# Pre-Design Verification - Using Continuous / Variables Data

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#### daamor

Hi all!

I've been so frustrated lately because I feel like I'm struggling with such a simple concept.

I'm used to performing design verification by choosing statistical C/ R intervals based on our risk analyses (95/90 or 95/95 usually) then selecting an attribute sample plan to test (n = 29/ 59 usually).

However, I can't for the life of me figure out how to set up the sample size for variable data collection.

Some of the specs are 2 sided. For example, lets say a pouch seal strength of 15 N +/- some number.

During Pre-DV, we may not necessarily know what our USL and LSL are yet. For most of the k-factor analysis determinations fro sample size, you have to know mean (ok lets make that 15) but standard deviation as well (how can we know this if we haven't gathered the data)?

I feel its a cart before the horse problem but I'm sure I'm missing something really critical.

1) Essentially, how do I go into a pre-DV study to collect data that will give me a statistically significant result that I can use to set specifications?
2) If we have identified specifications through other testing (challenge, etc.), and lets say we DO set the spec at 15 N +/- 1 N, how do you set up a variable sample plan at a C/R interval of 95/90 or 95/95?

#### Stijloor

Super Moderator
A Quick Bump!

Can someone help?

Thank you very much!!

#### Bev D

##### Heretical Statistician
Super Moderator
it IS a cart before the horse dilemma...however the solution is fairly simple: guess - using good engineering judgment. what do you think it should be? what do you think it probalby will be. then take some data to see how close you are. sounds silly but it?s how it?s done in real life.

First I would not use the process data to set specs. specs should be based on function for the Customer. Using process capability to ?set specs? results in throwing away good material or shipping bad material...

IF you have real specs, then the sample size is based on the confidence level and precision you want in the standard deviation estimate. This will give you the sample size needed to estimate the standard deviation and determine if any values are beyond the specifications. Both numerically and from a distributional standpoint.
I use the following formulas to determine the appropriate sample size to estimate the standard deviation. They are based on calculating the confidence interval. The confidence interval is the precision of the estimate; the greater the precision (smaller confidence interval), the larger the sample size. The greater the confidence (1-alpha), the larger the sample size.
The variation in sample standard deviations tends to follow a ChiSquare distribution for the formulas for the confidence intervals are:
Lower Confidence Interval: sqrt([n-1]s^2/chi_1-alpha/2^2)
Upper Confidence Interval: sqrt([n-1]s^2/chi_alpha/2^2)
The confidence intervals are not symmetrical like they are with means.

IN EXCEL:
Lower Confidence Interval = s/SQRT(CHIINV((alpha/2),(n-1))/(n-1))
Upper Confidence Interval = s/SQRT(CHIINV((1-(alpha/2)),(n-1))/(n-1))
You are better served to use the upper interval than the lower interval.
You must have some estimate for the ?expected? true standard deviation. This is where you guess or take a small sample to estimate it. 30-50 should be sufficient.
I use the attached spreadsheet to iterate the formulas and visualize what choice I make.

The caution here is that many processes are NOT homogenous. They can still be in statistical and practical control but they may have lot to lot or raw material to raw material shifts. SO you should spread your tests out across the components of variation in your process?

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