Sample Size Selection for Peel Strength for Variable Data using a 95%/99% Confidence

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Stijloor

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Super Moderator
#2
Re: Sample size selection for peel strength for variable data using a 95%/99% confide

A Quick Bump!

Can someone help?

Thank you very much!!

Stijloor.
 

bobdoering

Stop X-bar/R Madness!!
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#3
Re: Sample size selection for peel strength for variable data using a 95%/99% confide

How to calculate a sample size for peel strength for variable data using a 95%/99% confidence /reliability levels?
You have to be careful with physical testing. The test itself can pose significant variation versus the actual variation of the part. Gage R&R the test before jumping to an assumption that it is adequate to even provide accurate enough data itself at 95%/99% confidence /reliability levels. Otherwise, you will be chasing your tail.

Are you peel testing a tape? Is the backing significantly stronger than the peel strength (no stretching, no deformation)? The the line or interface of the peel a perfectly straight line? If not, the test may be a problem.
 

Statistical Steven

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#4
Re: Sample size selection for peel strength for variable data using a 95%/99% confide

How to calculate a sample size for peel strength for variable data using a 95%/99% confidence /reliability levels?:thanks:
If your specification is that ALL peel strength values must be within specification you use a tolerance interval to set the sample size based on the specification. The general form of the tolerance interval is

Xbar +/- K*S, where K is the coefficient for a tolerance interval (see ISO-16269-6). The K value is tabled by confidence, reliability and sample size (both one and two-sided).

If you set your specification as the interval width you can solve for K. Look up the sample size associated with that K value.
 
I

ilacatd

#5
Re: Sample size selection for peel strength for variable data using a 95%/99% confide

I haven't seen that ISO standard, however, I can confirm that Steven is correct from a couple of sources (which may be cheaper to obtain than buying the ISO standard): Juran's Quality Control Handbook, 4th Edition, discussion on pp. 23.52-56 and table of K values on p. AII.36-37. Also see Experimental Statistics, by Mary Natrella, National Bureau of Standards Handbook 91, issued 1963, pp. 2-13 to 2-15, "Statistical Tolerance Limits" and tables A-6 and A-7. The handbook also includes a formula for calculating K values for confidence / reliability percentages which are not in the tables.


I'd like to ask a couple of follow-up questions of Statistical Steven (pardon my statistical ignorance – I’m kind of a newbie):

1. Is there a way to use Minitab to perform these calculations rather than look up k in a table? Does it calculate K if you input Xbar, s, upper and/or lower spec limits, confidence level, and proportion (reliability)? I found something close in the discussion about "Acceptance Sampling by Variables - Accept / Reject Lot", which mentions the Xbar +/- K*s formula, but does not give you the option of inputting the desired confidence / reliability factors.


2. There seems to be a danger in calculating K just based on my best guess of the standard deviation from limited data. If I underestimate the true standard deviation of the population, and I start making parts and running tests, then if my future sample standard deviations are unexpectedly large, I might have to reject the lot and fail the test. It occurred to me that one way to handle this is to calculate a confidence interval of the standard deviation, to the desired level of confidence, in this case 95%, and then use the upper bound of the interval for the standard deviation in my K value calculations. Is this correct? This way I build in a safety margin, so the chance of future lots failing is only 5%.

Any insight you have would be appreciated. Thanks.

Ari
 

Statistical Steven

Statistician
Staff member
Super Moderator
#6
Re: Sample size selection for peel strength for variable data using a 95%/99% confide

I'd like to ask a couple of follow-up questions of Statistical Steven (pardon my statistical ignorance – I’m kind of a newbie):
1. Is there a way to use Minitab to perform these calculations rather than look up k in a table? Does it calculate K if you input Xbar, s, upper and/or lower spec limits, confidence level, and proportion (reliability)? I found something close in the discussion about "Acceptance Sampling by Variables - Accept / Reject Lot", which mentions the Xbar +/- K*s formula, but does not give you the option of inputting the desired confidence / reliability factors.

