X-bar & R Chart
For continuous data with subgroup sizes of 2-10. X-bar chart monitors process mean, R chart monitors process variability.
Statistical Process Control Charts
Control charts are statistical tools used to determine if a manufacturing or business process is in a state of control. They help identify special causes of variation and monitor process stability over time.
Control Limits = Center Line ± (Control Limit Factor × Process Variability)
Key concepts:
- Upper Control Limit (UCL): The highest value a process should produce when in control
- Lower Control Limit (LCL): The lowest value a process should produce when in control
- Center Line (CL): The average or median of the process data
- Special Cause Variation: Indicated by points outside control limits or non-random patterns
Select Control Chart Type
Choose the appropriate control chart for your data type:
X-bar & R Chart
X-bar & S Chart
P Chart
NP Chart
C Chart
U Chart
X-bar & S Chart
For continuous data with subgroup sizes >10. X-bar chart monitors process mean, S chart monitors process standard deviation.
P Chart
For proportion defective when subgroup sizes vary. Tracks the proportion of nonconforming items.
NP Chart
For number defective when subgroup sizes are constant. Tracks the number of nonconforming items.
C Chart
For count of defects when subgroup sizes are constant. Tracks the number of defects per unit.
U Chart
For defects per unit when subgroup sizes vary. Tracks the average number of defects per unit.
Control Chart Results
Chart will appear here after calculation
Control Limits
| Parameter | Center Line (CL) | Upper Control Limit (UCL) | Lower Control Limit (LCL) |
|---|
Data Points
Practical Examples
Example 1: X-bar & R Chart
Subgroup data: 10.2, 10.5, 10.3; 10.1, 10.4, 10.2; 10.3, 10.6, 10.4; 10.2, 10.3, 10.5
Subgroup size: 3 | Target: 10.3
X-bar CL: 10.35 | UCL: 10.56 | LCL: 10.14
R CL: 0.3 | UCL: 0.78 | LCL: 0
Example 2: P Chart
Defectives: 3, 5, 2, 4, 6, 3, 5, 2
Sample sizes: 50, 50, 50, 50, 50, 50, 50, 50
CL: 0.075 | UCL: 0.168 | LCL: 0
Example 3: C Chart
Defects: 5, 7, 3, 6, 4, 5, 8, 6
CL: 5.5 | UCL: 11.5 | LCL: 0
Control Chart Selection Guide
| Data Type | Subgroup Size | Appropriate Chart |
|---|---|---|
| Continuous (measurement) | 2-10 | X-bar & R |
| Continuous (measurement) | >10 | X-bar & S |
| Attribute (proportion defective) | Varies | P chart |
| Attribute (number defective) | Constant | NP chart |
| Attribute (count of defects) | Constant | C chart |
| Attribute (defects per unit) | Varies | U chart |