino3715]

Hi Tom, thanks for the video. You mentioned 3 times the standard deviation for the individual chart and 3 times the standard error in the xbar chart. As for my understanding the two formulas are different. The individual chart is based on the moving average and the xbar chart is based on the range (ofc these would be divided by d2 and multiplied by 3). Can you clarify why and how moving range and range are related respectively to standard deviation and standard error?

[@TomMentink]

Hi Dom, for individual charts, there is of course no average per subgroup - since there are no subgroups (size 1 doesn't really count as a group 😉). So in stead of calculating standard deviation from the range between values in each subgroup, we use the range between every pair of individual values (the moving range). The assumptions are the same: the range between two or more randomly drawn values from a population correlates strongly with the standard deviation of that population, which makes the range a good predictor of the SD. When your subgroup size is 2, the formulas will be identical for subgroup or moving range. But when the subgroup is larger, the chance for drawing a more extreme value also gets higher and higher - that's why the d2 value by which you divide the range gets higher for larger subgroups. So in both cases, the standard deviation of the whole population is estimated. But now we come to the control limits: For individual samples, we expect those values to also have a standard deviation equal to that of the population. For subgroups, we plot the average of that group. The averages of subgroups will be much closer to the mean, because extreme values inside a subgroup will usually be 'averaged out' by the other random samples in that subgroup - that's why the 'standard deviation' of the AVERAGES of subgroups is much smaller (this is the main part of the central limit theorem). In fact, that's why the SD of the averages is known by a different name: standard error. This is why, for x-bar charts, the control limits are not placed at 3 standard deviations, but at 3 standard errors - since you'll be plotting the averages in the chart, not judging each individual measurement. And as explained in the video, the relationship between standard deviation, sample group size and standard error is based on the square root of the sample group size.

[@domenicoscarpino3715]

Thank you Tom. The whole video addresses a very important topic for sure. I still struggle to get the last part about the measurement system variation. I thought that variation coming from measurement system was gonna be there regardless the type of chart... I would really appreciate if you can elaborate a bit more on why the subgroup chart helps in case of an iffy measurement system.

[@TomMentink]

@@domenicoscarpino3715 more great questions, thanks for ‘thinking aloud’ Dom, I’m sure there are others with those same questions 🤓 You’re right, the chart type doesn’t influence the quality of the measurement. But IF your measurement is correctly calibrated AND the variation is mainly from repeatability (so not really operator dependent), you can get a much more reliable result by subgrouping and using the average value of several measurements as one result. That’s why switching up your sampling from individual measurements to subgrouping can help in that specific case of poor repeatability. That’s what I mean with an “iffy measurement system” - difficult sampling and/or measurement (device). If the operator has a bias compared to other operators (poor repeatability) subgrouping will not help you, because that same operator will do all those analyses for the whole subgroup and thus introduce their same deviation to all the results.

[@domenicoscarpino3715]

@@TomMentink thank you, it's very clear now! Your videos are already so insightful and the topics you present are definitely not very often addressed. The measurement system bonus you gave on this video is a very good example of that. I do like to ask questions if there's something I don't fully understand and I'm super happy if this is also helpful to the other subscribers.

[@datascience1274]

Hi Tom, may I ask you how you calculate the expected process average and the expected process range-moving range? Do these come from historical data or you simply average the points in the chart?

[@TomMentink]

There's a difference between SPC and Cpk/Ppk here -> for SPC, you take a reference period (historical data, of at least 30+ subgroups or 50+ individual samples) to calculate the average and limits that will then be used to judge the ongoing process. When you've made a significant change to your process (usually an improvement effort, but can even be an 'accepted' worsening of conditions), you recalculate the control limits with 30/50+ new samples. Cpk/Ppk don't really use a chart, so I guess you're not referring to them, but when you calculate Cpk you always just take the samples from the current period/series of products (so that's more or less live data). There is a way to do SPC with continuously updating your average and limits, in which you use a relatively long (again 30+ subgroups / 50+ individual samples) moving period to keep updating your limits. I'm not a huge fan of this, because you shouldn't have process shift at all in the theory of SPC, but know that some companies will favour this approach because it automatically factors in the effects of process improvement and allows for seasonal changes (if they don't occur too quickly).

[@datascience1274]

Thank you. I am referring to SPC, and historical data seems like a very good way to go about it. I have seen people calculate average and control limits using the samples of the ongoing process (individual points, subgroup means depening on the chart of course). I wonder how it's possible to detect any special cause by using those same samples to calculate the main average. It doesn't make sense to me, but it's plenty of videos on youtube where for example the central mean of the chart is calculated by averaging the ongoing soubgroup means... What do you think about this approach?