Cpk and Ppk: what buyers should ask for

The short answer

Both indices compare the spread of a process with the tolerance and allow for the mean being off centre. The difference is the standard deviation in the denominator. Cpk uses the variation within subgroups. Ppk uses the overall variation of every reading.

That single difference changes the question. Cpk asks what the process could do if it were stable and only common causes were present. Ppk asks what the process did over the period that was measured, including drift, shifts and special causes.

The names are often used as if they were interchangeable, which leads buyers to compare a Ppk from a new tool with a Cpk from a mature line. The comparison is not like for like, and the lower number can unfairly disqualify a supplier.

The only difference that matters

Cpk is the distance from the process mean to the nearer specification limit, divided by three times the within-subgroup standard deviation. Ppk is the same distance divided by three times the overall standard deviation. The numerator is the same in both.

The within-subgroup sigma is usually estimated from the average range and a constant that depends on the subgroup size, or from a pooled standard deviation. The overall sigma is the ordinary sample standard deviation of all the readings. When a process is stable and the subgroup size is sensible, the two values come close. When the process drifts, they separate.

Both indices use the nearer specification limit. A process can have a good Cpk and a poor yield if the distribution is skewed or if the mean moves after the study. The index is a summary, not a substitute for the histogram.

Two different questions

Cpk is a capability index. It describes the best the process can do once special causes are removed, which is why it only makes sense when the process is in statistical control. A high Cpk on an unstable process is a statement about the gaps between the subgroups, not about the parts.

Ppk is a performance index. It includes the drift, so it is the honest number at the start of a programme when the process has not settled. That is why an initial submission study usually asks for Ppk, and why ongoing monitoring usually asks for Cpk.

Sample size and the data window

A Cpk study needs enough subgroups to estimate the within-subgroup variation. Twenty-five subgroups of five, or 125 readings, is a common minimum. A Ppk study needs a run of consecutive parts that represents production, and many programmes ask for 300 parts unless the customer agrees otherwise.

The date range matters as much as the count. A Ppk built from one good hour after a tool change does not represent the week. A Cpk built from parts selected because they looked good does not represent the process. Ask when the data was collected and whether the run was interrupted.

Subgroups should be chosen to capture the variation you want to understand. Consecutive parts within one hour show short term variation. Parts spread across shifts show drift. The subgroup size and the sampling interval are part of the study design, not an afterthought.

What the numbers mean

A Cpk of 1.00 means the nearer specification limit is three standard deviations from the mean. For a centred normal process that is about 2,700 parts per million outside the limits. A Cpk of 1.33 is about 63 parts per million. A Cpk of 1.67 is about 0.6 parts per million. These are illustrative conversions for a centred normal distribution, not a prediction for a skewed process.

The common programme targets are 1.33 for ongoing production and 1.67 for an initial approval study. Some customers use the same value for both, and some use 1.67 for safety related characteristics. The target belongs in the customer specific requirements, not in a generic rule.

Where the numbers mislead

Non-normal data breaks the conversion to parts per million. A flatness or a position result is often skewed, and a normal based Cpk will not describe the tail. Use the actual distribution, a transformation or an attribute measure instead of forcing a normal index.

Other traps are one-sided tolerances treated as two-sided, mixed streams from two cavities or two machines pooled into one number, and autocorrelated data from a continuous process. A capability study on a process that is not in control is the largest trap of all, because the number looks precise and means little.

What to ask for

Ask for the control chart, the raw data, the subgroup size, the sigma method and the date range. Ask whether the process was in control for the period and what action followed a low result. A single index in a table is not evidence.

If the supplier reports Cpk and Ppk far apart, ask why. A large gap usually means drift between subgroups, a tool wear pattern or a shift change that the control chart should show. That is useful information for the buyer, not a reason to pick the higher number.

Keep the study with the part records so a later change can be compared on the same basis. If the process moves to another machine, the old capability number no longer applies, even if the drawing has not changed.

• The characteristic and the specification limits.
• The sample size, the subgroup size and the date range.
• The sigma method used for each index.
• The control chart and the stability decision.
• The action taken if the result was below target.

Cpk and Ppk compared

The table summarises the practical split. It assumes a two-sided tolerance and a process that is being judged against that tolerance.