What Are Control Charts?

Control charts are graphical tools used to monitor process behavior over time, distinguish between variation caused by random chance and variation caused by identifiable sources, and signal when a process requires investigation or correction. Developed by Walter A. Shewhart at Bell Telephone Laboratories in the 1920s, control charts became the foundation of statistical process control (SPC) and remain among the most widely used instruments in quality management. The chart plots a process measurement or statistic on the vertical axis against time or sample number on the horizontal axis, with three horizontal reference lines: the center line representing the process average, the upper control limit (UCL) set at three standard deviations above the mean, and the lower control limit (LCL) set at three standard deviations below. The NIST/SEMATECH e-Handbook of Statistical Methods defines a control chart as a time-series plot used to determine whether the process is in a state of statistical control by observing whether points fall within the control limits.

Shewhart's key insight was that all processes exhibit variation, but that variation falls into two distinct categories: common-cause variation, which is inherent and stable, and special-cause variation, which arises from identifiable factors that can be corrected. A process operating with only common-cause variation is described as in control; the appearance of a point outside the control limits or a non-random pattern of points within them signals the presence of a special cause.

Types of Control Charts

Control charts are selected based on the type of data being measured. Variable control charts track continuous measurements: the X-bar and R chart monitors sample mean and range simultaneously and is appropriate when subgroups of two to ten measurements can be collected; the X-bar and S chart substitutes sample standard deviation for range when subgroup size exceeds ten. The individuals and moving range (I-MR) chart applies when only one measurement per time period is available, which is common in chemical batch and continuous processes. Attribute control charts handle count data: the p-chart tracks the proportion of nonconforming units per sample; the c-chart counts defects per unit when sample size is constant; and the u-chart extends the c-chart to variable sample sizes. Selecting the wrong chart type for the data structure produces misleading control limits and unreliable signals.

Statistical Basis and Variation

The three-sigma control limits are derived from the empirical rule and the properties of the normal distribution. Under the assumption of normality, approximately 99.73% of observations from a stable process fall within three standard deviations of the mean, so a point beyond the control limits occurs by chance less than 0.27% of the time. Western Electric rules, developed at Bell Labs in the 1950s, supplement the three-sigma test with pattern-based tests: eight consecutive points on one side of the center line, two of three consecutive points beyond two-sigma limits, and other non-random sequences all signal potential process shifts before a point breaches the three-sigma boundary. The JMP statistical knowledge portal provides a thorough treatment of control chart pattern interpretation and run rules covering both variable and attribute chart applications.

Integration with Quality Management

Control charts are one of the seven basic tools of quality identified in total quality management (TQM) frameworks and are central to Six Sigma methodology at the Control phase of the DMAIC cycle. They interact with other quality instruments: a Pareto chart identifies which special causes to prioritize, a fishbone diagram explores root causes, and a capability index quantifies how well the in-control process meets specification limits. The American Society for Quality's control chart resource describes the chart as a tool for making real-time decisions about whether to adjust a process or leave it alone.

Applications

Control charts have applications in a wide range of fields, including:

• Manufacturing, monitoring dimensional measurements, fill weights, and assembly defect rates
• Healthcare quality improvement, tracking infection rates, medication errors, and patient wait times
• Software development, measuring defect density and code review cycle times in software quality programs
• Food and beverage production, controlling critical parameters such as pH, moisture, and temperature
• Service industries, including call center response times and transaction error rates