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What is the Cpk formula?

Published in Process Capability 2 mins read

The Cpk formula assesses how close a process is to its target and how consistent it is around its average performance. It considers both the process spread and its centering between the specification limits. Cpk is calculated differently depending on whether the process mean is closer to the upper or lower specification limit.

Cpk Formula Breakdown

The Cpk formula is actually composed of two separate calculations, and the lower value of the two is taken as the Cpk. This ensures that the Cpk value reflects the worst-case scenario regarding process capability.

Here's a breakdown:

1. Understanding the Variables

  • USL: Upper Specification Limit - The maximum acceptable value.
  • LSL: Lower Specification Limit - The minimum acceptable value.
  • Mean (μ): The average of the process data.
  • Stdev (σ): Standard Deviation - A measure of the process variability.

2. The Two Cpk Calculations

The Cpk is the minimum of these two values:

  • *CpkUSL = (USL - Mean) / (3 Stdev)**
  • *CpkLSL = (Mean - LSL) / (3 Stdev)**

The formula with the smallest result becomes the overall Cpk.

3. Interpretation

The higher the Cpk value, the more capable the process is. Common benchmarks include:

  • Cpk < 1: Process is not capable. It produces a significant number of defects.
  • Cpk = 1: Process is minimally capable.
  • 1 < Cpk < 1.33: Process is capable, but could be improved.
  • Cpk = 1.33: Often considered a target for a capable process.
  • Cpk > 1.33: Process is highly capable.

Applying the Formula (with example)

Let’s imagine a scenario where a manufacturing company produces bolts. The specifications are:

  • USL: 10.5 mm
  • LSL: 9.5 mm
  • Mean: 10.2 mm
  • Stdev: 0.1 mm

Using the formula:

  • CpkUSL = (10.5 - 10.2) / (3 * 0.1) = 0.3 / 0.3 = 1
  • CpkLSL = (10.2 - 9.5) / (3 * 0.1) = 0.7 / 0.3 = 2.33

The Cpk is the minimum of these two values, so Cpk = 1.

Insights based on the example:

  • According to the reference, if the mean of the process data is closer to the upper spec limit USL, then Cpk = (USL-Mean) / (3 Stdev). However, the overall Cpk is the lower of the two calculations.
  • The Cpk value of 1 suggests the manufacturing process is minimally capable.

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