Section 7.1: Run Charts & Trend Analysis
Key Takeaways
- Run charts use a median as the center line, which requires exactly 50% of data points to lie above it and 50% below it, making it robust against outliers.
- A shift is defined as 6 or more consecutive data points falling entirely above or entirely below the median, indicating a significant process change.
- A trend is defined as 5 or more consecutive data points continuously increasing or decreasing, excluding flat points that do not break the sequence.
- An astronomical value is an extreme, visually obvious outlier that indicates an immediate, unusual event requiring qualitative investigation.
- A non-random process can be identified if the total number of runs is either too high or too low based on statistical probability tables.
Run Charts & Trend Analysis
In healthcare quality improvement, understanding process performance over time is essential for driving sustainable change. A run chart is a simple, powerful, and widely used graphical tool that plots data in chronological order. Unlike more advanced statistical tools, a run chart is easy to construct and interpret, making it an ideal starting point for frontline improvement teams. It helps organizations establish a baseline, identify process stability, and evaluate the impact of quality improvement interventions (such as a Plan-Do-Study-Act or PDSA cycle).
Understanding the Structure of a Run Chart
A run chart consists of a horizontal axis (X-axis) representing time or sequence (e.g., hours, days, weeks, months, or consecutive patients) and a vertical axis (Y-axis) representing the quality metric being monitored (e.g., percentages, rates, or counts).
The defining characteristic of a run chart is its center line, which is always the median.
Why Use the Median?
The median is the middle value of a data set when the values are arranged in ascending or descending order. If the data set has an even number of points, the median is the average of the two middle values. Using the median as the center line is a deliberate statistical choice:
- Robustness to Outliers: Unlike the mean (average), the median is not skewed by extreme, anomalous data points. For instance, if an emergency department's wait times are typically 30 minutes, but one patient waits 400 minutes due to an extreme clinical complication, the mean will rise significantly, while the median remains stable and reflective of typical performance.
- Equal Probability: By definition, exactly 50% of the data points will lie above the median, and 50% will lie below it (excluding points that fall exactly on the median line). This equal probability ($p = 0.5$) serves as the mathematical foundation for the probability rules used to detect non-random variation.
When calculating the median and analyzing a run chart, any data points that fall exactly on the median line are ignored. These points do not contribute to the analysis of patterns, and they are subtracted from the total count of data points to determine the number of 'useful data points.'
Four Rules for Identifying Non-Random Variation
The primary goal of analyzing a run chart is to determine if process changes have resulted in a genuine, non-random improvement or if the observed variation is simply random noise. Random variation is expected in any process. Non-random variation, however, suggests that a significant change has occurred in the system. The healthcare quality field (utilizing standards from the Institute for Healthcare Improvement [IHI] and statisticians like Jakob Anhoej) relies on four primary rules to identify non-random variation.
| Rule Name | Visual Criterion | Statistical Rationale | Handling of Equal/Median Points |
|---|---|---|---|
| Shift | 6 or more consecutive points entirely on one side of the median | Probability of 6 consecutive points on one side by chance is less than 2% ($0.5^6 = 1.56%$) | Ignore points on the median; they do not break or count toward the shift. |
| Trend | 5 or more consecutive points continuously increasing or decreasing | Probability of 5 consecutive directional steps by chance is less than 5% | If consecutive points are equal, ignore the duplicate and continue counting the trend. |
| Astronomical Value | A single point that is a blatant, extreme outlier | Qualitatively obvious anomaly indicating a temporary system failure or event | N/A |
| Runs Count | Too few or too many runs (crossings of the median) based on tables | The total number of runs falls outside expected statistical thresholds for the sample size | Points on the median are excluded from the useful point count. |
1. The Shift Rule
A shift is identified when six or more consecutive data points fall entirely above or entirely below the median line. Points that fall exactly on the median are ignored; they do not count toward the six points, but they also do not break the sequence. If you have three points above, one point on the median, and then three points above, you have a shift of six points. A shift indicates that the central tendency of the process has changed. For example, if a clinic implements a new scheduling protocol and subsequently observes six consecutive months of reduced patient wait times below the historic median, they have achieved a statistically significant shift.
2. The Trend Rule
A trend is signaled by five or more consecutive data points that are continuously increasing or continuously decreasing. If two consecutive points are equal, it does not count as an increase or decrease. You simply ignore the flat point and continue counting. For instance, values of 12, 14, 15, 15, 17, and 18 represent an increasing trend of five points (12 to 14, 14 to 15, 15 to 17, 17 to 18). A trend indicates a gradual drift or steady improvement in the process.
3. The Astronomical Value Rule
An astronomical value is an extreme data point that is visually obvious and immediately recognizable as different from all other points on the chart. This determination is qualitative and relies on the common-sense consensus of the improvement team. It indicates a singular, unusual event (such as a natural disaster or major equipment failure) that warrants immediate qualitative investigation. It is important to note that what is astronomical in one process might be normal variation in another; therefore, visual context is key.
4. The Runs Count Rule
A 'run' is a series of consecutive data points on one side of the median. A run ends when the data line crosses the median to the opposite side. The runs count rule evaluates the total number of runs across the entire chart. To apply this rule:
- Count the total number of runs (each cluster of points above or below the median constitutes one run).
- Count the number of useful data points (total points minus those on the median).
- Compare the actual run count against a standard statistical table of runs.
- Too Few Runs: If the number of runs is less than the lower limit in the table, it indicates that the process is changing very slowly or has shifted. The points are staying on one side of the median for too long.
- Too Many Runs: If the number of runs exceeds the upper limit, it indicates rapid oscillation. This often occurs when data from two distinct processes are blended together (e.g., combining compliance data from a high-performing daytime shift and a struggling night shift onto a single chart).
Clinical Application and CPHQ Exam Traps
Quality professionals frequently use run charts during pilots to test changes. If a run chart shows only random variation, the process is stable, and any perceived 'improvements' are likely temporary fluctuations. If a rule is triggered, the team must investigate.
CPHQ Exam Traps to Avoid
- Mean vs. Median: Control charts use the mean as the center line; run charts must use the median. Do not select 'mean' for run charts.
- Rule Numbers: Memorize the exact numbers: 6 for a shift, 5 for a trend. Do not confuse them with control chart rules (which often require 8 or 9 points for a shift).
- Specification Limits: Run charts never display customer specification limits or clinical targets. They only display actual process data and the median.
- Median Points: Remember that points on the median are deleted from calculations of runs and useful points.
A healthcare quality improvement team is analyzing monthly hand hygiene compliance rates using a run chart. If the median is 82% and the last six consecutive data points are 85%, 88%, 91%, 86%, 84%, and 89%, what does this pattern represent?
When constructing a run chart to monitor patient wait times in an emergency department, which statistical measure must be used as the center line, and what is the primary rationale for this choice?
A quality team is evaluating a run chart with 20 useful data points. They count a total of 5 runs. According to statistical run tables, the expected number of runs for 20 points ranges from 6 to 16. What conclusion should the team draw?