For the following example, we will be focusing on quality control charts for continuous data for when the sample size is greater than 10.

However, how can we determine the right quality control chart to use for monitoring a process? The following decision tree can be used to identify which is the correct quality control chart to use based on the given data:

Quality control charts represent a great tool for engineers to monitor if a process is under statistical control . They help visualize variation, find and correct problems when they occur, predict expected ranges of outcomes and analyze patterns of process variation from special or common causes. Quality control charts are often used in Lean Six Sigma projects and DMAIC projects under the control phase and are considered as one of the seven basic quality tools for process improvement.

x-bar chart

The x-bar and s-chart are quality control charts used to monitor the mean and variation of a process based on samples taken in a given time. The control limits on both chats are used to monitor the mean and variation of the process going forward. If a point is out of the control limits, it indicates that the mean or variation of the process is out-of-control; assignable causes may be suspected at this point. On the x-bar chart, the y-axis shows the grand mean and the control limits while the x-axis shows the sample group. Let’s take a look at the R code using the qcc package to generate a x-bar chart.

x-bar chart R codex-bar chart example using qcc R package

The x-bar chart generated by R provides significant information for its interpretation, including the samples (Number of groups), control limits, the overall mean (Center) the standard deviation (StdDev), and most importantly, the points beyond the control limits and the violating runs. Engineers must take a special look at these points in order to identify and assign causes attributed to changes in the system that led the process to be out-of-control.

s-chart

In order to use the s-chart along with the x-bar chart, the sample size n must be greater than than 10. On the s-chart, the y-axis shows the sample standard deviation, the standard deviation overall mean and the control limits, while the x-axis shows the sample group. Once you have created a x-bar chart, you will only need to add the following lines of code to generate the s-chart.

s-chart R code s-chart example using qcc R package

The s-chart generated by R also provides significant information for its interpretation, just as the x-bar chart generated above. In the same way, engineers must take a special look to points beyond the control limits and to violating runs in order to identify and assign causes attributed to changes on the system that led the process to be out-of-control.

Process Capability Analysis

The process capability is a statistical measure of the inherent process variability of a given characteristic. In other words, the ability of a process to meet the given specifications (e.g. customer requirements, engineering tolerances or other specifications).

Once you have generated the x-bar and R-charts using R, you will only have to add the following lines of code specifying the lower control limit, upper control limit and the target. Once you have done so, add the last line of code below to generate the process capability summary chart.

Process capability analysis R codeProcess Capability Analysis using qcc R package

Concluding Thoughts

We have gone through one of the many industrial engineering applications that R and the qcc package have to offer. As you might have noticed, just with few lines of code we were able to construct quality control charts and get significant information to be used during Lean Six Sigma and DMAIC projects for process improvement. Once again, I invite you to continue discovering the amazing stuff you can perform using R as an industrial engineer.

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If you found this article useful, feel welcome to download my personal code on GitHub. You can also email me directly at [email protected] and find me on LinkedIn. Interested in learning more about data analytics, data science and machine learning applications in the engineering field? Explore my previous articles by visiting my Medium profile. Thanks for reading.

– Robert