What Is a Control Chart?
A control chart is a statistical tool used in statistical process control to monitor and control a process over time. It helps to determine if a process is stable and predictable, or if it is exhibiting variation that indicates a problem requiring attention. By graphically displaying process data points relative to a central line and upper and lower control limits, control charts distinguish between common cause variation (inherent to the process) and special cause variation (due to external, identifiable factors). This distinction is critical for effective quality control and continuous process improvement.
History and Origin
The control chart was invented by Walter A. Shewhart while he was working at Bell Telephone Laboratories in the 1920s. Bell Labs engineers sought to enhance the reliability of their telephony transmission systems, particularly for equipment buried underground, which necessitated a reduction in failure rates and repairs. Shewhart recognized that continuous adjustments made in reaction to non-conformance often increased variation rather than improving quality.
On May 16, 1924, Shewhart created the first documented control chart as part of an internal memo, introducing it as a tool to differentiate between common and special causes of variation6,5. His work laid the fundamental groundwork for modern statistical process control by proposing a method to monitor processes using statistical principles. Shewhart's ideas were later formalized in his 1931 book, Economic Control of Quality of Manufactured Product, and further popularized by W. Edwards Deming, especially in Japan after World War II4. The centennial of Shewhart's invention was celebrated in May 2024, underscoring its enduring significance in quality management.3
Key Takeaways
- A control chart visually distinguishes between natural process variation (common causes) and unexpected variation (special causes).
- It consists of a central line, upper control limit (UCL), and lower control limit (LCL), all derived from historical process data.
- Points falling outside the control limits signal the presence of special cause variation, indicating a process is "out of control."
- Control charts are fundamental tools in statistical process control and various quality management methodologies.
- Their primary purpose is to monitor process stability and identify opportunities for process improvement.
Formula and Calculation
The fundamental components of a control chart are the central line (CL), upper control limit (UCL), and lower control limit (LCL). The specific formulas vary depending on the type of control chart (e.g., X-bar and R charts for variable data, P charts for attribute data). However, the general structure involves:
Central Line (CL): Represents the average or mean of the process characteristic being monitored.
Where (\bar{\bar{X}}) is the grand average of sample means.
Control Limits (UCL, LCL): Typically set at three standard deviations from the central line. This "three-sigma" approach is based on the empirical rule for normal distributions, where approximately 99.73% of data points are expected to fall within these limits if the process is stable.
Where:
- (A_2) is a constant factor that depends on the subgroup size, used to calculate the control limits for the mean.
- (\bar{R}) is the average range of the subgroups.
These formulas are for an X-bar chart, which monitors the average of a process. Other charts, like R charts (for range), P charts (for proportion of defectives), or C charts (for number of defects), utilize different constants and calculations adapted to their specific data types. The goal is to establish boundaries that indicate the expected range of variation when a process is operating under stable conditions.
Interpreting the Control Chart
Interpreting a control chart involves observing the pattern of data points relative to the central line and control limits. A process is considered "in statistical control" when all data points fall within the upper and lower control limits and show no discernible patterns, shifts, or trends. This indicates that only common cause variation is present, and the process is stable and predictable.
Conversely, a process is considered "out of control" if any points fall outside the control limits or if specific non-random patterns are observed within the limits. These patterns, such as consecutive points above or below the central line, trends upwards or downwards, or cycles, suggest the presence of "special causes" of variation. Identifying and addressing these special causes is crucial for process improvement and achieving consistent performance measurement. Ignoring a process that is out of control can lead to unpredictable outcomes and inefficiencies.
Hypothetical Example
Consider a financial services firm that aims to process customer loan applications within a certain timeframe. To monitor their efficiency, the firm decides to use an X-bar control chart, tracking the average processing time (in days) for batches of 10 loan applications submitted daily over several weeks.
For the initial period, they collect data for 20 batches. The average processing time across all 20 batches is 7 days. This becomes their central line. They calculate their upper control limit (UCL) to be 9 days and their lower control limit (LCL) to be 5 days, based on the historical variation and a standard A2 factor for their sample size.
Each day, they plot the average processing time for the latest batch of 10 applications.
- Day 1-5: Averages are 6.8, 7.2, 7.0, 6.9, 7.1 days. All within limits and around the central line.
- Day 6: Average shoots up to 9.5 days. This point falls above the UCL.