In Minitab 16 under Stat > Quality Tools > Tolerance Intervals you can put in summary statistics and get the tolerance intervals, though it seems to only calculate the 2-sided.
2. There seems to be a danger in calculating K just based on my best guess of the standard deviation from limited data. If I underestimate the true standard deviation of the population, and I start making parts and running tests, then if my future sample standard deviations are unexpectedly large, I might have to reject the lot and fail the test. It occurred to me that one way to handle this is to calculate a confidence interval of the standard deviation, to the desired level of confidence, in this case 95%, and then use the upper bound of the interval for the standard deviation in my K value calculations. Is this correct? This way I build in a safety margin, so the chance of future lots failing is only 5%.
The ISO standard tables give K for known and unknown S. In general you are correct that under estimating the standard deviation can be dangerous, but the same goes for any calculation of sample size or power. After collecting your samples you can go back and recompute the actual confidence and reliability based on the observed S. If the risk is still acceptable, you are fine. I would NOT use the confidence interval on the variance. Remember that the CI for variance would be at 95% and 95% confidence for the TI gives you an effective 90% overall confidence.

Any insight you have would be appreciated. Thanks.

Ari
 
I

ilacatd

#7
Re: Sample size selection for peel strength for variable data using a 95%/99% confide

Thanks very much, Steve. I checked Stat, Quality Tools, Tolerance Intervals in my Minitab 16 demo version, and they now they include upper and lower bound as well as two-sided. I guess they're getting better. But what I meant to ask was this: Is there any way to obtain the sample size in Minitab instead of looking it up in the ISO standard or other table (by first calculating K using Xbar, s, and the spec limits)? Maybe that's under sample size and power determination? I need to check Minitab help, I suppose, and learn how to use that. I just checked it out, and I didn't see fields for entering the spec limits.

Thanks for the tip about the compound effect of stacking confidence level upon confidence level - evidently you have to multiply the two. So if you want to end up with 95% overall confidence, you have to use 97.5% for the confidence interval for the standard deviation, and 97.5% for the confidence level when looking up K in the tables (and there is no column of K values for 97.5% confidence, which makes that difficult).

I'm curious about the ISO values of K for known vs unknown S. I would guess the K values are higher for unknown S - is that right? If so, then the tables of K based on unknown S already include the safety factor I was looking for, so I can trust the sample size indicated, as long as my estimate for S is reasonably good (whatever that means).
 
B

Barbara B

#8
Re: Sample size selection for peel strength for variable data using a 95%/99% confide

Minitab doesn't provide a sample size calculator depending on tolerance limits, but the menus in "power and sample size" could help with a little bit of prework:
  1. Select the parameter which is used to determine the sample size (e.g. mean or std deviation or proportion nonconformance)
  2. Calculate the critical difference:
    • for mean: how much could a mean differ until it is too much?
    • for std deviation: How much could the ratio of actual std. deviation to new std. deviation differ until the new variation is too different?
    • for proportion: what increase in the proportion nonconformance should be detected?
  3. Choose alpha (default 5%) and power (1-beta, value depends on the consequences of a false decision if quality is bad)
  4. Select the statistical test (e.g. 1t-test for mean differences, 1 variance for standard deviation/variation, 1P-test for proportion tests).
    E.g. for a 1t-test fill in
    • sample size: [leave this blank, sample size will be calculated]
    • difference: value for critical difference (see list above)
    • power: value for minimal power (1-beta)
    • If you want to assure only one-sided differences: use a one-sided option as Alternative Hypothesis (you'll find this under the "Option"-button).
  5. Press OK :)
You can find additional informations about sample size calculation in the thread Sample size for Design Verification / Design Validation (even if FDA requirements aren't an issue for you).

Hope this helps :bigwave:
 

Statistical Steven

Statistician
Staff member
Super Moderator
#9
Re: Sample size selection for peel strength for variable data using a 95%/99% confide

But what I meant to ask was this: Is there any way to obtain the sample size in Minitab instead of looking it up in the ISO standard or other table (by first calculating K using Xbar, s, and the spec limits)? Maybe that's under sample size and power determination?

I'm curious about the ISO values of K for known vs unknown S. I would guess the K values are higher for unknown S - is that right? If so, then the tables of K based on unknown S already include the safety factor I was looking for, so I can trust the sample size indicated, as long as my estimate for S is reasonably good (whatever that means).

I attached a spreadsheet that gives the K-values for n=3 to 100. You can always expand the table. It is based on the NIST approach.

You are correct the K values for unknown S are higher to incorporate the variation in estimating S.
 

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