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.

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.

Specification Spread vs Process Spread: Process Performance (Pp, Ppk)
Specification Spread vs Process Spread

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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Process Meets Specifications: Good Potential Performance

good potential performance
good potential performance

Process Does NOT Meet Specifications: Bad Potential Performance

Bad Potential Performance: Process Performance (Pp, Ppk)
Bad Potential Performance
This is what happens when your specification spread does not match your specification spread!
This is what happens when your process spread does not match your specification spread!

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?

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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 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.

That Process was poorly centerned! Unacceptable! An unsuccessful Process Performance (Pp, Ppk).
That process was poorly centered! Unacceptable!

Calculating Ppk

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

Actual performance Ppk: Process Performance (Pp, Ppk)
Actual performance 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.

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

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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_pop

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:

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

You would immediately discount the Variability range as we judge a good process with 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, decreasing the index.

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Comments (36)

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

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

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

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

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.

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

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?

Being a more difference between Cpk and Ppk looks like special cause exists in the process. Remove those special cause/s and again check whether any point going out of UCL/LCL.
If then there is marginal difference between Cpk and Ppk and any point still showing out of control limit then it it should be acceptable since absolute values of Cpk and Ppk are much higher than six sigma level.

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

This is what happens when your specification spread does not match your specification spread!

I think you wanted to say:

This is what happens when your process spread does not match your specification spread!

BR,
Ivan

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.

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?

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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