Control chart (SPC) — individuals I-MR
Paste your measurements in time order. See the mean, moving range, control limits and the rule violations that show the process going out of control, on the chart and in a list.
One value per measurement; separator space, new line, tab or ; (a column from Excel can be pasted). Use a point or a comma for decimals. Values must be in time order; if the order is scrambled the limits lose their meaning. At least 20–25 values are recommended for the limits.
The calculation runs in your browser; the measurements you paste are not sent anywhere.
30 values read.
- Mean X̄ (centre line)
- 10.028
- Upper control limit (UCL)
- 10.111
- Lower control limit (LCL)
- 9.9442
- Average moving range MR̄
- 0.031379
- Estimated sigma σ̂ = MR̄ / 1.128
- 0.027823
- MR chart UCL (3.267 × MR̄)
- 0.10252
- Number of values
- 30
- Flagged points
- 2
Individuals (I) chart
The ±1σ and ±2σ zone lines are drawn faintly.
Moving range (MR) chart
Rule violation
Rule check (Nelson rules)
A violation is marked at the point where the rule is completed. Point numbers follow the order of the measurements (starting at 1).
| 1 · One point more than 3σ from the centre (beyond a control limit) | points: 29, 30 |
|---|---|
| 2 · 9 points in a row on the same side of the centre line | points: 30 |
| 3 · 6 points in a row steadily increasing or decreasing | — |
| 4 · 14 points in a row alternating up and down | — |
| 5 · 2 of 3 points in a row beyond 2σ on the same side | points: 30 |
| 6 · 4 of 5 points in a row beyond 1σ on the same side | points: 30 |
| 7 · 15 points in a row within ±1σ (less variation than expected) | — |
| 8 · 8 points in a row beyond ±1σ (on either side) | — |
The limits are computed from all points. Points with special causes widen the limits; once the root cause is found and removed, those points are excluded and the limits recalculated.
X̄ ± 2.66 · MR̄ (2.66 = 3/d₂, d₂ = 1.128) · MR chart: UCL = 3.267 · MR̄, LCL = 0 · σ̂ = MR̄ / 1.128
A control chart shows whether a process is statistically stable, not whether it meets the specification (that is capability: Cp/Cpk). The rules are warning signals; not every violation is a real cause, and false alarms increase when rules are combined. This tool gives a first assessment.
Let's look at which deviations in your process data could be spotted early.
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How to use it
A
Paste your measurements in time order (copying one column from Excel is enough) or load the example data.
B
Study the centre line, the control limits and the MR chart.
C
Look at the points flagged in the rule check table: look for a real cause, then recalculate the limits.
02
The I-MR chart and control limits
The individuals (I-MR) chart is used when measurements are taken one at a time and forming subgroups makes no sense: an hourly reading from one machine, a daily tank analysis, the time trace of a vibration level. The centre line is the mean. Short-term variation is estimated by the moving range (MR), the absolute difference between two consecutive measurements.
Control limits are computed as mean ± 2.66 × MR̄; 2.66 is 3 / d₂ (d₂ = 1.128 for a moving range of two). That is roughly ±3σ̂ around the mean. The limits are not specification limits: control limits show what the process does, specification limits show what the customer wants.
03
Nelson and Western Electric rules
A single point beyond the limits is not the only signal; a process can change while staying within the limits. That is why zone-based rules are used. The tool checks the eight Nelson rules: a point beyond the limits (1), a long run on one side of the centre (2), a steady rise or fall (3), alternating up and down (4), the 2σ and 1σ zone rules (5, 6), too little variation (7) and staying beyond 1σ on both sides (8). The Western Electric rules are the forms of rules 1, 5, 6 and 2.
Every rule adds a chance of false alarm. Adding rules increases sensitivity but also unnecessary investigation. Which rules to use should be agreed beforehand with the process and its cost in mind.
04
Reading the limits and common mistakes
The data must be in time order; sorted or shuffled data produces meaningless limits. If individual measurements are not normally distributed (for example skewed), the false alarm rate of 3σ limits can change; a transformation or another method is then needed. If the data has strong dependence between consecutive values (autocorrelation), the moving range understates the variation and the limits come out too narrow.
A control chart answers "is the process stable?". The question "does the process meet the specification?" needs a capability calculation; the Cp/Cpk of an unstable process is not meaningful.
FAQ
- When is an I-MR chart used?
- When measurements are taken one at a time and no sensible subgroup can be formed: infrequent measurements, one measurement per batch, single readings over time in continuous processes. With subgroups, X̄-R or X̄-S charts are preferred.
- Why are control limits computed with 2.66?
- The limits are meant to be X̄ ± 3σ̂, and σ̂ is estimated as MR̄ / 1.128. Since 3 / 1.128 ≈ 2.66, the limits become X̄ ± 2.66 × MR̄.
- Are control limits and specification limits the same?
- No. Control limits are calculated from process data and show the natural variation of the process. Specification limits are set by the customer or the design. Comparing the two is the subject of capability analysis (Cp/Cpk).
- How many measurements are needed?
- At least 20–25 measurements are recommended to compute the limits with confidence. With less data the tool still gives a result, but the limits are uncertain and a warning is shown.
- A rule was violated, what should I do?
- Investigate what happened leading up to the flagged point: material batch, shift, tool change, adjustment. If a real cause is found, remove it and recalculate the limits without those points. If none is found, record it as a false alarm; not every violation is a real deviation.
Catch process deviations early
Let's look at which deviations in your machine and process data could be seen in advance, and what that means for quality and downtime.