Ppk vs Cpk - A Good, clear explanation and How Mini-Tab Handles Certain Statistics

Indices vs Volume

I don’t believe volume has an effect on the indices; at least not directly. However, volume does affect the sample size. The MIL standard clearly shows that relationship; as well as confidence tables. The number in the sub-groups (5 vs 3) and frequency of the samples (5 pcs/ 1/2 hrs vs 3 pcs/2 hrs) would thus have an effect on the indices. The more samples, the better picture you have of the process.

Nice capability form. What about where you take 30 random samples from a lot and do a study? Attached is a form I have used.

Capability Study Forms

You can use the form I provided for your example. The form may be used for sub-groups of 2 to 5 pcs. However, since your example is based on random individuals taken from the population, the form will still work. In this case you must use the Ppk index and ignore Cpk and the chart. For your example the chart must be for individuals, not X bar & R.

Ppk is based off of the sigma calculation for the population (n-1). The samples may be taken randomly from anywhere in the lot. This also means that the samples are not sequential or consecutive. Sample 19 may have been produced before sample 6.

Cpk is based off of the average of the sub-groups and the samples must be sequential and consecutive. Cpk sigma is based off of the average using R-bar/d2.

Therefore, either form will provide the correct result; however, the form you provided is incorrectly labled. Since the calculation is based off of n-1 for the population, the index should be Ppk not Cpk. Additionally, your form can only be used for this type of analysis.

It all comes down to understanding the data. (I hope I understood it correctly)

For your comparison, attached is my form using 2 sets of data from your example.

Capability Study Form


I am re-attaching the Capability Study form I submitted earlier. In reviewing the problem above, I noted an error in the Range Chart scale.

I have also added the calculation for Machine Capability Study.

The attached Capability Study Form may be used for:
- Bilateral or Unilateral tolerances
- Data from Sub-groups or Individuals
- Machine Capability using a specified Target Value

The above may be done in various combinations. The form includes several built-in demonstrations.

I hope this is helpful.

cpk.pdf

Hi Don
I am a new subscriber and don't know where to find your cpk.pdf
Appreciate if you could guide me.

ye

Try using plain english words such as " Short term" or "long term" capability

I can understand confusion about Pp, Cp, Ppk and Cpk due to different books and software use same symbols with different meaning to indicate for short term or long term capability. It is desirable to use plain english word like "short term" capability or "long term capability" to make sure that other person is on same page about interpretation.

There is again confusion regarding what to call as short term or long term. The term refers to sources of variation which influences process output. It could be raw material variation or tool wear or any other common cause variation. Short term capability generally refers to a batch produced & is expected to be more homogeneous compared to variation from batch to batch which will have higher sources of variation. Six sigma always refers to short term capability.
Due to additional uncontrollable sources of variation, long term capability is always lower than short term.
Here is some useful tips.

Cp or Pp-
1) Higher the better.
2) Considers only spread of the distribution and compares with specifications.
3) DOES NOT consider where mean value of data lies with respect target (which in many cases is mean of upper and lower specification)
3) Lower the spread, higher is the value.
4) Can not be a negative value

Cpk or Ppk
1) Also higher the better
2) Can never be higher than corresponding Cp or Pp. In limiting case it can equal corresponding Cp or Pp when mean of data coincides with target.
3) Considers where mean lies with respect to target
4) Can be negative if mean value of data lies outside the specification.

-----------Sigma value ------------Short term capability-------Long term capability
------------3.0----------------------1.0------------------------0.5
------------4.0----------------------1.33-----------------------0.83
------------5.0----------------------1.67-----------------------1.17
------------6.0----------------------2.0-------------------------1.50
To summarize above table.
a) Long term sigma= Short term sigma-1.5
b) Capability= Sigma/3

Which one of the following is a "low hanging fruit" ?
Consider two scenarios?
a) Cp or Pp= 1.07, Cpk or Ppk= 1.03
b) Cp or Pp= 2.2 Cpk or Ppk= 0.8

Making improvement is process a) is a tough job because reducing spread or variability is always difficult.
Making improvement process b) is relatively easy since spread is already low as seen from high Cp value. All that you need to do is to shift mean to the target which maintenance or skilled trade person can do quite satisfactorily.

Arvind

yetint said:

Hi Don
I am a new subscriber and don't know where to find your cpk.pdf
Appreciate if you could guide me.

ye

Click to expand...

Welcome to the Cove, yetint.

Here's the link for the file you are looking for:
https://elsmar.com/pdf_files/CPK.pdf

Re: Ppk vs Cpk - A Good, clear explanation and How Mini-Tab Handles Certain Statistic

Hi All,
I am new to this forum.I have gone thru the info given for Cp and Cpk and its very much handy. I would like to get my doubt clarified regarding estimated sigma i.e R-Bar/d2. Actually I am writing formula to calculate Cp and Cpk. Can anyone pls let me know from where should I get the D2 value in order to calculate R-bar/d2.

You have given one chart where D2 values are pre defined. Pls tell me how and on what basis those values have been defined. I need more info about D2.

Thanks one & All....
aWaiting ur reply
Ur help will be greatly appreciated

Sangisetti.Vk
tata consultancy services

Re: Ppk vs Cpk - A Good, clear explanation and How Mini-Tab Handles Certain Statistic

we actually addressed this very question in a previous thread ("Formulas for Factors d2 and d3 for range charts") but in summary:

d2 comes from a table. Any decent stats book will have such a table. There are formulas for the calculation but they are sadistic.

if you have a large sample size and can't find a table that has a d2 value for that sample size - use the standard deviation. It's a better estimator of the variation anyway...

Re: Ppk vs Cpk - A Good, clear explanation and How Mini-Tab Handles Certain Statistic

Here is a ppt. on CpK and PpK. As for how mini-tab handles stats. don't use it.

just my