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

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

(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

(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