controlchart

A control chart is a statistical tool used in statistical process control to monitor a process over time and determine whether the process is in a state of statistical control. It plots a measured variable in time order and is centered on a process mean, with upper and lower control limits that define the expected range of natural variation. Data points outside these limits or patterns within the limits may indicate special causes or a change in the process.

There are several common chart types. X-bar and R charts monitor the mean and range of subgroups for variable data; X-bar and S charts use the standard deviation instead of the range. Individuals and moving range (I-MR) charts track single measurements and their moving differences. For attributes, p-charts and np-charts monitor defectives in samples, while c-charts and u-charts track counts of defects.

Construction involves collecting baseline data to estimate the center line (mean) and control limits, typically set at the center line plus or minus three standard deviations. Points are plotted in time order, and common rules—such as points outside the control limits or nonrandom patterns—are used to identify signals of assignable causes and potential process changes.

Interpretation focuses on distinguishing common cause variation, which is inherent to the process, from special cause variation requiring investigation or corrective action. Applications span manufacturing, healthcare, service operations, and software processes. Limitations include assumptions of process stability, independence, and normal distribution for certain charts; misinterpretation of signals or lag between changes and detection can reduce effectiveness. The control chart concept was developed by Walter A. Shewhart in the 1920s and later popularized in quality practice.