Table of Contents
Control limits are statistical boundaries used in quality control processes to monitor whether a process is in a state of control. They are calculated based on data from the process and help identify variations that may require attention.
Basics of Control Limits
Control limits are typically set at three standard deviations above and below the process mean. These limits define the expected range of variation due to common causes in a stable process.
Statistical Foundations
The calculation of control limits relies on the statistical properties of the process data. The process mean (μ) and standard deviation (σ) are fundamental components. The upper control limit (UCL) and lower control limit (LCL) are computed as:
UCL = μ + 3σ
LCL = μ – 3σ
Calculating Control Limits
To determine control limits, data from the process are collected over time. The process mean is calculated from the sample data, and the standard deviation is estimated. For subgroup data, the average of subgroup means and the average subgroup standard deviation are used.
For example, if the average process measurement is 50 units and the standard deviation is 2 units, the control limits are:
UCL = 50 + (3 × 2) = 56
LCL = 50 – (3 × 2) = 44
Application of Control Limits
Control limits are used in control charts to monitor process stability. Points outside the limits indicate potential issues, prompting investigation and corrective actions. Consistent points within the limits suggest the process is in control.