Control chart

Xbar_chart_for_a_paired_xbar_and_R_chart

A control chart is a statistical tool used in quality control to monitor and control a process. It helps in determining whether a manufacturing or business process is in a state of statistical control. Control charts are also known as Shewhart charts or process-behavior charts.

History

The control chart was developed by Walter A. Shewhart while working at Bell Telephone Laboratories in the 1920s. Shewhart's work laid the foundation for the field of statistical process control (SPC).

Components

A control chart typically consists of the following components:

• **Center Line (CL)**: Represents the average or mean of the data.
• **Upper Control Limit (UCL)**: The upper threshold, usually set at three standard deviations above the mean.
• **Lower Control Limit (LCL)**: The lower threshold, usually set at three standard deviations below the mean.
• **Data Points**: Individual measurements or averages plotted over time.

Types of Control Charts

There are several types of control charts, each suited for different types of data:

• **X-bar and R Chart**: Used for monitoring the mean and range of a process.
• **X-bar and S Chart**: Used for monitoring the mean and standard deviation of a process.
• **P Chart**: Used for monitoring the proportion of defective items in a process.
• **NP Chart**: Used for monitoring the number of defective items in a process.
• **C Chart**: Used for monitoring the count of defects per unit.
• **U Chart**: Used for monitoring the count of defects per unit, where the sample size varies.

Applications

Control charts are widely used in various industries, including manufacturing, healthcare, and service industries. They help in:

• Identifying process variability
• Detecting trends or shifts in the process
• Improving process stability and capability
• Reducing waste and defects

Interpretation

Interpreting a control chart involves looking for patterns or signals that indicate a process is out of control. Common signals include:

• Points outside the control limits
• A run of seven or more points on one side of the center line
• A trend of seven or more points increasing or decreasing
• Cycles or other non-random patterns

Related Pages

• Statistical process control
• Quality control
• Six Sigma
• Lean manufacturing
• Total quality management

See Also

• Process capability index
• Histogram
• Pareto chart
• Fishbone diagram