Run chart

What Is a Run Chart?

A run chart is a line graph that visually displays observed data points in chronological order to reveal trends, shifts, or patterns over time. Often employed within the broader field of statistical process control, a run chart helps monitor the behavior of a process and understand its variation. By plotting data sequentially, analysts can quickly identify non-random patterns that might indicate a change in the underlying process, making it a fundamental tool for process improvement and quality control. A run chart typically includes a horizontal line representing the median of the data, which aids in observing whether subsequent data points fall above or below this central tendency.

History and Origin

The conceptual underpinnings of the run chart are deeply rooted in the history of quality control and the pioneering work of Walter A. Shewhart. In the early 20th century, as industrial processes became more complex, there was a growing need for methods to monitor and manage product quality efficiently. Walter A. Shewhart, an engineer at Bell Laboratories, is widely recognized as the "father of modern quality control" for his development of the control chart in the 1920s⁶. While run charts predate formal statistical process control charts in their simplest form as time series plots, Shewhart's work laid the foundation for understanding process variation and identifying "in-control" versus "out-of-control" states. The run chart serves as a more basic version of these sophisticated tools, allowing for simpler visual analysis of data over time without the need for complex statistical limits.

Key Takeaways

• A run chart is a time-series graph used to visualize data points in chronological order.
• It helps identify trends, shifts, and patterns in a process over time.
• A central line, typically representing the median of the data, is often included for reference.
• Run charts are simpler to create and interpret than more advanced statistical analysis tools like control charts.
• They are valuable for initial process improvement efforts and ongoing monitoring.

Interpreting the Run Chart

Interpreting a run chart involves looking for patterns that suggest non-random behavior in the underlying process. While run charts do not use statistical control limits to definitively declare a process "out of control," they can reveal important insights by examining the sequence of data points. Key patterns to observe include:

• Runs: A "run" is a sequence of consecutive data points that are all either above or below the median line. An unusually long run can indicate a sustained shift in the process. For instance, a sequence of seven or more consecutive points above or below the median suggests a non-random shift⁵.
• Trends: A trend is a continuous series of increasing or decreasing data points. A run chart can clearly show whether a metric is consistently improving, deteriorating, or remaining stable. A series of six or seven consecutive increases or decreases is typically considered a significant trend⁴.
• Cycles: Repeated patterns of highs and lows that occur at regular intervals may indicate a cyclical influence on the process, such as seasonal variation.
• Outliers: Isolated outlier points that fall significantly outside the general pattern can signal an unusual event or a special cause of variation, prompting further investigation.

By identifying these patterns, organizations can make more informed decision-making regarding process adjustments.

Hypothetical Example

Consider a financial analyst at a fund management firm who wants to monitor the daily tracking error of an exchange-traded fund (ETF) against its benchmark index over a month. The tracking error represents the daily difference between the ETF's return and the benchmark's return.

The analyst collects the daily tracking error data points for 20 trading days:

To create a run chart:

1. Plot the data: The horizontal axis represents the trading days (time), and the vertical axis represents the tracking error percentage. Each daily tracking error value is plotted as a data point.
2. Draw the median line: The median of this dataset (sorted: 0.01, 0.02, 0.03, 0.03, 0.04, 0.04, 0.05, 0.05, 0.06, 0.06, 0.07, 0.08, 0.09, 0.10, 0.11, 0.11, 0.12, 0.13, 0.14, 0.15) is (0.06 + 0.07) / 2 = 0.065%. A horizontal line is drawn at 0.065% across the chart.

Upon visual inspection of the run chart, the analyst would observe that after Day 10, the tracking error consistently stays above the median line and shows an upward trend. This sustained shift suggests that something may have changed in the ETF's management, the benchmark's composition, or market conditions, warranting further investigation beyond a simple visual analysis.

Practical Applications

Run charts are versatile tools applied across various sectors for monitoring and analysis, including finance. In financial modeling and investment analysis, run charts can track various performance metrics over time, such as daily stock price changes, portfolio value fluctuations, or trading volume. By plotting time series data, analysts can quickly identify unusual trends or significant shifts in financial instruments or market conditions³. For example, a run chart could be used to monitor:

• Investment Performance: Tracking the monthly returns of a fund or an individual stock to identify periods of sustained growth or decline.
• Operational Efficiency: A financial institution might use a run chart to monitor the number of customer service calls received per hour, the time taken to process loan applications, or the rate of data entry errors.
• Risk Monitoring: In risk management, run charts can track key risk indicators, such as the number of failed transactions, cybersecurity incidents, or compliance breaches over time.
• Public Health: Government agencies like the Centers for Disease Control and Prevention (CDC) utilize run charts to visualize public health data, such as infection rates or hospital readmissions, allowing for immediate recognition of critical changes and effectiveness of interventions².
• Project Management: Tracking the completion rates of tasks or budget burn rates in project management to ensure projects stay on track.

These applications demonstrate how run charts provide a straightforward method for continuous monitoring and early detection of changes that require attention.

Limitations and Criticisms

While useful for initial visual analysis, run charts have notable limitations compared to more advanced statistical analysis tools. A primary criticism is their inability to distinguish between common cause variation (natural, inherent fluctuations in a stable process) and special cause variation (unpredictable factors outside the normal process). Without statistically calculated control limits, a run chart cannot definitively determine if a process is "in control" or "out of control"¹. This can lead to misinterpretation, where a natural fluctuation might be seen as a significant trend or shift, prompting unnecessary interventions. Conversely, a true problem might be overlooked if it doesn't manifest as an obvious run or trend.

Furthermore, the interpretation of a run chart can be subjective. While rules exist for identifying runs and trends (e.g., seven consecutive points above/below the median, or six to seven consecutive increases/decreases), these are guidelines, and different observers might draw different conclusions. This subjectivity means that a run chart alone may not provide enough rigor for high-stakes decision-making or formal process improvement initiatives where a clear statistical signal is required. For more robust analysis and to quantify process stability, a control chart is generally preferred.

Run Chart vs. Control Chart

The run chart and the control chart are both graphical tools used to analyze time series data and monitor process performance, but they serve different analytical purposes. The primary distinction lies in their ability to differentiate between types of variation.

While a run chart is excellent for a quick visual overview and detecting general patterns, a control chart provides a more rigorous statistical assessment, enabling users to make evidence-based decision-making about whether a process is stable or requires intervention. The confusion often arises because both visualize data over time, but their analytical power differs significantly.

FAQs

Q1: What kind of data is best suited for a run chart?

A run chart is best suited for continuous time series data that can be plotted sequentially. This could include measurements like daily temperatures, hourly production rates, weekly sales figures, or monthly investment returns.

Q2: How do I identify a "shift" in a run chart?

A "shift" in a run chart is often indicated by a sustained sequence of data points that fall entirely above or below the median line. A common rule of thumb is a run of seven or more consecutive points on the same side of the median, which suggests a non-random change from the established baseline.

Q3: Can a run chart predict future performance?

A run chart can help identify historical trends and patterns, which might offer insights into potential future behavior if the underlying process remains unchanged. However, it does not provide statistical predictions or guarantees about future performance metrics. For more robust forecasting or to establish statistical predictability, more advanced analytical methods are needed.