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Cp, Cpk and Process Capability Analysis

Capability analysis determines if a process will deliver a product that meets the customers specifications (USL/LSL) and how well it is centered between the specification limits.

The  Histogram and templates calculate several process capability analysis metrics. Descriptions and formulas for these metrics are described below.

Cp and Cpk Process Capability Metrics

  • Cp measures how well the data fits within the spec limits (USL, LSL)
  • Cpk measures how centered the data is between the spec limits.
    A Cpk of 1.33 is considered to be at 4-Sigma.

Use Cp when you have a sample, not the population, and are testing the potential capability of a process to meet customer needs. Cp and Cpk use Sigma estimator.

Sigma estimator Formula

sigma estimator formulas
d2 is a constant based on subgroup size
c4 is a constant based on subgroup size

Rbar = Average(Ri) (Average of the Ranges in samples)
sbar = Σ(σi)/n

Cp, Cpk Formula

Cp, Cpk formulas(Cpk > 1.33 is desirable)

Cr Formula

The Capability Ratio (Cr) indicates what proportion of tolerance is occupied by the data.

Cr = 1/Cp        Cp = 1.33 ~ Cr = 0.75 (data fits 75% of tolerance)

Cpm Formula

Cpm = (USL-LSL)/(6√(sigma2+(Xbar-Target)2))
(Cpm can be used when you have a target value.)

One-Sided Specifications or Unilateral Spec Limits

Use CpU (USL) or CpL (LSL) for Cpk.

Pp, Ppk Process Performance Metrics

Use Pp when you have the total population and are testing the performance of a system to meet customer needs. Pp, Ppk use standard deviation.

Pp, Ppk formulas

Pp, Ppk formulas(Ppk > 1.33 is desirable)

σ = stdev(Xi)

Cp, Cpk vs Pp, Ppk

Use Cp, Cpk when you have a sample and are testing the potential capability of a process to meet customer needs.

Use Pp, Ppk when you have the total population and are testing the performance of a process to meet customer needs.

For example, if you test a sample of 10 widgets from a batch of 100 widgets:

  • Use Cp, Cpk to measure and make a statement about just the 10 widgets.
  • Use Pp, Ppk to measure and make a statement about the whole batch of 100 widgets you measured.

When Cp > 1.5 Pp or Cpk > 1.5 Ppk, the process is probably out of control and you cannot determine capability.

Source: QI Macros

 

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