Process capability indices

MINI PAPER
Process Capability Indices
By Robert H. Mitchell
3M Company

Process capability indices have been popular for over
20 years, since Joseph Juran12 popularized the Capability
Ratio (Cr) in his Quality Control Handbook. Eagerness to establish a single index to measure process capability has resulted in the proliferation of indices: Cp/Cpk, Vp/Vpk,
Pp/Ppk, Cpm, Tz, %OOL, PPM, and more recently –
“Generalized” Cp/Cpk. Abuse of these indices is well documented (Gunter)8. Though simple to compute, they can lead to scorekeeping by management, incorrect interpretations and tampering, with little or no product or process improvement. This article reviews the basics of estimating process capability and introduces new process capability indices.

Values of Cp exceeding 1.33 indicate that the process is adequate to meet the specifications. Values of Cp between 1.33 and 1.00 indicate that the process, while adequate to meet specifications, will require close control. Values of Cp below 1.00 indicate the process is not capable of meeting specifications.

Cp is called the “Process Potential” - it simply relates the Process Capability (6σ) to the Spec Range; it does not relate the location of the process with respect to the specs.
Consider the three distributions in fig. 1, all from processes having a Cp of 1.00 or better.
Figure 1

Cp, Cpk
The original Capability Index published in Juran’s
Quality Control Handbook is defined as Tolerance Width divided by Process Capability.
Cp = Process Potential
= (Tolerance Width) / (Process Capability).
Juran defines Process Capability as six standard deviations for a process in statistical control. Process Capability =
6σ where σ is the in-control process standard deviation.
The easiest method to determine process standard deviation is from the control chart of a stable process: Process
Std. Dev. = R-bar/d2, where the appropriate value of d2 is read from a table for the subgroup size.
For