Quality managementReading time 12 min

Cp, Cpk and Ppk: Read the Numbers in Context

Capability indices are useful only when the measurement system and process behavior support them. See what each index measures, why centering matters and when a good-looking Cpk is misleading.

Cpk

01What each index measures

Index	Which variation	Accounts for offset	Answers
Cp	Within-subgroup (short term)	No	Is the spread of the process small enough
Cpk	Within-subgroup (short term)	Yes	How much margin is left once the offset is taken off
Pp	Overall (long term)	No	Spread including between-lot variation
Ppk	Overall (long term)	Yes	What you actually shipped

C indices use within-subgroup variation; P indices use overall variation across the sample.

Cp compares the specification width with the process spread; it does not say whether the process is centered. Cpk also measures how close the process mean is to the nearest limit. That is why Cpk cannot exceed Cp, and why the two numbers should be read together.

02Capability and defect rates

Cpk	Equivalent sigma level	Theoretical defect rate (two-sided)	Where it is usually required
1.00	3σ	2700 ppm	No longer accepted in most industries
1.33	4σ	63 ppm	The basic threshold in general industry
1.67	5σ	0.57 ppm	Automotive, critical characteristics
2.00	6σ	0.002 ppm	The six sigma target

Defect-rate conversions depend on distribution and centering assumptions; verify them before use.

Converting capability indices to defect rates requires assumptions about the distribution. Characteristics with a natural boundary, such as runout or roundness, may not follow a normal distribution. Check the data before using a textbook conversion.

03Check process stability first

A capability index describes a process only if the process is stable. If the mean drifts or special causes are still active, the calculated Cpk summarizes the sample period but is a poor prediction of future output.

How to confirm it

Plot a control chart (X̄-R or X̄-s) and confirm no points fall outside the control limits.
Look for non-random patterns: seven consecutive points on one side, seven consecutive rising or falling, cyclic behaviour, or data hugging the centre line (which usually means the subgrouping is wrong).
Confirm the sources of variation have been identified and controlled: tool changes, material changes, shift changes, temperature.
Only once all of that holds should you calculate a capability index.

04Choosing a sample

Too few observations make an index uncertain. Sample across operators, shifts, lots and enough time to capture the variation that production actually sees; then report the sample size with the result.

Sample size n	95% lower confidence limit on a point estimate of Cpk 1.33	What it asks
30	About 1.02	A very wide interval; easy to misjudge
50	About 1.10	Still wide
100	About 1.18	Acceptable
200	About 1.23	More reliable

Capability estimates have uncertainty, especially with small samples.

05Use the drawing limits

Capability needs measured values, not just pass/fail marks. Keep the numbers so you can see centering, drift and spread even while every part remains within tolerance.

Finally, verify the specification limits themselves. An incorrectly copied tolerance can make a mathematically correct index meaningless. Trace the limits back to the current drawing revision.