Is it possible to get Pp,Ppk more than the within subgroup (Cp,Cpk's) indices?

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cyberjyothi

#1
We are manufacturer's of Battery plates.

Our sampling frequency is 1 plate (weight) once in 5 minutes in a mix of paste.Total Paste Mix run length is about 45 minutes.

Some of the times will obeserved Pp,Ppk > Cp,Cpk. Is it possible? If yes How can we interpret (with-in subgroup variation is > the overall variation) and conclude the same.

Rgds,
Jyothiswar.M
 

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caversluis

#2
I presume you are using Minitab. The overall and within capability normally are discussed a lot. See also minitabs explantation here

http://www.minitab.com/support/answers/answer.aspx?log=0&id=605

Remember that Cp/Cpk is used for long term capability studies whereas Pp/Ppk are uses for preliminary studies. Normally long term studies can take month and include alle the possible variations over time.

In some cases, this is not possible to do. For example when running in new product. In this case, you will have to use Pp/Ppk but this will be run over a shorter period of time. By doing that, wou will not have all the possible variantions and the requirements for Pp/Ppk are normally higher that for Cp/Cpk.
 

Miner

Forum Moderator
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#3
Your data is not normal. There is a large peak at 508.0, and there are more results at the integer value (#.0) than there are at the #.5 value (possible rounding by some operators?). This violates the assumptions that the capability indices are based upon, and can give odd results such as you have seen.

Regarding the previous post by caversluis, this was once true in the early days, when Ford first proposed these indices. However, today Pp/Ppk is calculated using total variation (long term), and Cp/Cpk is calculated using within subgroup variation (short term).
 
D

David DeLong

#4
Regarding the previous post by caversluis, this was once true in the early days, when Ford first proposed these indices. However, today Pp/Ppk is calculated using total variation (long term), and Cp/Cpk is calculated using within subgroup variation (short term).
I was a bit confused with your answer above since Pp/Ppk is usually short term capability studies while Cp/Cpk are long term taken from control charts and using the average range/d2. That's how I have understood it.

I took out my AIAG SPC second edition and reviewed page 207 and 208 Glossary of Terms and Symbols.

Pp The performance index, typically defined as (USL - LSL)
6 est. stand. deviations

The estimated standard deviations had a subscript "P" so I checked it out and it states "The estimate of the standard deviation of a process using the sample standard deviation of a set of individuals about the average of the set . This is an estimate of the total process variation of the process"

Cp is the same formula but the standard deviation was developed by, and I quote "The estimate of the standard deviation of a stable process using the average range of subgrouped samples taken from the process,usually within the context of control charts, where d2 factor is table in Appendix E.

I think you have it reversed about long and short term.
 
D

Darius

#5
Donald Wheeler wrote about the posibility to find such behabiur, in such case he said (more or less) that it could be blamed to the wrong subgrouping (with 5 as subgroup size looks normal).

IMHO, it could be that both numbers are escencially equal:bonk:

:notme:Remember that capability indicators are just an estimate of the real thing, as I posted before the sample size affects the confidence interval of such estimates, so escencially could be both numbers equal.

http://elsmar.com/Forums/attachment.php?attachmentid=1605&d=1070548921:magic:
 

Miner

Forum Moderator
Staff member
Admin
#6
I was a bit confused with your answer above since Pp/Ppk is usually short term capability studies while Cp/Cpk are long term taken from control charts and using the average range/d2. That's how I have understood it.

I took out my AIAG SPC second edition and reviewed page 207 and 208 Glossary of Terms and Symbols.

Pp The performance index, typically defined as (USL - LSL)
6 est. stand. deviations

The estimated standard deviations had a subscript "P" so I checked it out and it states "The estimate of the standard deviation of a process using the sample standard deviation of a set of individuals about the average of the set . This is an estimate of the total process variation of the process"

Cp is the same formula but the standard deviation was developed by, and I quote "The estimate of the standard deviation of a stable process using the average range of subgrouped samples taken from the process,usually within the context of control charts, where d2 factor is table in Appendix E.

I think you have it reversed about long and short term.
You are correct in your formulae, but not in the application of the indices.

From Minitab HELP: Cpk vs Ppk - Minitab calculates Ppk using the overall variation Both the between-subgroup and within-subgroup contributes to the overall variation. Cpk is calculated using the within-subgroup variation, but not the shift and drift between subgroups. Ppk is for the whole process. If Cpk and Ppk are the same, then the overall standard deviation approximately equals the within-subgroup standard deviation.

In short, Cp is the best that your process can do when centered and in control. Pp is what your process is actually doing long term.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#7
Donald Wheeler wrote about the posibility to find such behabiur, in such case he said (more or less) that it could be blamed to the wrong subgrouping (with 5 as subgroup size looks normal).

IMHO, it could be that both numbers are escencially equal:bonk:

:notme:Remember that capability indicators are just an estimate of the real thing, as I posted before the sample size affects the confidence interval of such estimates, so escencially could be both numbers equal.

http://elsmar.com/Forums/attachment.php?attachmentid=1605&d=1070548921:magic:
yes Wheeler wrote about this phenomenon. the OP has "chunky" data. the short term capability index is Cpk and is calculated by using the within subgroup standard deviation. The OP has s30 ingle values. His software therefore calculates the standard deviation using the range method. (actually the MOVING range) Ranges are very susceptable to chunky data - data that has very few possible values. The OP's data is chunky. possibly due to rounding...chunky data OVERESTIMATES the standard deviation particularly when you use the range instead of the standard deviation. The long term capability index is calculted using the total standard deviation (both within and between subgruop variation). in this case the total standard deviation is calculated using the standard deviation formula and is less affected by the chunky data.

I'm not sure yet that in real life the indexes are the same. there are 2 distinct lower value regions in the data. (plot it in 'time series' assuming that the data is sorted in time series!) this suggests that there is some shifting or between subgroup variation.

my question for the OP is: are these 30 sequential values or are they 30 random values? if they are random, are the data sorted vertically in time sequence??? this is critical to understanding your results and providing you the appropriate advice...

and of course previous posters are correct about the one time Ford attempt to reverse the definitions of Cpk and Ppk. Cpk is short term capability using within subgroup variation and Ppk is long term capability using total standard deviation. Ford's deviation was for a very special case and only confused people. today's software follows the standard convention not Ford's bastardization.

that said this whole thread is just one more reason why weshoudl abolish the Cpk/Ppk thing! plot your data look at your data and then think about your data!
 
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cyberjyothi

#8
Yes! The data posted here is follows sequential order(once in 5 minutes) and the date has not been rounded off. Our Gage L.C is 0.1 grams.
 
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