The Real History of Cpk vs Ppk: Why the Definitions Changed and Why There Is Confusion
Not familiar with Capability Indices (Cpk and Ppk)? Check out our Capability Analysis course if you want to learn more. This article assumes you have knowledge of how Cpk and Ppk are calculated.
For decades, process capability metrics have been a source of widespread confusion. Many quality and process engineers along with their managers still say “Cpk” while actually calculating “Ppk.” Others use the terms interchangeably when software packages such as Minitab and JMP clearly treat them as different indices.
If you’ve ever been confused by the calculations for Cpk and Ppk, this article explains the history of capability metrics, why Ppk was introduced, how Cpk’s definition changed over time, and where the modern terminology is documented.
Cpk was the original metric, Ppk was added later
When capability indices first entered industrial use in the 1970s–1980s, there was no Ppk term. Cpk was the only metric. It used the overall standard deviation calculated from all the data in the denominator of the formula, which was based on the traditional standard deviation formula.
Original Cpk formula (pre-1990s):
Where s was equal to the long-term standard deviation, denoted by the standard deviation formula below:
Short-term vs long-term variation did not yet exist as separate concepts in SPC.
Motorola Six Sigma introduced short-term vs long-term in mid-1980s
Motorola’s Six Sigma program started in the early 1980’s. One of the new additions was the inclusion of the short term standard deviation to separate how it can vary from the long term standard deviation (indicating problems with stability).
The calculation is calculated from the moving range for individual readings, and R-bar (range average) divided by a constant (d2 or c4) for subgroups (n > 2).
Short-term standard deviation formulas:
They still maintained the Cpk term, using short-term Cpk and long-term Cpk to distinguish them apart. However, Ppk was not mentioned yet.
This shift created the first generation of confusion:
- Old-school Cpk = long-term standard deviation
- Motorola-era Cpk = short-term and long term standard deviation (based on how it was labeled)
Both groups used the same word but might differ in how standard deviation was calculated.
Ppk emerges from the auto industry (AIAG)
The earliest formal informal appearance of Ppk in an industry-standard reference occurs in the Automotive Industry Action Group (AIAG), specifically the AIAG Statistical Process Control (SPC) Manual, 1st Edition (1991).
These books were the standardized documents for how suppliers to major automotive manufacturers (OEMs) should conduct quality and Six Sigma analysis. These blue books were given to me by my early mentors in 1999 and 2000, who had come from the automotive industry, and used these books as references for how to perform many of the Six Sigma and quality system tools.
The first major appearance of Pp and Ppk occurred AIAG SPC Manual, 2nd Edition (1995).
This edition clearly defines:
- Cp, Cpk → capability indices using within subgroup standard deviation
- Pp, Ppk → performance indices using overall standard deviation
- Long-term performance must reflect all sources of variation (within and between subgroup) variation
- Short-term capability must reflect only common-cause (within subgroup) variation
These definitions became the standard for automotive suppliers under QS-9000, TS16949, and now IATF 16949.
Because AIAG standards governed tens of thousands of suppliers, software companies started to align with the AIAG.
Engineers and managers trained before 1995 learned that Cpk uses overall standard deviation and that it was the only term available, and haven’t gotten used to using Ppk as a term (referring to everything as Cpk). People now often calculate Ppk but call it Cpk because the term Cpk is more familiar.
Minitab adopts the AIAG definitions in late 1990s
Minitab’s help documentation (Release 14 and later) states:
“Ppk is based on the overall standard deviation.
Cpk is based on the within-subgroup standard deviation.
Minitab follows the AIAG definitions.”
– Minitab Support: “Difference Between Cpk and Ppk”
Minitab also explicitly positions Cpk = short-term and Ppk = long-term.
JMP (SAS) follows the same convention
JMP’s Quality and Process Engineering Guide (JMP 7 and later) states:
“Capability indices (Cp, Cpk) are based on within-subgroup
standard deviation. Performance indices (Pp, Ppk) are based on the overall
standard deviation. This distinction is consistent with AIAG SPC definitions.”
– JMP Documentation, Process Capability chapter
Academic references that document the transition
1. Bothe, D.R. — “Measuring Process Capability” (1997) – One of the earliest books to explicitly distinguish Cp/Cpk (short-term) from Pp/Ppk (long-term).
2. Montgomery, Douglas, “Introduction to Statistical Quality Control,” 4th ed. (2001) – He notes that historically, “Cpk” was computed using overall sigma (standard deviation), which “can lead to confusion.
Summary
Before the 1990s, Cpk was calculated using the overall (long-term) standard deviation.
When Motorola introduced short-term vs long-term sigma (standard deviation), the automotive industry formalized this split in the AIAG SPC Manual (1991–2005), creating Ppk as the long-term metric and redefining Cpk as a short-term metric.
Modern software follows the AIAG definitions, which is why Minitab and JMP report Cpk using within-subgroup sigma and Ppk using overall sigma.
Here are the most up-to-date versions of the formulas:
Despite these changes from many decades ago, there is still confusion today. In my experience, when I only see Cpk and no mention of Ppk, typically the original Cpk formula is being used (which should be renamed to Ppk, as it is calculated using the long-term standard deviation formula).
Want to learn more about these formulas for Cpk and Ppk? Check out our Capability Analysis course
