## 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:

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.  We call the difference between the two 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. We sometimes refer to this as the Voice of the Process.

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 exceeds 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.

### Cp, Cpk, Pp, Ppk Practice Questions and Z Charts

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### 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

## Is the Process Acceptable? Ppk (Capability)

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

We tell this by trying to see how centered the process is. If the process is not centered well, it is deemed not acceptable.

### Calculating Ppk

There are two ways to calculate Ppk, depending on how your process aligns.

#### 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 dividing 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

### Cp, Cpk, Pp, Ppk Practice Questions and Z Charts

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## Author

• I originally created SixSigmaStudyGuide.com to help me prepare for my own Black belt exams. Overtime I've grown the site to help tens of thousands of Six Sigma belt candidates prepare for their Green Belt & Black Belt exams. Go here to learn how to pass your Six Sigma exam the 1st time through!

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amrita says:

Stephen says:

Kiran Chaudhari says:

Idris kayode says:

If a process has a variance of 4 units and a specification
of 96 ± 4, what is the process performance index (Pp)?

(A) 0.33
(B) 0.66
(C) 1.00
(D) 1.50

Idris- can you tell me the steps you took to try to solve this?

SAGAR says:

USL = 96+4 = 100
lSL = 96-4 = 92
VARIANCE = 4

Pp = (USL – LSL)/(6 x sq. root of VARIANCE)
= (100 – 92)/(6 x 2)
= 0.666

pankaj says:

thankyou so much for providing solutions.

I’ve added this question and a full answer walkthrough to the thousands of others available in the paid membership areas.

Chaminda Jayasinghe says:

0.66

Suresh says:

USL = 100
LSL = 92
Variance is 4
Standard deviation = Square root (4) = 2
Pp = (USL-LSL)/ (6*Standard deviation)
Pp= (100-92) / ( 6*2)
Pp= 8/ 12
Pp = 0.6667
Pp is 0.66

pham quang thao says:

Hi Ted Hessing.
If we calculate like this, the Ppk and Cpk is equal?
Because the recipe to calculate them are the same.

Hans says:

It is the same calculation:
Calculating CPK (from https://sixsigmastudyguide.com/process-capability-cp-cpk/):
Cpl = (Process Mean – LSL)/(3*Standard Deviation)
Cpu = (USL – Process Mean)/(3*Standard Deviation)

Calculating PPK (from https://sixsigmastudyguide.com/process-performance-pp-ppk/):
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.

Thanh says:

What would the Ppk be for a process with average of 50, standard deviation of 5, and specification limits of 36 and 72 ?

Chaminda Jayasinghe says:

0.93

Suresh says:

PpK is 23.3333

Xuande Zhang says:

Great guide, thanks for your help!

What is the best value and acceptable range of Cp ,Cpk & Pp,PPK

sai moravineni says:

what if the CPK value is at 5.63 and Ppk at 2.58 but the xbar chart is having some points out of control limits.

How I should evaluate?

Kate Horbach says:

Great example about a car and garage, it is much simpler to understand!

Ivan says:

Hello, I like your articles. But it seems like you had a typo hidden:

I think you wanted to say:

BR,
Ivan

Ramana PV says:

Thank you, Ivan for the feedback, we have updated the sentence.

Thanks

Pablito Pastor Yumena says:

When do we get Ppk form OSAT?
What is the minimum Sample Size to compute the Ppk?

Pablito, tell me more of what you are thinking here. I don’t want to give people direct answers to their homework problems. I do want to help people think through these concepts.

Wiebke Zuch says:

Cp is generally referred to as Process Capability. Pp as Process Performance. In this article, Pp is however called Process Capability. Is that a typo?

Gloria Peralta says:

Is there a guide available that shows how to calculate cpk for runout on a sample?

Ramana PV says:

Hi Gloria Peralta,

Runouts are specified with a single value: a not-to-exceed value. For example, the specification for runout could be 0.0005 inches. This means that the Upper Spec Limit (or USL) = 0.0005 in and the Lower Spec Limit is obviously zero.

Assuming that we have a normal distribution, then Cpk for runout:

Cpk = Cpu = (USL – Mean)/(3 * Sigma),

where, Sigma is the rational subgroup estimate of sigma (often referred to as the short-term standard deviation).

Thanks

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