How this calculation works
Estimate within-subgroup spread from pooled residuals and overall spread from the full sample. Use the same overall mean with both spread bases when calculating centered and off-center capability summaries.
Within sigma = sqrt(sum within-group residual SS / (N − groups)); Cp = (USL − LSL)/(6 sigma)A worked example
The three example subgroups each have sample variance one. Pooled within sigma is one and the overall mean is ten, giving Cp and Cpk = 10/6 for specifications 5 to 15.
Good to know
Descriptive estimates, not proof of stability, normality or process approval. Uses pooled residual SD, not range/d2 or c4 correction. No capability interval or guaranteed defect rate.
Reference: NIST: process capability indices (opens in a new tab) ↗
Subgroup design defines the within estimate
Rational subgroups should reflect the process structure and sampling plan. Arbitrarily dividing a long list into lines can change the within estimate without changing the overall sample.
The estimator here is explicitly pooled sample residual standard deviation. It should not be confused with an average range divided by a subgroup-size constant.
The individuals moving range control chart calculator adds build an I/MR chart from a frozen initial baseline, with consecutive moving ranges, individual and MR limit flags, and an optional same-side run rule.
Centering changes Cpk even at the same spread
Cp compares specification width with six within-standard-deviations. Cpk uses the smaller distance from the process mean to a specification boundary.
A mean outside the specification produces a negative Cpk or Ppk. Those signs are retained because replacing them with an absolute value would hide the off-center condition.
Capability requires more than a favorable number
A calculation from observed data cannot establish that the generating process is statistically stable or normal. Check time behavior and the meaning of the specifications independently.
Pp and Ppk use overall sample spread, which includes subgroup-to-subgroup shifts. Comparing them with the within-based values can expose a spread difference but does not identify its cause.
Use the result with the next measurement
The individuals moving range control chart calculator checks a time-ordered baseline for selected signals. Capability indices do not replace that kind of process-behavior investigation.
Descriptive estimates, not proof of stability, normality or process approval. Uses pooled residual SD, not range/d2 or c4 correction. No capability interval or guaranteed defect rate.
A few questions, answered
Which within-sigma estimator is used?
Pooled residual sample SD across entered subgroups.
Can Cpk be negative?
Yes, when the mean lies outside specifications.
Does a high index prove stability?
No, time behavior and assumptions need separate checks.