Capability indices compare what a process naturally does against what it is required to do. Cp compares the specification width to the process spread. Cpk does the same but accounts for where the process sits within the specification.
Both exist because a process can be tight and badly positioned. Cp cannot see that — a narrow spread pressed against one specification limit scores well and produces defects anyway. Cpk penalises the offset, so it is always the lower of the two.
The gap between them is where the reading is. Cp much higher than Cpk means the variation is fine and the process simply needs centring, which is a different and usually far cheaper problem than reducing variation.
As rough conventions: 1.0 means the spread just fills the specification, 1.33 is a common minimum, 1.67 for critical characteristics. These vary by industry and are worth confirming rather than assuming.
None of it means anything for an unstable process. Cpk calculated on something still drifting describes a situation that has already passed, which is why control charts come first — stability, then capability, in that order. Quoting the index to two decimals from thirty data points is the other way this goes wrong.
