Upper Control Limit Calculator

What Control Limits Mean

Control limits mark expected variation in a stable process. Points outside the upper control limit (UCL) or lower control limit (LCL) suggest special-cause variation rather than normal random noise. Related tools: Process Capability Index Calculator and Standard Deviation Calculator.

UCL and LCL Formulas

$$UCL = \mu + L \times \sigma$$

$$LCL = \mu - L \times \sigma$$

Here $\mu$ is the process mean, $\sigma$ is the process standard deviation, and $L$ is the sigma multiplier. Three-sigma limits ($L = 3$) are the most common choice in statistical process control.

Example

If a process mean is 40 minutes and the standard deviation is 2 minutes with $L = 3$, then $UCL = 46$ and $LCL = 34$. Observations above 46 or below 34 may warrant investigation.