369. Cpk

369.1. (Process Capability Index with Centering)

Minimum distance from mean to nearest spec limit divided by 3 standard deviations. Process capability considering centering and variation.

If process is centered:

If process mean is off center, the smaller side of the process-to-limit ratio determines :

If , process is not centered

Value Meaning Quality Impact
Process not capable,
output falls outside specs
Many defects,
poor performance
Process just meets
specification limits
Acceptable only
if well centered
Process is capable,
centered or nearly so
Fewer defects,
reliable quality
Excellent capability,
Six Sigma level
Near-perfect
quality
Example

Suppose a company manufactures metal rods, and the specification limits for the diameter of the rods are:

  • Target: 10 mm
  • Lower Specification Limit (LSL): 9.8 mm
  • Upper Specification Limit (USL): 10.2 mm

The process has:

  • A standard deviation of 0.05 mm.
  • A process mean of 10.1 mm.

Step 1: Calculate the distance from the mean to the USL:

Step 2: Calculate the distance from the mean to the LSL:

Step 3: Determine :

Interpretation:

= 1.33 means the process spread (6 ) fits 1.33 times within the tolerance range (the distance between the Upper Specification Limit and Lower Specification Limit.

  • = 1.00: Process mean is exactly at the midpoint of the specification limits, and the process variation fits exactly within these limits. 99.73% of the output will be within specifications, indicating a capable process (3 sigma process).
  • : The higher the , the more capable and stable the process is, meaning it can consistently produce parts within tolerance with minimal risk of defects.
  • : The process mean is off-center or the variation is wider than the specification limits, or both. A significant portion of the output may fall outside the specification limits.