Laney P′/U′ Control Chart: Correcting Over- and Under-Dispersion
What is the Laney P′/U′ Control Chart?
Traditional P charts assume binomial variation, but with very large sample sizes or process fluctuation beyond the theory, the limits distort: overdispersion makes them too narrow (frequent false alarms) and under-dispersion too wide (missed signals). Laney's method estimates the actual process variation σ_z from the moving range of the rates and corrects the control limits to match real behavior.
When to Use It
Use it for high-volume, high-yield processes such as million-piece electronic inspections or SMT placement defect monitoring, and whenever defect data cluster or spread so much that ordinary P/U charts alarm constantly or miss signals. P′ applies to fraction-nonconforming data and U′ to defects-per-unit data; the tool selects the right method from the data type.
How to Use It (Step by Step)
Enter the per-batch nonconforming counts (or defect counts) with their batch sizes, and the tool computes σ_z = MR̄/1.128, corrects the limits and marks violations. Read σ_z: near 1 means the chart matches the ordinary P chart, greater than 1 means overdispersion with widened limits, and less than 1 means under-dispersion with tightened limits.
Key Formulas / Example
σ_z = MR̄/d2 with d2 = 1.128; corrected limits are p̄ ± 3·σ_p·σ_z where σ_p = √(p̄(1−p̄)/n) for P′ (or √(ū/n) for U′). At least 20–25 subgroups are needed to estimate σ_z reliably, and the per-batch limits must be recomputed as sample sizes change.