## Process Capability

How do you know if your process is capable? Process Capability Pp measures the process spread vs the specification spread. In other words, how distributed the outcome of your process is vs what the requirements are.

If you’d like more depth including calculations, etc, see these articles:

- Process Capability & Performance (Pp, Ppk, Cp, Cpk) Overview
- Process Capability (Cp, Cpk)
- Z score and process capability

**Note:** use Pp & Ppk when you are initially setting up your process. After a process has reached statistical control, use Cp & Cpk.

Let’s imagine that your process has 2 specifications; a Lower Specification Limit (LSL) which is the lowest value allowed and an Upper Specification Limit (USL), the highest value allowed. The difference between the two is the **specification spread**; sometimes referred to as the **Voice of the Client.**

The **process spread** is the distance between the highest value generated and the lowest. This is sometimes referred to as the **Voice of the Process.**

### Process Spread vs Specification Spread

Think of the Specification Spread as the sides of your garage – those are static, they are not moving, and it is important that your process puts values inside those bounds. The Process Spread is the size of the car you are trying to fit in.

### Can A Process Meet Specifications?

The answer is in the amount of variation in your process. If your process spread is greater than the specification spread, then the answer is no. However, if the process spread is less than the specification spread, then process variation is low enough for it to fit.

#### Process Meets Specifications: Good Potential Performance

#### Process Does NOT Meet Specifications: Bad Potential Performance

### Calculating Process Capability (Pp)

Pp = (USL – LSL) / 6* s : where s the standard deviation, or the ‘fatness’ or dispersion of the bell curve.

#### What is a ‘Good’ Process Capability (Pp) Number?

According to Six Sigma, we want a Pp of above 1.5 because that would reflect a process with less than 3.4 DPMO – the definition of 6 Sigma quality.

How do we come to that?

Well, we want to have 6 sigmas (standard deviations) between the mean of the process and the LSL. Since a normal distribution is symmetric, that means we also want 6 sigmas between the mean and the USL. That’s a total of 12 sigmas between the USL and LSL.

In other words, USL – LSL should = 12 for us to reach 6 σ quality standards of 3.4 DPMO.

See how that is reflected in the equation Pp = (USL – LSL) / 6* s ?

Let’s replace (USL – LSL) with 12: Pp = (USL – LSL) / 6* s = 12 σ / 6 * s = 2 σ / s

## Process Capability Index

## Is the Process Acceptable? Ppk (Capability)

Ppk is another performance index that measures how close the current process mean’s proximity is to the specification limits. In other words, does this process deliver acceptable results?

The way we tell this is trying to see how centered the process is. If the process is not centered well, it is deemed not acceptable.

### Calculating Ppk

There are 2 ways to calculate Ppk, depending on how your process is aligning.

#### Process Mean close to USL

If your Process Mean (central tendency) is closer to the USL, use: Ppk = [ USL – x(bar) ] / 3 s, where x(bar) is the Process Mean.

#### Process Mean close to LSL

If your Process Mean (central tendency) is closer to the LSL, use: Ppk = [x(bar) – LSL ] / 3 s, where x(bar) is the Process Mean.

### Interpreting Ppk Scores

A Ppk of 1 means that there is “half of a bell curve” between the center of the process and the nearest specification limit. That means your process is completely centered.

## Pp, Ppk In Relation to Z Scores

Ppk can be determined by diving the Z score by three. A z score is the same as a standard score; the number of standard deviations above the mean.

Z = x – mean of the population / standard deviation.

Ppk = ( USL – µ) / 3σ = z / 3

## ASQ Six Sigma Green Belt Process Performance Questions

**Question:** Which of the following measures is increased when process performance is improved?

(A) Variability range

(B) Capability index

(C) Repeatability index

(D) Specification limits

Answer: (B) Capability Index. The capability index increases as the process improves.

You would immediately discount the Variability range as we judge a good process to have low variability. We can also discount specification limits as those hold steady regardless of the performance of the process (because they are defined by the voice of the customer.)

Repeatability is the variation between measurements that occurs when one person measures the same item several times, under identical conditions, and using the same measuring equipment. The standard Six Sigma BOKs do not list a repeatability index but there is a repeatability coefficient in biology that increases as sigma (the standard deviation) increases. In that case, a process with better performance would have smaller standard deviations and that index would decrease.

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