Histogram for Process Capability — Six Sigma Cp/Cpk Tolerance Distribution
A process capability histogram plots measured part dimensions across micrometer or millimeter tolerance bins to assess process centering ($mu$) and spread ($6\sigma$) relative to Lower and Upper Specification Limits ($LSL, USL$).
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Potential capability: Cp = (USL - LSL) / (6 * sigma). Centered capability: Cpk = min((USL - mu) / (3 * sigma), (mu - LSL) / (3 * sigma)).
Chart Design & Use-Case Tips
- 01Potential capability: Cp = (USL - LSL) / (6 * sigma). Centered capability: Cpk = min((USL - mu) / (3 * sigma), (mu - LSL) / (3 * sigma)).
- 02A well-centered capable process (Cpk >= 1.33) exhibits a tight, symmetric bell-shaped histogram peaked at the nominal target dimension with near-zero tail counts near LSL/USL.
- 03If the histogram peak shifts toward one specification boundary, recalibrate tool offset to restore centering (Cp vs. Cpk).
- 04If the histogram is centered but wide across all bins, reduce machine vibration, thermal drift, or raw material variance.
Frequently Asked Questions
What is the difference between Cp and Cpk on a process histogram?+
Cp measures whether the histogram's width (6 sigma) fits inside the tolerance window (USL - LSL), whereas Cpk accounts for whether the histogram's peak (mean) has drifted off-center toward either limit.
How many parts should be sampled for a capability study?+
Automotive and aerospace quality standards (AIAG PPAP) typically recommend at least 100 to 250 consecutive parts grouped into 7 to 10 measurement bins.
What if my process histogram has a sharp cliff on one side?+
A truncated cliff usually indicates 100% post-production sorting or rework where out-of-spec parts were manually removed from the batch.