Monitor defect proportions across samples with fast, consistent analysis today. Get limits, alerts, and summaries. Export results, share reports, and tighten process control now.
| Sample | n | d | p = d/n |
|---|---|---|---|
| S1 | 100 | 6 | 0.0600 |
| S2 | 120 | 9 | 0.0750 |
| S3 | 80 | 3 | 0.0375 |
| S4 | 150 | 15 | 0.1000 |
| S5 | 90 | 2 | 0.0222 |
| S6 | 110 | 8 | 0.0727 |
| S7 | 95 | 5 | 0.0526 |
| S8 | 130 | 7 | 0.0538 |
A p chart monitors the proportion defective in each sample.
P charts track attribute quality when each unit is classified as conforming or defective. If 8 samples total 975 inspected units with 55 defectives, the pooled estimate is p̄ = 55/975 = 0.05641, meaning 5.64% defective overall. The center line reflects your current baseline, not a target, so improvement projects should be validated by sustained shifts in p̄ across future samples.
Because n can change by shift or batch, limits are computed per sample. For n = 80 with p̄ = 0.05641, σ = √(p̄(1−p̄)/n) = 0.02582, giving UCL = 0.13387 and LCL = 0.00000 after clamping. For n = 150, σ falls to 0.01884, tightening limits to UCL = 0.11293 and LCL = 0.00000.
A point outside the 3σ limits indicates special-cause variation. If a sample shows p = 0.18 while UCL is 0.11, treat it as a true signal until proven otherwise: confirm measurement rules, check material lots, review operator changes, and document corrective actions. Recalculate limits only after the cause is removed and a stable period is re-established.
Use rational subgrouping: each sample should represent a short, consistent production window. Mixing multiple days into one sample can hide spikes. Keep inspection criteria fixed, and record n and d directly from the same definition of “defective.” For low defect rates, increase n to reduce σ and avoid limits that are too wide to detect meaningful changes.
The CSV and PDF exports capture p, LCL, CL, and UCL for each sample plus the status flag. This supports traceability during ISO-style audits: you can attach the PDF to a nonconformance report, or import the CSV into a dashboard for monthly trending. Always store the raw counts alongside the chart output for reproducibility. Use this calculator after each lot release to standardize reporting, reduce debate, and speed corrective-action approvals internally.
When the chart is in control, focus on reducing p̄ through structured improvement: Pareto the defect types, run designed trials, and confirm gains with new samples that stay within limits while trending lower. When it is out of control, prioritize containment and root-cause analysis before capability claims, because unstable processes invalidate yield forecasts and customer risk estimates.
Provide at least two samples with inspected count n and defectives d. Labels are optional. Keep the defect definition consistent across samples, and avoid mixing multiple time periods into one sample.
When sample sizes vary, the standard error uses σᵢ = √(p̄(1−p̄)/nᵢ). Larger n tightens limits and smaller n widens them, so each point is judged against its own limits.
It means the observed proportion pᵢ falls outside the 3σ control limits. Treat it as a potential special cause, verify data integrity, and investigate changes in materials, methods, machines, or people.
Proportions cannot be negative or exceed 1. Clamping keeps LCL and UCL within valid bounds, especially when p̄ is low or n is small, where statistical limits may otherwise extend beyond reality.
Recalculate after removing special causes or after a deliberate process change, using a stable window of recent samples. Avoid updating p̄ every point, because that can mask emerging shifts.
You can start with 10–15 samples, but 20–25 provides a stronger baseline for p̄ and typical variation. More samples are helpful when defect rates are very low or sampling is irregular.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.