# Process Capability Analysis

A capable process meets customer requirements 100% of the time. Customer requirements are defined using an upper specification limit (USL) and a lower specification limit (LSL). Think of these specification limits as goal posts.

Not Capable |
Capable |
Not Capable to Centered & Capable |
---|---|---|

Cp < 1, Cpk <1 |
Cp >= 1, Cpk >= 1 |

**Process capability analysis** determines how well the output of a stable process meets these specifications using the following metrics:

### Cp and Cpk

Process Capability Metrics

**Cp**measures how well the data**would****fit within**the spec limits (USL, LSL)**Cpk**measures how centered the data is between the spec limits.

Use **Cp Cpk ** 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.**

### Pp and Ppk

Process Performance Metrics

**Pp**measures how well the data**would****fit within**the spec limits (USL, LSL)**Ppk**measures how centered the data is between the spec limits.

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

**Pp, Ppk use standard deviation.**

### Cp vs Cpk Examples

#### Fits But Is Not Centered

Process improvement goal is to make changes that will move the output closer to the target without increasing variation.

#### Centered But Does Not Fit

Process improvement goal is to reduce variation so that the process fits between the spec limits.

### Capability Analysis Metrics Rules of Thumb

**Cp>1 **Process is capable (product will fit between the customer’s upper and lower specification limits if the process is centered).

**Cpk>1** Process is capable and centered between the LSL and USL.

If Cp=Cpk the process is centered at the midpoint of the specification limits.

If Cp>Cpk the process is off-center.

Cp and Cpk should be close in value to Pp and Ppk.

If Cp and Cpk are much greater than Pp or Ppk (*33% greater*), your process may not be stable enough to conduct a capability analysis. Use control charts to evaluate the stability of your process.

**Capability Suite of Six Charts Created Using the QI Macros**

### The Capability Suite Six Charts:

These are the same six charts included in Minitab’s Capability Sixpack™

- X Chart (XmR for individual data, Xbar for 2+ samples) to evaluate
*stability*. - Range or Standard Dev Chart (R for n<5; S for n<4) to evaluate
*stability.* - Values Plot of individual data points.
- Histogram with Cp, Cpk, Pp, Ppk to evaluate
*capability*. - Probability Plot for analysis of
*normality*of the data. - Capability Plot of within and overall variation vs specification limits.

**One Sided Spec Limits**

If you need to perform a one tailed capability analysis, just delete the formula in either the USL or LSL field.

**Cp and Cpk Calculation Mistakes to Avoid**

Most people try to calculate Cp as the upper spec limit minus the lower spec limit divided by six times the standard deviation:

Cp = (USL-LSL)/6*Stdev

However, this is actually the formula for process performance (Pp).

The **QI Macros Cp Cpk template** uses the correct formula which estimates the standard deviation from the average of the ranges divided by a constant (Rbar/d2).

Cp = (USL-LSL)/6*Rbar/d2

The same is true for Cpk.