- Please enter at least 3 numeric observations.
| # | Observation |
|---|---|
| 1 | 10.02 |
| 2 | 9.98 |
| 3 | 10.01 |
| 4 | 10.03 |
| 5 | 9.99 |
| 6 | 10.04 |
| 7 | 10.00 |
| 8 | 10.02 |
| 9 | 10.01 |
| 10 | 9.97 |
| 11 | 10.20 |
| 12 | 10.18 |
| 13 | 10.21 |
| 14 | 10.19 |
| 15 | 10.22 |
| 16 | 10.17 |
| 17 | 10.20 |
| 18 | 10.18 |
| 19 | 10.21 |
| 20 | 10.19 |
| 21 | 10.55 |
| 22 | 10.23 |
| 23 | 10.20 |
| 24 | 10.22 |
| 25 | 10.21 |
- Centerline (CL): mean of baseline points, or your override value.
- Sigma estimate (σ):
- Sample SD: σ = sqrt( Σ(xᵢ−x̄)² / (n−1) ).
- Moving range: σ ≈ MR̄ / d₂ with d₂ = 1.128.
- Known sigma: σ provided directly.
- Control limits: UCL = CL + kσ, LCL = CL − kσ.
- Zones: ±1σ and ±2σ bands around the centerline.
- Paste a time-ordered sequence of measurements.
- Select a sigma method and optional baseline size.
- Keep k at 3 unless you have a standard.
- Enable the rules your quality system requires.
- Run the test and review triggered rules and points.
- Download CSV or PDF to share with stakeholders.
Why out-of-control tests matter
Out-of-control tests separate routine variation from special-cause signals. When a process drifts, shifts, or spikes, reacting quickly prevents scrap, rework, and complaints. This calculator evaluates sequential measurements using control limits and pattern rules so teams respond consistently. It suits continuous variables like cycle time, weight, thickness, or temperature, and supports baseline studies plus ongoing monitoring in production or service operations.
Control limits and centerline selection
The centerline represents expected performance, typically the baseline mean. You can override it with a target when engineering requirements matter. Control limits are computed as CL ± kσ, where k is commonly 3. Wider limits reduce false alarms, while tighter limits increase sensitivity. Because limits depend on baseline stability, choose a window that reflects normal operation.
Sigma estimation options for real data
Variation can be estimated three ways. Sample standard deviation works when baseline points are independent and plentiful. Moving range estimation suits individual measurements, using the average absolute difference between consecutive points divided by d2 = 1.128. Known sigma fits when studies or control plans already define σ. Matching the method to your sampling scheme improves comparability over time.
Rule-based signals beyond a single point
Many issues do not cross limits immediately. Run and trend rules detect sustained shifts and gradual drift before defects appear. Zone rules, such as two of three points beyond two-sigma, capture clustering near normal boundaries. Alternating patterns can suggest over-adjustment, while tight clustering may indicate stratified sampling or limited resolution. The report lists each triggered rule and the involved observations for root-cause analysis.
Operationalizing results and reporting
Use the point table to link signals to events like material lots, tool changes, or staffing shifts. When new tooling, suppliers, or settings change, annotate the timestamped data so investigations connect signals to actions quickly with confidence. If the process is out of control, fix the cause first, then recompute limits using a stable baseline. Export CSV for audit trails and dashboards, or share PDF during corrective-action reviews. Consistent rule use improves decision speed, reduces unnecessary adjustments, and supports continual improvement. Pair signals with containment actions and document decisions to strengthen training and prevent recurrence across future shifts.
What is an out-of-control signal?
An out-of-control signal means the pattern of measurements is unlikely under normal random variation. It suggests a special cause such as a change in material, equipment, method, environment, or measurement system that deserves investigation and corrective action.
How many observations should I enter?
Use at least 20 points when possible. Short series can still be analyzed, but limits and rule detection become less reliable. If you are establishing limits, start with a stable baseline period that reflects typical operating conditions.
Which sigma method should I choose?
Use moving range for individual measurements collected sequentially. Use sample standard deviation when baseline points are independent and plentiful. Use known sigma when your control plan already defines process variation from prior studies or validated historical data.
Why do results show multiple rules for one point?
A single observation can participate in different patterns, such as a trend and a zone cluster. The calculator flags every applicable rule so you can see whether the signal is isolated, sustained, or part of a broader shift.
What should I do after an out-of-control decision?
Do not recalculate limits immediately. First, identify and remove the special cause, then confirm stability. After the process is stable, rebuild limits using the corrected baseline so future signals remain meaningful and comparable.
What is included in the CSV and PDF exports?
Exports include settings, centerline, sigma, limits, triggered rules, and a point-by-point table with flags. CSV is suited for spreadsheets and dashboards. PDF is designed for sharing in reviews, audits, and corrective-action meetings.
Note: Interpret signals alongside context, measurement system evidence, and documented operating changes.