Paste your subgroup data and instantly get Shewhart control charts. For variables data the tool builds X̄ and R charts using the standard A2, D3 and D4 constants for your subgroup size; for attribute data it builds a p-chart. Center lines, ±3σ control limits and out-of-control points are computed live in your browser.
| n | A2 | D3 | D4 | d2 |
|---|---|---|---|---|
| 2 | 1.880 | 0.000 | 3.267 | 1.128 |
| 3 | 1.023 | 0.000 | 2.574 | 1.693 |
| 4 | 0.729 | 0.000 | 2.282 | 2.059 |
| 5 | 0.577 | 0.000 | 2.114 | 2.326 |
| 6 | 0.483 | 0.000 | 2.004 | 2.534 |
| 7 | 0.419 | 0.076 | 1.924 | 2.704 |
| 8 | 0.373 | 0.136 | 1.864 | 2.847 |
| 9 | 0.337 | 0.184 | 1.816 | 2.970 |
| 10 | 0.308 | 0.223 | 1.777 | 3.078 |
Control charts are the core tool of statistical process control (SPC). They separate the normal, random variation of a stable process (common cause) from unusual signals that indicate something has changed (special cause). This builder constructs X̄ and R charts for variables (measurement) data and a p-chart for attribute (pass/fail) data, computing center lines and ±3σ control limits from your subgroups using the standard Shewhart constants. Everything runs in your browser — no data leaves your machine.
For variables data you collect rational subgroups — small samples (typically n = 4 or 5) taken close together in time. For each subgroup you compute the mean X̄ and the range R (max − min). The grand mean X̿ is the average of the subgroup means and becomes the center line of the X̄ chart; R̄ (the average range) is the center line of the R chart.
The control limits use tabulated constants that depend only on the subgroup size n: X̄ chart UCL/LCL = X̿ ± A2·R̄, R chart UCL = D4·R̄, and R chart LCL = D3·R̄ (which is 0 for n ≤ 6). These constants bake in the ±3σ width and the relationship between the average range and the process standard deviation, so you never have to estimate σ directly. This tool also reports σ̂ = R̄ / d2 for reference.
Always interpret the R chart (variation) before the X̄ chart (location). The R chart limits assume the within-subgroup spread is stable; if the R chart is out of control, the estimate of σ — and therefore the X̄ chart limits — is unreliable. Bring the range chart into control first, then judge whether the process average is stable. A common mistake is reacting to X̄ points while the underlying variability is still drifting.
When you classify each item as conforming or non-conforming (rather than measuring it), use a p-chart for the fraction defective. The center line p̄ is the total defectives divided by the total inspected across all subgroups. The control limits are p̄ ± 3·√(p̄(1−p̄)/n), where n is the sample size of that subgroup. Because the limits depend on n, they widen for smaller subgroups and narrow for larger ones — this calculator computes per-subgroup limits so unequal sample sizes are handled correctly. The lower limit is floored at zero since a fraction cannot be negative.
The most basic signal is a single point beyond the ±3σ control limits, which this tool flags in red. In practice engineers also apply the Western Electric / Nelson rules to catch subtler shifts: 2 of 3 points beyond 2σ, 4 of 5 beyond 1σ, 8 (or 9) consecutive points on one side of the center line, 6 points steadily increasing or decreasing (a trend), and other patterns. Any such signal warrants investigation for an assignable cause. Crucially, do not adjust a process that is in control — reacting to common-cause noise (over-control or "tampering") actually increases variation.
An X̄-R chart is used for variables (continuous measurement) data such as length, weight, or temperature — it tracks the subgroup average (X̄) and range (R). A p-chart is used for attribute data, where each item is classified as good or defective, and it tracks the fraction defective. Choose the chart by the type of data you collect.
The ±3σ limits, proposed by Walter Shewhart, balance two error costs: a false alarm (reacting when nothing changed) and a missed signal (failing to detect a real shift). For a normal distribution, about 99.73% of points fall within ±3σ when the process is stable, so points outside are rare enough to be worth investigating but not so frequent that you chase noise. Note these are control limits computed from the data, not specification limits set by the customer.
For X̄-R charts a subgroup size of 4 or 5 is most common — large enough to make subgroup means approximately normal, small enough to keep within-subgroup variation purely common cause. This tool supports n from 2 to 10 using standard A2, D3 and D4 constants. For n greater than about 10, an X̄-S (standard deviation) chart is preferred because the range becomes a less efficient estimator of spread.
No. Control limits describe what the process actually does — they are calculated from your data (X̿ ± A2·R̄). Specification limits describe what the customer requires and are set independently. A process can be in control (stable) yet still produce out-of-spec parts if its natural spread is wider than the tolerance. Comparing the two is the job of process-capability analysis (Cp, Cpk).
It signals a likely special (assignable) cause — something changed: a new material lot, tool wear, an operator change, a measurement error. The correct response is to investigate and remove the cause, not to widen the limits. If you confirm a data-entry error or a one-off event, you may remove that point and recompute the limits; otherwise the signal is real and the process needs attention.