Methods used to calculate Cpk value - Need help for Cpk Calculation

jerry_Malaysia

Quite Involved in Discussions
Dear all,

I am new in learning about SPC. And I noticed that there are many methods that could be used to calculate Cpk value. However, when i input the same 50 data into different methods, Cpk value obtained are different. Please refer to attached file, that i have used same set of data for 4 different types of calculation methods.

Question is,
1) Is there anything wrong with the calculation method that i use?
2) Which is the correct / more suitable method to calculate Cpk value? Why?
3) What is the reason for getting different cpk value by using different methods?

:confused::bonk:
 

Attachments

  • 4 Types of Cpk Calculations.xls
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Bev D

Heretical Statistician
Leader
Super Moderator
Re: Need help for Cpk Calculation

welcome to the cove!

first I would recommend reading some of the excellent posts on this topic (they can be found by using the search feature or by scrolling to the bottom of the page.)

In general each method is designed for a specific situation and will - by design - give you different answers. In order to know which method is the appropriate one, we would need to know at a minimum:
  • What is the process?
  • How did you sample the process? (random or structured subgroups?)
    • If a structured subgroup, what was the subgroup size?
  • Is your process in statistical control?
  • Why do you want to know the capability? are you trying to predict defect rates or are you interested in the spread of the process vs tolerance range?

there is no attachment in this post as I believe you have to hit a minimum of 5 or so posts in order to attach a file...
 

Bev D

Heretical Statistician
Leader
Super Moderator
Re: Need help for Cpk Calculation

Ah now I see - you have posted the attachment in a new thread. OK.
my original questions concerning the process and sampling scheme still apply. This is essential to knowing which method to use.

It appears that in this case you are just using some 'example' data? to explore the various formulas??

Please note that the sampling scheme is a critical element and one cannot get meaningful results by trying different schemes on already collected data. by this I mean that if you took 50 truly random samples from a completed lot and you have no ability to determine the time sequence in which the parts were made - such as by a serial number - then any attempt to group the parts into subgruops of 3 or 5 or wahtever will yield meaningless results...

Aside from subgrouping the 50 data points in groups of 5 (first two tabs) or 1 (last tab usign the Movign range approach) the reason you are gettign different results is that you are calculating Cpk for the first two tabs and the 4th (movign range) tab and you are calculating Ppk for the third tab. The difference between the two Cpk values for tab 1& 2 and the 4th tab is the subgroup size. Cpk only utilizes the within subgroup variation. when you have different subgroup sizes for the same data you will naturally get different results. Ppk uses both the within and the between subgroup variation - in other words the standard deviation of all of the data poitns regardless of subgrouping...this will naturally yield a smaller value than Cpk as the standard deviation used is always larger...
 
A

adamsjm

Re: Need help for Cpk Calculation

Bev D’s description of sampling is correct.

But, for this response I will assume that the data shown in the 3rd and 4th worksheets are sequentially plotted (i.e.: a run chart) and “real” data.
If this assumption is true, I would have to ask a couple of initial / basic questions.

1st question: Which of the four processes from which the parts were produced are you trying to calculate Cpk? (Yes, there are at least four.)

2nd question: Why would we calculate Cpk when one of these processes is not capable of meeting requirements and a process change is required?

3rd question: What is the gage error for the CMM measurement system? (first, for believing the data, second, yes, it is important to the process's capability)

4th question: Who measured what parts? The second process should be replicated, IF the Appraiser Variation is comparable to other appraisers.

5th question: I think the appraiser of the third process is biased and giving you the answers that you want. Don’t you?

Another question: Why are you averaging five samples on the first two worksheets?

Overall question for the thread --- Why do you want to calculate Cpk or Ppk anyway? If you want numbers for a form, just put one / some in. The person reading it won’t know the difference between real and imaginary indices.

These dreadful questions are being asked so that practitioners will THINK about quality before training Excel how to produce garbage. They are not to discourage anyone for pursuing a passion for excellence. We learn from our search to answer tough questions, not plug & chug.

Joe Adams
** Company name removed **
 
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bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
Re: Need help for Cpk Calculation

Bev D is correct, there is no way to provide an accurate answer to you question without understanding the process and how the measurements are taken. There is a possibility that none of the calculations are correct. (By looking at the data, a very high probability)
 
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M

M Komarmy - 2012

Re: Need help for Cpk Calculation

Adamsjm, your response to this describes exactly the problem with spc applications in today's business environment. Most process owners just care about filling in the box and reporting a quality indice without really understanding them.

Cpk is a predictive index that assumes a stable process with little or no between subgroup variation. If that is not the case, the index is not meaningful and should not be reported.

I have seen a trend in the automotive sector, especially in Europe, where software suppliers such as Q-Das have sold customers on the idea that non-normal variation is unavoidable and that capability indices can be reported using different distribution models. The have invented different distribution models and indices to describe various process outputs. Cmk, Tpk, Cgk, Po/Pok are some examples. The distribution models are mixed distributions (multimodal), folded normal, log normal, etc. They have even been successful in getting this into the German VDI specifications.

The primary issue with the Q-Das methodology is with sampling. They have no issue with collecting dependent data and from multiple sources of variation. To the manager who doesn't know any better, the numbers look great. The users allow the process gauges to collect and report reams of charts, and none of it is worth the powder to blow it to you know where.
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
Re: Need help for Cpk Calculation

I have seen a trend in the automotive sector, especially in Europe, where software suppliers such as Q-Das have sold customers on the idea that non-normal variation is unavoidable and that capability indices can be reported using different distribution models.

In many ways, I think they are on the right track in recognizing the limitations of normality. I am only aware of one rock-solid capability value - and it is because the distribution is rock-solid (and non-normal). But, typically the value of a capability number is very limited. You have to be a lottery winner to think that one number will represent an infinite number of individual values.
 
M

M Komarmy - 2012

Re: Need help for Cpk Calculation

Due to the abuses of the concept, I would prefer to do away with the reporting of indices. That is about as likely as me winning the lottery, unfortunately. The tool of spc is fairly robust to non normality if used to monitor changes in a process, particularly if multiple part samples are used. Deming warned about letting theoretical statisticians take over the use of the simple tools of spc. SPC usefulness is becoming less apparent as managers increasingly ask for checksheets or green boxes instead of striving for stable processes and reducing variation.
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
Re: Need help for Cpk Calculation

The tool of spc is fairly robust to non normality if used to monitor changes in a process, particularly if multiple part samples are used.

The tools of spc are robust to any distribution, if the correct tool is used. Some folks erroneously think that SPC and the X-bar R chart are synonymous. Could not be further from the truth. But, using statistics to guide control decisions is valid. Hence the name...perhaps?:tg:
 
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