Upon seeing the 9.5-day average, the firm immediately investigates. They discover that a key loan officer was on unexpected leave, causing a backlog and slowing down processing for that day's batch. This is identified as a special cause. By addressing the staffing issue (e.g., reassigning tasks or bringing in temporary support), they bring the process back into control. Without the control chart, the increase might have been dismissed as normal daily fluctuations until it became a chronic problem impacting customer satisfaction.
Practical Applications
Control charts are widely used across various sectors to monitor and improve the stability and predictability of processes. While originating in manufacturing, their application extends significantly into financial services, risk management, and other business operations.
In financial institutions, control charts can be employed to monitor the consistency of data entry, the accuracy of transaction processing, or the adherence to regulatory compliance procedures. For instance, a bank might use a control chart to track the number of errors in daily wire transfers or the time taken to approve credit applications. They can also be applied to monitor trading system performance, identifying unusual latency or error rates that could signal underlying issues.
Beyond specific processes, these charts aid in performance measurement and forecasting by providing insights into process stability. If a process is stable (in control), its future performance can be predicted within the control limits. The National Institute of Standards and Technology (NIST) Engineering Statistics Handbook details the practical uses of control charts in various industries for assuring quality and improving processes. Similarly, organizations like the American Society for Quality (ASQ) provide extensive resources on how control charts are applied to drive operational excellence and enhance decision making across diverse business functions.2
Limitations and Criticisms
While powerful, control charts have limitations and are subject to criticisms if misused. A primary limitation is that they assume the data being plotted are statistically independent and identically distributed, which is not always true for all types of financial data, especially time-series data with autocorrelation. Applying standard control chart rules to such data without adjustments can lead to misinterpretations, generating false signals (Type I errors) or missing real problems (Type II errors).
Another criticism is that control charts are backward-looking; they detect when a process has gone out of control, rather than predicting when it will go out of control. Effective use requires timely intervention based on the signals observed. Furthermore, simply identifying a process as "out of control" does not automatically provide the solution; it merely indicates that an investigation into the special cause is necessary. The selection of the correct control chart for a given process and data type is also critical, as using an inappropriate chart can lead to misleading conclusions.
Over-reliance on automated charting software without a deep understanding of the underlying statistical principles can also lead to poor decision making. Walter Shewhart's original insight was that control charts are not just mathematical tools, but rather instruments for learning and continuous process improvement through disciplined observation and action, distinguishing between inherent process variation and specific disturbances1.
Control Chart vs. Process Capability
A control chart and process capability are distinct but related concepts in quality and process management. A control chart is a time-series graph used to monitor a process's stability over time, indicating whether it is in a state of statistical control (i.e., operating predictably within its natural variation). It helps to identify special causes of variation that make a process unstable.
Process capability, on the other hand, assesses whether a stable process is capable of meeting predefined specification limits or customer requirements. It quantifies how well the process output fits within these desired limits, often expressed through metrics like Cp and Cpk. While a control chart tells you if a process is consistent, process capability tells you if that consistent process is actually good enough. A process can be in control but not capable (consistently producing output that doesn't meet specifications), or it can be capable but out of control (meeting specifications on average, but with unpredictable swings). They complement each other, with control charts typically used first to establish stability before assessing capability.
FAQs
What is the main purpose of a control chart?
The main purpose of a control chart is to monitor a process over time to determine if it is stable and predictable or if it is being affected by unusual factors that need investigation. It helps distinguish between normal, inherent variation and abnormal, assignable causes.
What are the key components of a control chart?
A typical control chart has three main components: a central line (CL) representing the average or target value of the process, an upper control limit (UCL), and a lower control limit (LCL). These limits define the expected range of variation when the process is in statistical control.
How do you know if a process is out of control on a chart?
A process is considered "out of control" if any data point falls outside the upper or lower control limits. Additionally, specific non-random patterns within the limits, such as a run of several consecutive points above or below the central line, or a clear trend, can also indicate an out-of-control condition requiring investigation and corrective action.
Can control charts be used in finance?
Yes, control charts are applicable in finance, though less commonly than in manufacturing. They can be used to monitor the stability of financial processes like transaction error rates, data entry accuracy, or the consistency of processing times for financial applications. They help identify deviations from expected performance and pinpoint areas for process improvement.