Authors: Ahmed Taher, Lucas Chartier

You are attending your monthly ED business meeting. There has been a recent effort to decrease the time it takes a patient to be transferred to the imaging department for a STAT CT scan. The project team has concluded the first two PDSA cycles after wide stakeholder engagement, and a root cause analysis. Two interventions were carried out: one, redesigning the process for patient pick up and transport, and two, a new expedited imaging request to the radiology department. Your ED Chief asks you to help prepare a statistical process control (SPC) chart – or Shewhart chart – to assist studying the effects of the interventions. You scratch your head as it has been a long time, but you roll your sleeves up and dig in.

Welcome to another HiQuiPs post! In this series, we review the basics of understanding and preparing SPC charts. This may sound overwhelming at first, but we will break it down and walk you through the details.

#### Why Statistical Process Charts

SPC charts were initially developed in the manufacturing industry and have found their way into healthcare. They are a powerful tool for monitoring a process over time and determining if an intervention is actually causing changes. They are also used with monitoring a process to see if unwanted changes have underlying causes or are due to random chance; that is, determining a “signal” through the “noise”.(1) To understand their true potential however, we need to review process variation.

#### Process Variation

How do you know if the variation you are observing in a process is due to a change you have implemented? As discussed in a previous post, the concept of process variation comes into play. There are two types of process variation, common cause variation and special cause variation.

A process with common cause variation, is a stable process with variation that is expected and predictable. (2,3) For example, getting a result from the hospital lab for routine blood work in the ED usually takes any value between 40–50 minutes on any given day.

A process with special cause variation is an unstable process with variation that is unexpected and unpredictable, i.e. something external to the process is acting on it.(1,2) For example, if the tube system sending the blood samples breaks down, the result may take over 120 minutes a certain day.

Determining if a process has either common or special cause variation is essential to choosing the correct intervention strategy. (4)

A process with only common cause variation is stable and optimized, therefore any interventions must change the process itself.

A process with special cause variation is unstable and unoptimized, and something external may be affecting the process. Therefore, interventions may seek to decrease variation or alter the external factors.

#### Run Charts

In a previous post we discussed run charts, including the probability-based rules that are used to determine if changes are statistically significant. They only show part of the picture; specifically, they can only detect if a change is happening, either graphically or through median-based probability rules. They do not indicate if variation is common cause or special cause. That means they cannot tell you if changes you notice are due to the natural variability of the process.

So why do we use run charts? We use them because they are more easily used when there is less data available, and they don’t need any specific software to construct, unlike SPC charts. A common strategy while starting a new process is therefore to set up a run chart until enough data points are available to construct an SPC chart.(3)

#### Preparation of an SPC Chart

Before constructing an SPC chart, it is essential to have team members who know the system and its details so they know how to collect the process data and can interpret the variation.(5,6) There are two main phases of an SPC chart: a baseline period and an ongoing monitoring period. (7) The baseline period is important to interpret any future changes and requires a minimum number of data points to show stability. The length of the baseline period will differ based on the type of chart being used (more on this in subsequent posts!). The ongoing monitoring period will track successive Plan-Do-Study-Act (PDSA) cycles.

#### SPC Chart Basic Interpretation

Just like Run Charts, SPC charts plot the process variable being observed (y-axis) over time (x-axis). In the figure below the y-axis represents the ED time to obtain a STAT CT scan, plotted against each month on the x-axis. You will also notice blue dots each representing a “subgroup”. The SPC chart also has a mean for the values (light blue line) and control limits (red line), which we will get into below.

#### Subgroups

Each point on the SPC chart is called a subgroup. These can have an equal or unequal of observations in each subgroup. In our example in Figure 1, each data subgroup is the mean of the data points collected over that month. These are unequal size subgroups, i.e. 10 STAT scans in January, 7 in February and 15 in March, etc. Other charts may have equal subgroups with each subgroup being the mean of the same number of observations.

#### Control Limits

SPC charts usually plot data over time with three main lines:(5)

The center line (CL), aka the ‘main’ line, is usually based on the mean. This the central light blue line in Figure 1.

The upper control limit (UCL) and lower control limit (LCL), which are each based on three standard deviations (SDs) above and below the mean. These are the red upper and lower lines in Figure 1. They change over time if or when the sizes of the subgroups change (due to the way they are statistically calculated).

#### Summary

Now with this introduction in mind you feel ready to look into the data further and see if the variation noted is due to the effects of the interventions that took place. You initially create a run chart, but elaborate on that and you are able to construct an SPC chart for your ED chief.

An SPC chart is a powerful tool that can illustrate variation in healthcare processes. We have discussed preparation prior to constructing an SPC chart, and the common elements in interpreting an SPC chart. Join us for the following SPC chart posts where we discuss a more in depth interpretation of the SPC chart along with different types of SPC charts, how to choose an appropriate SPC chart, rules for determining special cause variation, and much more.

Copyedited by: Daniel Dongjoo Lee

#### References

Woodall WH, Adams BM, Benneyan JC. The Use of Control Charts in Healthcare. In: Statistical Methods in Healthcare. John Wiley & Sons, Ltd; 2012:251-267. doi:10.1002/9781119940012.ch12

Shewhart W. Economic Control of Quality Of Manufactured Product. ASQ Quality Press; 1980.

Deming WE. Out of the Crisis. Massachusetts Institute of Technology; 1986.

Provost L, Murray S. The Health Care Data Guide: Learning from Data for Improvement. Jossey-Bass; 2011.

Mohammed MA. Using statistical process control to improve the quality of health care. Quality and Safety in Health Care. Published online August 1, 2004:243-245. doi:10.1136/qshc.2004.011650

Mohammed MA, Worthington P, Woodall WH. Plotting basic control charts: tutorial notes for healthcare practitioners. Quality and Safety in Health Care. Published online April 1, 2008:137-145. doi:10.1136/qshc.2004.012047

Woodall WH. Controversies and Contradictions in Statistical Process Control. Journal of Quality Technology. Published online October 2000:341-350. doi:10.1080/00224065.2000.11980013

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