SPC control chart and rule checker (I-MR, X-bar R, p)

Paste your data in time order. The tool calculates the centre line and 3-sigma control limits, plots the chart and flags points that break the run rules. Use it to check that a process is stable before you calculate Cpk, or to check whether a corrective action changed the process.

Runs in your browser. Nothing you enter is sent or stored.

I-MR (single values) X-bar and R (subgroups 2–10) p chart (defectives)

Values in time order, separated by spaces or new lines (use a dot as decimal point) Also apply rules 5–8 (trend, alternation, stratification, mixture)

2 out-of-control signals found. The process is not shown to be stable: find and remove the cause before you calculate Cpk.

Individuals (I): CL 10.185 · UCL 11.0249 · LCL 9.3451

Point 20: rule 1 (1 point beyond 3 sigma)

Moving range (MR): CL 0.3158 · UCL 1.0317 · LCL 0.000

Point 20: rule 1 (1 point beyond 3 sigma)

σ within (R̄/d₂ or MR̄/d₂) = 0.2800, mean = 10.185. Use it for Cpk only after the signals are resolved.

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Formulas and constants

I-MR: limits = mean ± 3·MR̄/d₂ (d₂ = 1.128, i.e. ± 2.66·MR̄); MR chart UCL = 3.267·MR̄.
X-bar and R: limits = X̿ ± A₂·R̄; R chart UCL = D₄·R̄, LCL = D₃·R̄; σ within = R̄/d₂. Subgroup size 2 to 10.
p chart: limits = p̄ ± 3·√(p̄(1 − p̄)/n), calculated per point when sample sizes differ; LCL is not shown below 0.
Constants A₂, D₃, D₄ and d₂ are the standard Shewhart table values (as published in the NIST/SEMATECH e-Handbook of Statistical Methods). They are unit-tested against that table and d₂ against numerical integration.

Run rules

Rules 1 to 4 are the Western Electric rules: 1 point beyond 3σ; 2 of 3 beyond 2σ on the same side; 4 of 5 beyond 1σ on the same side; 8 in a row on one side. Optional rules 5 to 8 follow the Nelson pattern: 6 points trending; 14 alternating; 15 within 1σ; 8 beyond 1σ on both sides. Zone rules are applied to the X, X-bar or p chart only; the R and MR charts are checked for points outside the limits. Every point that completes a pattern is flagged. Your customer or control plan may use a different rule set; check it.

Limits of this tool

Limits are trial (Phase I) limits calculated from the data you enter. Use at least 20 to 25 subgroups or values; with fewer, the limits are preliminary and the tool says so. Remove points with a confirmed assignable cause and recalculate, then freeze the limits for ongoing monitoring (entering fixed limits is not included). Not included: X-bar and S, np, c and u charts, EWMA/CUSUM, subgroups larger than 10, and non-normal data handling. The I-MR chart assumes roughly normal, independent data; autocorrelated data gives false signals. A signal is a statistical flag, not proof of a cause, and the result is advisory, not a customer or audit decision.

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