Control charts are tools for watching a process over time and deciding whether its variation is stable or unusual. They are widely used in manufacturing, laboratories, healthcare, software systems, and any setting where repeated measurements matter. A control chart separates normal random fluctuation from signals that the process may have changed.
This helps people act based on evidence instead of reacting to every small up and down.
Key Facts
- Center line: CL = process average, often x-bar for measurement data.
- Upper control limit: UCL = CL + 3σ for a basic individuals chart when σ is known.
- Lower control limit: LCL = CL - 3σ for a basic individuals chart when σ is known.
- A point outside the control limits is a strong signal of special-cause variation.
- Common-cause variation is the natural background variation of a stable process.
- A run of many points on one side of the center line can indicate drift or a process shift.
Vocabulary
- Control chart
- A graph of process measurements over time with a center line and control limits used to monitor stability.
- Center line
- The horizontal reference line that represents the average or expected value of a stable process.
- Control limits
- Statistical boundaries on a control chart that show the range expected from common-cause variation.
- Common-cause variation
- The routine random variation that is naturally present when a process is stable.
- Special-cause variation
- Variation caused by a specific change, error, disturbance, or new condition affecting the process.
Common Mistakes to Avoid
- Treating control limits as specification limits is wrong because control limits describe process stability, while specification limits describe customer or design requirements.
- Reacting to every point above or below the center line is wrong because normal common-cause variation makes points fluctuate around the average.
- Ignoring a pattern that stays within the limits is wrong because runs, trends, or drift can signal a process change before any point crosses a limit.
- Recalculating limits after every unusual point is wrong because it can hide special causes and make the chart less useful for detecting real changes.
Practice Questions
- 1 A process has CL = 50 and σ = 2. Calculate the UCL and LCL using UCL = CL + 3σ and LCL = CL - 3σ.
- 2 Ten measurements are 20, 21, 19, 20, 22, 21, 20, 23, 21, 20. Find the center line using the sample mean.
- 3 A chart shows eight points in a row above the center line, but all are inside the control limits. Explain why this may still be a warning signal.