Is your process in control? The XmR chart is a great statistical process control (SPC) tool that can help you answer this question, reduce waste, and increase productivity. We'll cover the concepts behind XmR charting and explain the XmR control constant with some super simple R code. Lastly, we'll cover how to make the XmR plot by hand, with base R code, and the ggQC package. Objectives: When you’re done with this post, you should: Grasp the XmR chart concept and utility Understand the math necessary to create the XmR chart by hand, and why moving range should be used instead of standard deviation to determine control limits. XmR Chart…


XmR Control Limits  Why Moving Range, not Standard Deviation
So, you want to know why we use mean moving range, mean(mR), and not standard deviation to determine XmR control limits. Before answering, let's do a quick review to make sure we are starting on the same page. The mean(mR) is determined by first finding the absolute difference between sequential pairwise measurements. This gives you a series of moving ranges – mR. Next, you calculate the mean of those ranges to give you mean(mR). Below are some sample calculations. Once you've determined the mean(mR), you are in a position to calculate the sequential deviation: mean(mR) / 1.128. By multiplying the sequential deviation by ± 3, we can establish the XmR…

Control Chart Constants  Tables and Brief Explanation
Jump to Control Chart Constants: Bias Correction Constants: d2, c4, d3, d4 XmR Constants (n=2): d2, A2, D3, D4 XbarR Constants: d2, d3, A2, D3, D4 XbarS Constants: c4, A3, B3, B4 Control chart constants are the engine behind charts such as XmR, XbarR, and XbarS. And, if you've made a control chart by hand or sat in a class, you'll likely have memories of bizarre constants like d2, A2, etc. To me, control chart constants are a necessary evil. Why? Because, it's a nuisance to look up a constant to make a chart, and I suspect that has likely frightened away many would be users over the years. These…

Estimating Control Chart Constants with R
In this post, I will show you how a very basic R code can be used to estimate quality control constants needed to construct XIndividuals, XBar, and RBar charts. The value of this approach is that it gives you a mechanical sense of where these constants come from and some reinforcement on their application. If you work in a production or quality control environment, chances are you’ve made or seen a control chart. If you’re new to control charting or need a refresher check out Understanding Statistical Process Control, Wheeler et. al. If you want to dive in and start making control charts with R, check out R packages ggQC:…