3.2 Statistical Process Control and Run Charts

3.2 Statistical Process Control and Run Charts

To improve patient safety, healthcare leaders must determine whether changes in clinical outcomes are the result of deliberate quality improvement efforts or merely random fluctuation. Statistical Process Control (SPC) is a branch of quality science that utilizes statistical methods to monitor, control, and improve processes. The primary visual tools used in SPC are run charts and control charts. A run chart is a line graph displaying data plotted in chronological order. By analyzing data over time, run charts help safety professionals distinguish between random variation and non-random, statistically significant changes in process performance.

Understanding Variation: Common Cause vs. Special Cause

A foundational concept of SPC is that every process exhibits variation. Walter Shewhart, the pioneer of SPC, classified process variation into two distinct categories:

• Common Cause Variation: This is the natural, random variation inherent in any stable process. It is predictable and arises from the system's design, technology, and environment. For example, slight variations in daily patient turnaround times in the emergency department are usually due to common cause variation. Reducing common cause variation requires a fundamental redesign of the entire system, rather than reacting to individual data points.
• Special Cause Variation: This is non-random variation that arises from a specific, external event or factor that is not part of the normal process design. Special cause variation is unpredictable and indicates that the process is unstable. For example, a sudden spike in surgical site infections on a specific unit due to a faulty sterilizer is a special cause. When special cause variation is detected, quality teams must investigate immediately to identify and resolve the root cause.

A critical error in quality improvement is tampering, which occurs when management adjusts a process in response to common cause variation. For example, if a hospital administrator changes the nursing schedule immediately because a single shift experienced minor medication delays (which fell within normal process limits), they are tampering. According to Deming's Quality Theory, tampering invariably increases overall process variation and worsens system performance.

Anatomy of a Run Chart

A run chart is the simplest tool for monitoring process data over time. It consists of the following elements:

1. X-axis: Represents time or chronological sequence (e.g., days, weeks, months, or consecutive cases).
2. Y-axis: Represents the measure of interest (e.g., infection rate, wait time in minutes, or compliance percentage).
3. Data Points: The individual measurements plotted in order.
4. Median Line: A horizontal line drawn at the middle value of the baseline data. The median splits the data points so that half are above and half are below. The median is used rather than the mean because it is less sensitive to extreme outliers.

To establish a reliable baseline and apply run chart rules, a quality team should collect a minimum of 10 to 12 data points. Once the baseline is set, the median line is drawn, and future data points are plotted to monitor for signs of process change.

Run Chart Rules for Special Cause Variation

Non-random process changes (special cause variation) are identified on a run chart by applying four standardized rules developed by quality statisticians. If any of these rules are met, it indicates a statistically significant change has occurred in the process:

• Rule 1: The Shift: A shift is defined as 6 or more consecutive data points that plot entirely on one side of the median line (either all above or all below). Data points that plot exactly on the median line do not count toward this rule; they are ignored, and the count continues with the next point. A shift indicates that the average level of the process has changed.
• Rule 2: The Trend: A trend is defined as 5 or more consecutive data points that are continuously increasing or continuously decreasing. If two consecutive points have the exact same value, the duplicate value is ignored and does not break the trend, but it also does not count as a new point in the trend. A trend indicates a gradual change in process performance.
• Rule 3: The Runs (Too Few or Too Many): A "run" is a series of consecutive data points on one side of the median. A new run begins when a data point crosses the median. The total number of runs on a chart must fall within a statistically defined range based on the number of data points not on the median. If the number of runs is too few or too many, it indicates non-random variation. Too few runs suggest a process shift, while too many runs suggest data from two different processes are being mixed.
• Rule 4: The Astronomical Point: This is a single data point that is an obvious, dramatic outlier. It represents a value that is far outside the normal range of variation. Unlike the other rules, which are mathematical, the astronomical point is qualitative and immediately obvious to anyone reviewing the chart. It indicates a sudden, massive failure or extreme event in the system.

Applying these rules allows patient safety teams to determine if a quality improvement intervention was successful. For example, if a team implements a new hand hygiene checklist and subsequently observes a shift of 7 consecutive months of infection rates below the median, they have statistical proof that the checklist led to a sustained improvement.