Cpk Formula | Cp Formula | Process Capability Analysis Formulas

Cp, Cpk and Process Capability
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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.

Not Capable	Capable	Not Capable to Centered & Capable
Cp < 1, Cpk <1	Cp >= 1, Cpk >= 1

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

Cp and Cpk Process Capability Metrics

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

Use C_p when you have a sample, not the population, and are testing the potential capability of a process to meet customer needs. C_p and C_pk 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(R_i) (Average of the Ranges in samples)
sbar = Σ(σ_i)/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

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

One-Sided Specifications or Unilateral Spec Limits

Use C_pU (USL) or C_pL (LSL) for C_pk.

Pp, Ppk Process Performance Metrics

Use P_p 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(X_i)

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. Stabilize the process and redo the capability study.