Definition
A run chart is a time-series plot that tracks a single metric — defect count, cycle time, changeover duration, production output — over time. Data points are plotted in chronological order and connected by lines. A horizontal line typically marks the median (the middle value).
The run chart is the simplest of the time-series tools. Unlike a control chart, it does not require calculating statistical control limits. It answers straightforward questions: Is this metric getting better? Getting worse? Stable? Did the change we made last week have an effect?
The run chart is often the verification tool — the chart that appears in the “Follow-up” section of an A3 report to show whether a countermeasure actually worked.
Japanese Origin
折れ線グラフ (oresen gurafu) combines:
- 折れ線 (oresen) — broken line, zigzag line (折れ = bent/broken, 線 = line)
- グラフ (gurafu) — graph (borrowed from English)
The name simply describes what it looks like: a series of data points connected by line segments, creating a zigzag pattern. In some Japanese QC literature, the more general term グラフ (graph) is used as the 7th QC tool, encompassing run charts, bar charts, and other graphical representations.
The 7th Tool Question
The identity of the seventh QC tool has varied across sources. Ishikawa’s original formulation included graphs (グラフ) as a general category or stratification (層別, sōbetsu) as a data analysis technique. Some modern formulations specify the run chart as the seventh tool, emphasizing its role as the primary time-series visualization tool that is simpler and more accessible than the control chart. The first six tools are consistent across all formulations.
History
Time-series plots are among the oldest forms of data visualization — Florence Nightingale’s coxcomb charts from the 1850s tracked mortality rates over time. As a QC tool, the run chart (or graph) was included in Ishikawa’s 7 QC Tools framework as the simple, accessible counterpart to the more statistically rigorous control chart.
At Toyota — Run charts are used ubiquitously: on shop floor information boards tracking daily production targets vs. actual, in QC circle reports showing defect rates before and after countermeasures, in A3 reports tracking improvement over time, and in management reviews showing trends in key performance indicators. Their simplicity makes them the default visualization tool for shop floor communication.
How to Construct
- Choose the metric — What are you tracking? Defect count per shift? Changeover time? Output per hour? Be specific.
- Define the time axis — Plot time on the horizontal axis. Choose an appropriate granularity: hourly, daily, weekly, monthly.
- Collect data over time — Record the metric at each time interval. A minimum of 20-25 data points is recommended for reliable pattern detection.
- Plot the points — Each data point represents the metric value at that time.
- Connect with lines — Draw lines between consecutive points to make the trend visible.
- Add the median line — Calculate the median of all data points and draw a horizontal reference line. The median is preferred over the mean because it is not distorted by outliers.
How to Read a Run Chart
Trend — Six or more consecutive points moving in the same direction (up or down). This indicates a genuine shift in the process, not random variation.
Shift — Eight or more consecutive points on the same side of the median line. This suggests the process center has moved — something has changed.
Too few runs — If the data crosses the median far fewer times than expected (for random data, approximately n/2 + 1 crossings are expected for n points), there may be a systematic pattern.
Too many runs — If the data crosses the median far more often than expected, the data may be oscillating — possibly due to over-adjustment (tampering).
Random scatter around the median — No trends, shifts, or unusual patterns. The process is stable at its current level.
Run Chart vs. Control Chart
| Feature | Run Chart | Control Chart |
|---|---|---|
| Reference line | Median | Mean (X̄) |
| Control limits | None | UCL and LCL (±3σ) |
| Statistical rigor | Low (rule-of-thumb tests) | High (statistically calculated limits) |
| Skill required | Minimal | Moderate (must calculate limits) |
| Best for | Quick visual check, verification | Ongoing process monitoring, SPC |
| Detects | Trends, shifts | Special cause variation precisely |
The run chart is a screening tool — quick and easy, good for initial investigation and verification. The control chart is a diagnostic tool — more powerful, essential for ongoing process monitoring and formal SPC programs. Many teams start with a run chart and upgrade to a control chart when the process is important enough to warrant ongoing statistical monitoring.
Common Mistakes
Not plotting enough data points. A run chart with 8-10 points is unreliable — apparent trends may be random. Collect at least 20-25 points for the statistical rules (trends, shifts, runs) to be meaningful.
Connecting points over time gaps. If data was not collected for a period (a weekend, a holiday, a shutdown), do not draw a connecting line across the gap. The gap may coincide with a change. Show it as a break in the line.
Using the mean instead of the median. The median is more robust — it is not influenced by extreme values. A single outlier can shift the mean line, distorting the picture of where the process center truly is.
Over-interpreting normal variation. Not every up-and-down movement is a trend. Random variation naturally produces sequences of consecutive increases or decreases. Use the formal rules (6+ consecutive same-direction for a trend, 8+ consecutive same-side for a shift) to distinguish real signals from noise.
Plotting the chart but not marking the countermeasure. When a run chart is used to verify an improvement, draw a vertical line on the chart at the point when the countermeasure was implemented. This makes it immediately visible whether the metric changed after the action — the most important information on the chart.