Measuring Capability on a One Sided Variable (Surface Finish)

ScottK

Not out of the crisis
Staff member
Super Moderator
#1
By one sided I mean the specification is X <= 32 and surface finish cannot physically go below 0.
There is no target, you have the whole 0-32 range to play with.

I suppose you could make it an attribute by just saying it has to be <=32.
But we have customers who want the data analyzed.

On a 30 piece sample it's a pretty wide, (and pretty normal) distribution so I'm getting one sided Cpk vaues in the range of .65.
But all pieces are in spec with a range of 8 - 29.

When I calculate z it comes out to better than 3.0.

How do I defend this to a customer who is hung up on Cpk?

The only way to get better is to slow down the cutting process, which will add cost.
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#2
please post your data. this will enable us to provide a very clear answer
 

Tim Folkerts

Super Moderator
#3
Perhaps, if the customer wants analysis, you could "over-analyze" the data and baffle him! ;-)

But seriously, with a Cpk of 0.65, you are just 2 st dev from the spec limits. If you really aren't getting data over the spec limits, then perhaps the data is not normally distributed and hence the Cpk does not accurately predict error rates.

Have you actually done checks for normality? Perhaps a transformation of the data would make the data closer to normal, and in the process give a better Cpk value. This is most likely "over-analysis", but if the customer wants analysis, give the customer some more in-depth analysis that better tells you about the true quality of data.

Tim F
 

ScottK

Not out of the crisis
Staff member
Super Moderator
#4
Okay - I just did a histogram. It's not totally normal. I don't have software to do a normality test.

Attached is the latest test. On this data set I'm getting a Cpk of .76 and z of 2.86.

This is a 30 piece "qual lot".
The Cpk is calculated using the STDEV function in excel... isn't this really Ppk?
I'm going along with it because I adapted it from a GE capability study spreadsheet and figured they'd know better.
 

Attachments

Bev D

Heretical Statistician
Staff member
Super Moderator
#5
the first thing I see is that you are using the incorrect numbers in your Cpk calculation.
you have Cpk = (Maximum of your data set - the average of your data set)/3*stdev of your data set.

the formula for Cpk = (USL - average of your data)/3SD

if you use the correct formula your Cpk increases to .95 and makes more sense.

(OK the whole Cpk/Ppk thing has been addressed in this forum many times. the formula you are using is Ppk, but most customers actually mean Ppk when they ask for Cpk. GE Aircraft Engines does this. they write Cpk, but hten give you the formula for Ppk. some years ago it became unfashionable to say Ppk adn people started to use Cpk as a generic term and included the modifiers short term and long term if they thought about it.)

I woudl also add that for the qual lot you do not have a Normal distribution - although with only 30 pieces that is a tough call. Were these 30 sequential pieces or were they randomly - and I mean randomly - selected from a much larger lot?

The distribution you have shown us is skewed to the rough (or right) side and may be more uniform than bell shaped. if this is true you have a 'heavy standard deviation' (oen that is larger than the distribution width would seem to warrant becasue of the heavy end). You also could very well have a perfectly conforming process with no defects but wehn you apply the Normal distribution math you get an underestimation of the Cpk...In this case - you are better off having the discussion with your customer and showing them multiple samples with no defects and the heavy tail OR simply using a different distribution than the Normal to calculate the Cpk.

and for those long term posters that know me: yes this is why I am petitioning that we abolish the Cpk/Ppk abomination....
 

Jim Wynne

Staff member
Admin
#6
Okay - I just did a histogram. It's not totally normal. I don't have software to do a normality test.

Attached is the latest test. On this data set I'm getting a Cpk of .76 and z of 2.86.

This is a 30 piece "qual lot".
The Cpk is calculated using the STDEV function in excel... isn't this really Ppk?
I'm going along with it because I adapted it from a GE capability study spreadsheet and figured they'd know better.
1) Not enough data for Cpk analysis to be meaningful. Cpk calculation assumes average-and-range data (rational subgrouping), not just a bunch of individuals. For calculating Cpk, n=30 doesn't mean much.
2) You need to control for measurement error, if you haven't done so already. Repeatability and reproducibility are often a problem with surface testing.
 

ScottK

Not out of the crisis
Staff member
Super Moderator
#7
the first thing I see is that you are using the incorrect numbers in your Cpk calculation.
you have Cpk = (Maximum of your data set - the average of your data set)/3*stdev of your data set.

the formula for Cpk = (USL - average of your data)/3SD

if you use the correct formula your Cpk increases to .95 and makes more sense.

(OK the whole Cpk/Ppk thing has been addressed in this forum many times. the formula you are using is Ppk, but most customers actually mean Ppk when they ask for Cpk. GE Aircraft Engines does this. they write Cpk, but hten give you the formula for Ppk. some years ago it became unfashionable to say Ppk adn people started to use Cpk as a generic term and included the modifiers short term and long term if they thought about it.)

I woudl also add that for the qual lot you do not have a Normal distribution - although with only 30 pieces that is a tough call. Were these 30 sequential pieces or were they randomly - and I mean randomly - selected from a much larger lot?

The distribution you have shown us is skewed to the rough (or right) side and may be more uniform than bell shaped. if this is true you have a 'heavy standard deviation' (oen that is larger than the distribution width would seem to warrant becasue of the heavy end). You also could very well have a perfectly conforming process with no defects but wehn you apply the Normal distribution math you get an underestimation of the Cpk...In this case - you are better off having the discussion with your customer and showing them multiple samples with no defects and the heavy tail OR simply using a different distribution than the Normal to calculate the Cpk.

and for those long term posters that know me: yes this is why I am petitioning that we abolish the Cpk/Ppk abomination....
D'oh.

I mis-typed when I converted from the GE based spreadsheet I'm doing the actualy study on. Thanks for pointing that out.
And thanks for the feedback.
 

ScottK

Not out of the crisis
Staff member
Super Moderator
#8
1) Not enough data for Cpk analysis to be meaningful. Cpk calculation assumes average-and-range data (rational subgrouping), not just a bunch of individuals. For calculating Cpk, n=30 doesn't mean much.
2) You need to control for measurement error, if you haven't done so already. Repeatability and reproducibility are often a problem with surface testing.
1) Yeah - I know. Yet SO many customers want to see a "Cpk"
based on a small sample. I even pointed this out on the phone that our "Real" Cpk based on the data collected in our SPC program was much better - I'd happliy send them the control charts and histograms instead. I guess they just want a number they can latch on to.
2) I saw a thread here about GR&R on surface finish testing. Seems probably best to assume this will suck.


I guess I should be dishonest next time and cherry pick the parts for the qual lots.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#9
1)


I guess I should be dishonest next time and cherry pick the parts for the qual lots.
now we're back to my rant about blind adherence to "standards"...we are forced or compelled to spend more time trying to just check the darned box off and not enough really understanding how to use statistics to HELP us and actually improving our processses. This blind application of the 'standards' force us away from what they were intended to do...
 

ScottK

Not out of the crisis
Staff member
Super Moderator
#10
now we're back to my rant about blind adherence to "standards"...we are forced or compelled to spend more time trying to just check the darned box off and not enough really understanding how to use statistics to HELP us and actually improving our processses. This blind application of the 'standards' force us away from what they were intended to do...
I will be jumping on your bandwagon.
 
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