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Statistical process control charts with R

Jacob Anhøj ([email protected])
October 2021

This one-day masterclass is for R programmers who want to learn statistical process control (SPC) for continuous quality improvement.

Statistical Process Control is not about statistics, it is not about “process-hyphen-control”, and it is not about conformance to specifications. […] It is about the continual improvement of processes and outcomes. And it is, first and foremost, a way of thinking with some tools attached.
– Donald Wheeler, Understanding Variation, 2nd ed. p. 152

In this masterclass you will learn the tools, most notably the process control chart, which is a simple an elegant graph that helps to distinguish between common and special cause variation in processes in time or space.

The control chart above shows the monthly number of hospital acquired bacteremias in a large university hospital. Since all data points fall between the control limits (grey area), which represent the natural (common cause) variation, the process is said to be stable, meaning predictable. That is, if nothing changes, we should in the future expect on average 25 and no less than 10 and no more than 40 cases per month. If, on the other hand, one or more data points show up outside the control limits that would be a signal that the process is changing (for better or worse), and that you should seek to find the special cause that produced that change.

What will you learn?

As mentioned, the main focus of this masterclass is on the tools – how to construct and interpret basic control charts.

After the masterclass you will be able to …

  • construct I, C, U, and P control charts according to Mohammed 2008 using base R functions;

  • apply different statistical rules to identify special cause variation;

  • explain how different rules affect the chart’s sensitivity and specificity;

  • explain how to reconcile the voice of the process (the control chart) with the voice of the customer (specifications and standards);

  • construct multidimensional (faceted) and multi-part control charts using functions from the qicharts2 package.

The masterclass is 100% PowerPoint-free and contains a mixture of lecturing, discussion, Q&A, live R coding, and exercises. During the day, you will build your own R function for control chart construction.

Who are you?

You may be an analyst, data scientist, statistician, healthcare professional, researcher – or somebody else – with an interest in continuous quality improvement and an affinity for numbers and programming.

You …

  • are familiar with the basic ideas of SPC, specifically the distinction between common cause and special cause variation;

  • have experience using the R programming language to manipulate, analyse, and plot data;

  • understand basic statistical concepts including probability, population, sample, distribution, and measures of central tendency and dispersion.

How should you prepare for the masterclass?

First, download the course files to a separate folder (e.g. “r4spc”) on your computer:

… or get everything from this GitHub repo: https://github.com/anhoej/r4spc (click the green Code button, then Download ZIP).

Next, to get the most out of the masterclass and to help the masterclass to a flying start it is important that you have the necessary knowledge and skills mentioned above.

To shape your SPC thinking you should have read these two articles:

  1. Anhøj J, Hellesøe AB. The problem with red, amber, green: the need to avoid distraction by random variation in organisational performance measures. doi: 10.1136/bmjqs-2015-004951.

  2. Mohammed MA, Worthington P, Woodall WH. Plotting basic control charts: tutorial notes for healthcare practitioners. doi: 10.1136/qshc.2004.012047. If you are working in the NHS, here is a direct link to the full paper.

Finally, you need to bring a computer with recent versions of R (≥ 4.1) and RStudio (≥ 1.4) and the qicharts2 package installed.

Please check that your R installation is fully functional as there will be no time during the masterclass to fix individual installation problems. If you are able to run the two .R files without errors or warnings, you are good to go.

You may want to set a day aside before the masterclass to prepare. Just saying 😉

Who am I?

Me on a bad-hair day after 6 months corona lockdown

I am a medical doctor working at Rigshospitalet in Copenhagen, Denmark.

I graduated in 1992 and after nine years of clinical work and research I worked for four years in a pharmaceutical company with research and health IT. At the same time, I took a diploma in information technology at the IT University of Copenhagen.

Since 2005 I have worked almost exclusively with patient safety and quality improvement in healthcare. My main interest and area of research is use of statistical methods in quality improvement. At present, my main job involves surveillance of hospital infections and antibiotic use in the Capital Region of Denmark.

I have used R since 1999 and am the maintainer of the qicharts2 R package.

I have written several articles on SPC:

  1. Anhøj J, Olesen AV. Run charts revisited: a simulation study of run chart rules for detection of non-random variation in health care processes. PLoS One. 2014 Nov 25;9(11):e113825. doi: 10.1371/journal.pone.0113825.

  2. Anhøj J. Diagnostic value of run chart analysis: using likelihood ratios to compare run chart rules on simulated data series. PLoS One. 2015 Mar 23;10(3):e0121349. doi: 10.1371/journal.pone.0121349.

  3. Anhøj J, Hellesøe AB. The problem with red, amber, green: the need to avoid distraction by random variation in organisational performance measures. BMJ Qual Saf. 2017 Jan;26(1):81-84. doi: 10.1136/bmjqs-2015-004951.

  4. Anhøj J, Wentzel-Larsen T. Sense and sensibility: on the diagnostic value of control chart rules for detection of shifts in time series data. BMC Med Res Methodol. 2018 Oct 3;18(1):100. doi: 10.1186/s12874-018-0564-0.

  5. Wentzel-Larsen T, Anhøj J. Joint distribution for number of crossings and longest run in independent Bernoulli observations. The R package crossrun. PLoS One. 2019 Oct 1;14(10):e0223233. doi: 10.1371/journal.pone.0223233.

  6. Anhøj J, Wentzel-Larsen T. Smooth operator: Modifying the Anhøj rules to improve runs analysis in statistical process control. PLoS One. 2020 Jun 4;15(6):e0233920. doi: 10.1371/journal.pone.0233920.

Further up, further in

SPC is almost 100 years old – older than the randomised controlled trial – so it is no surprise that there are wast amounts of resources out there. However, these three books are my go-to SPC resources:

  1. Donald J. Wheeler (2000). Understanding Variation – The Key to Managing Chaos. SPC Press.

  2. Douglas C. Montgomery (2019). Introduction to Statistical Quality Control. John Wiley & Sons.

  3. Western Electric (1956). Statistical Quality Controll Handbook. Western Electric.

Wheeler gives a brilliant and compelling introduction to SPC thinking, and Montgomery delivers a comprehensive explanation of the tools of the trade including formulas for all the basic SPC charts plus many more advanced charts and other tools for specialist purposes. The WE handbook is not only interesting for historical reasons, it is highly relevant today and gives detailed instructions to the practical use and interpretation of SPC charts.

Specifically for making control charts with R, you may find the qicharts2 vignette useful.