Shewhart (SQC) control lines
Overview
Shewhart Statistical Quality Control (SQC) uses control charts to determine whether a process is operating in a state of statistical control. Developed by Walter A. Shewhart, the method distinguishes between:
- Common-cause variation (natural process variation)
- Special-cause variation (unexpected process changes)
A Shewhart control chart plots observations over time against statistically derived control limits, helping identify when a process may require investigation.
In Cloud QC, the centre line is the CRM’s certified value and σ its certified standard deviation when “Use CRM provided statistics” is ticked; otherwise they are the mean and standard deviation of the results on the chart. The chart also shows the median of the results.
On the Precision charts, the same SD-based (SQC) control lines are drawn on the RD values of the duplicate pairs: the mean RD ± 2 and ± 3 standard deviations, for each check stage.
When to use
Shewhart control charts are commonly used for laboratory quality control and assay performance monitoring. They are particularly effective for detecting moderate to large shifts in process performance.
Control chart formula
Centre line: CL = x̄ Upper control limit: UCL = x̄ + 3σ Lower control limit: LCL = x̄ − 3σ
| Symbol | Description |
|---|---|
| xi | Individual observation |
| x̄ | Process mean (centre line) |
| σ | Process standard deviation |
The ±3σ limits represent the expected range for approximately 99.73% of observations when the process is stable and normally distributed.
Cloud QC also draws warning limits at ±2σ (light orange) as well as the action limits at ±3σ (deep red). The chart is shaded green within ±2σ, amber between 2σ and 3σ and red beyond 3σ, and each result is coloured by its zone. About 95% of results from a stable process fall within ±2σ, so an occasional result in the amber zone is expected; a result beyond ±3σ is an outlier.
Signal rules
A process may be considered out of control when:
- Rule 1: a single observation falls beyond either control limit, xi > UCL or xi < LCL.
- Rule 2 (optional): additional run rules such as the Nelson 8 rules may also be applied to increase sensitivity. In Cloud QC, tick “Run Nelson 8 rules”.
Control zones
Many Shewhart control charts divide the area around the mean into zones, which are commonly used with Nelson and Western Electric rule analyses:
| Zone | Range |
|---|---|
| Zone C | Within ±1σ |
| Zone B | Between 1σ and 2σ |
| Zone A | Between 2σ and 3σ |
| Out of control | Beyond ±3σ |
Worked example
Process mean x̄ = 100 and standard deviation σ = 2, so:
UCL = 100 + (3 × 2) = 106 LCL = 100 − (3 × 2) = 94
| Obs | Value | Deviation from mean | Status |
|---|---|---|---|
| 1 | 99.8 | −0.2 | In control |
| 2 | 100.5 | 0.5 | In control |
| 3 | 101.2 | 1.2 | In control |
| 4 | 98.7 | −1.3 | In control |
| 5 | 100.9 | 0.9 | In control |
| 6 | 101.5 | 1.5 | In control |
| 7 | 99.2 | −0.8 | In control |
| 8 | 97.8 | −2.2 | In control |
| 9 | 103.4 | 3.4 | In control |
| 10 | 107.1 | 7.1 | Out of control |
For Observation 10, x = 107.1 > UCL = 106, so it exceeds the upper control limit and triggers an out-of-control signal. With Cloud QC’s warning limits at 96 and 104, Observations 1–9 are all in the green zone, and Observation 10 is beyond the action limit and shown in red.
Interpretation
- Observations 1–9 fall within the expected range of process variation.
- Observation 10 exceeds the upper control limit. Such an occurrence is statistically unlikely under normal process conditions.
- The process should be investigated to determine whether a special cause has affected performance. Potential causes may include equipment issues, operator changes, environmental effects, sampling errors, or process drift.
Advantages and limitations
| Advantage | Description |
|---|---|
| Simple to understand | Easy to calculate and interpret |
| Industry standard | Widely used in SPC programmes |
| Detects major shifts | Effective for identifying large process changes |
| Visual monitoring | Clear graphical representation of performance |
| Foundation for advanced methods | Supports Nelson Rules, Western Electric Rules, CUSUM and EWMA analyses |
| Limitation | Description |
|---|---|
| Less sensitive to small shifts | Small mean changes may not trigger a signal |
| Uses only current observation | Does not accumulate historical information |
| Assumes stable process estimates | Mean and standard deviation should be representative |
| Can miss gradual drift | Slow changes can remain undetected |
Summary
Shewhart Statistical Quality Control (SQC) charts provide a simple and effective method for monitoring process stability by comparing observations against statistically derived control limits. A process is considered in control when observations remain within the expected range of variation and exhibit no unusual patterns. Observations outside the control limits indicate potential special-cause variation and should be investigated. Shewhart control charts form the foundation of modern statistical process control and are frequently used alongside Nelson Rules, CUSUM, EWMA, Z-Score, and MAD analyses to provide comprehensive process monitoring.