# Capability ratios (Cp/Pp indices)

Capability ratios (Cp/Pp) describe the variability of a process relative to the specification limits.

A capability ratio is a unit-less value describing the ratio of process distribution spread to specification limits spread. A value of less than 1 is unacceptable, with values greater than 1.33 (1.25 for one-sided specification limits) widely accepted as the minimum acceptable value, and values greater than 1.50 (1.45 for one-sided specification limits) for critical parameters (Montgomery, 2012). The higher the value, the more capable the process of meeting specifications. A value of 2 or higher is required to achieve Six Sigma capability which is defined as the process mean not closer than six standard deviations from the nearest specification limit.

All of the indices assume a normally distributed process quality characteristic with the parameters specified by the process mean and sigma. The process sigma is either the short-term or long-term sigma estimate.

Indices computed using the short-term sigma estimate are called Cp indices (Cp, Cpl, Cpu, Cpk, Cpm). While those using long-term sigma estimate are called Pp indices (Pp, Ppl, Ppu, Ppk, Ppm). If the Cp indices are much smaller than the Pp indices, it indicates that there are improvements you could make by eliminating shifts and drifts in the process mean.

Various indices measure how the process is performing against the specification limits:
Index Purpose
Cp/Pp Estimates the capability of a process if the process mean were to be centered between the specification limits.
Note: If the process mean is not centered between the specification limits the value is only the potential capability, and you should not report it as the capability of the process.
Cpl/Ppl Estimates the capability of a process to meet the lower specification limit. Defined as how close the process mean is to the lower specification limit.
Cpu/Ppu Estimates the capability of a process to meet the upper specification limit. Defined as how close the process mean is to the upper specification limit.
Cpk/Ppk Estimates the capability of a process, considering that the process mean may not be centered between the specification limits. Defined as the lesser of Cpl and Cpu.
Note: If Cpk is equal to Cp, then the process is centered at the midpoint of the specification limits. The magnitude of Cpk relative to Cp is a measure of how off center the process is and the potential improvement possible by centering the process.
Cpm/Ppm Estimates the capability of a process, and is dependent on the deviation of the process mean from the target.
Note: Cpm increases as the process mean moves towards the target. Cpm, Cpk, and Cp all coincide when the target is the center of the specification limits and the process mean is centered.
Note: There is some confusion between terms "Cp" and "Pp" as some authors suggest the use of Pp indices when a process is not-in-control and Cp indices when a process is in control. However, it is nonsense to interpret the indices when the process is not-in-control as no probability distribution can describe the process performance. We make the distinction between Pp and Cp indices on the estimate of sigma used not on the state of the process.

Published 8-Jan-2017
Version 4.90