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Control Limits Formula:
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Control limits, specifically Lower Control Limit (LCL) and Upper Control Limit (UCL), are statistical boundaries used in quality control and process monitoring. They define the range of variation expected from a stable process.
The calculator uses the standard control limit formulas:
Where:
Explanation: These 3-sigma limits indicate that 99.73% of data points from a normally distributed process will fall within these boundaries if the process is in control.
Details: Control limits help distinguish between common cause variation (inherent to the process) and special cause variation (due to external factors). They are essential for statistical process control and quality improvement initiatives.
Tips: Enter the process mean and standard deviation. The calculator will compute the 3-sigma control limits. Standard deviation must be a non-negative value.
Q1: Why use 3-sigma limits instead of 2-sigma?
A: 3-sigma limits provide 99.73% confidence level, reducing false alarms while still detecting significant process shifts effectively.
Q2: When should control limits be recalculated?
A: Control limits should be recalculated when process improvements are made or when the process fundamentally changes.
Q3: What if data points fall outside control limits?
A: Points outside control limits indicate special cause variation that requires investigation and corrective action.
Q4: Are control limits the same as specification limits?
A: No, control limits are statistical boundaries based on process data, while specification limits are customer requirements or engineering tolerances.
Q5: Can these formulas be used for non-normal distributions?
A: The 3-sigma rule assumes normal distribution. For non-normal data, other methods like transformation or non-parametric approaches may be needed.