# Destructive Test Sample Size Reduction

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#### Aileen84

Hi! Been browsing the forum hoping I'd be able to find help on this.
But, unfortunately wasn't able to find one.

So, I hope someone can help me on the right mathematical approach to reduce destructive tests sample size.

Example: We get 30 readings per unit and perform it on 3 units. Total of 90 readings.

Now, we want to reduce this sample size - but how? how many readings in a unit? how many units?

#### Bev D

##### Heretical Statistician
Super Moderator
Can you provide more information? What characteristic or property are you measuring? What is your sampling plan: How many pieces in a lot? Do you take your 3 pieces randomly from a lot or beginning, middle, end?

This will help us give you more directly useful advice

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#### Aileen84

Hi Bev D! Thanks for your time. We are taking ball shear testing. Three units in a lot are taken randomly. The 30 readings in a unit are also taken randomly. We would like to propose to management for sample size reduction. Now, we are still on planning stage and thinking of how to approach our study.

We have already six months data of this sampling scheme. So far no failure observed.

I hope you can help at how to do this study. Thanks again!

#### Bev D

##### Heretical Statistician
Super Moderator
can you post your data? this i sreally the only way to help you other than vague general descriptions of things you can do.

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#### Aileen84

Hi Bev D! Let me arrange my data and send to you once done. Thanks for the time!

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#### Aileen84

Hi Bev D and everyone else!

I have attached here sample data on one of the characteristics we are also measuring. Whatever approach identified will be followed to all other characteristics (I suppose).

Characteristic/Test: Mechanical pull Test of pins
Unit:gmf
Lower Specs Limit: 10 gmf (one-sided specs, higher the better)
Upper Specs Limit: N/A
Current Sampling Method: 30 pins per unit per lot, 3 units (TOTAL: 90 readings per lot)
Lot Size: 2000 units
Note: There are already 6 months data using this sampling method

We want to reduce sample size. Help needed:
1. How can we use our current 6-month data to justify reduction and propose new sampling scheme (i.e. # of pins/unit, #units/lot).
2. If we can't use current data, what data gathering should we do and analysis method to have acceptable sample size?

I've been reading alot about sample size determination but I don't know how to apply the concepts in this scenario.

This would great help in unit scrap cost and productivity. Thanks in advance!

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#### supreecha

Let's me to clarify the only formula you need is the one you gave us this :
n =(1.96 x SD)/Error))2

Where n is the sample size , SD.is standard deviation and error is Delta /or whatever you want to refer it as.

Designing an X-R Chart
Sampling Frequency - ARL
A good way is to start evaluating sampling frequency statistically using Average Run Length (ARL) and finally weigh the results with sound engineering judgement.
Recall that:
For a process that is in-control:

For a process out-of-control:

Sampling Frequency: In-Control ARL
For the X-chart with 3s limits, a = 0.0027
Therefore, in-control ARL = 1/0.0027 = 370.
This means that if the process
remains unchanged, one
out-of-control signal will be
generated every 370 samples.
If the sampling interval is 1 hr,
one false alarm will be seen
every 370 hrs typically.

Sampling Frequency: Out-of-Control ARL
Now suppose the process has drifted by 3s.
Probability of X still within the 3s limits = 0.5
Thus, out-of-control ARL = 1/(1 - 0.5) = 2.
This means from the time the
process shifted, the chart needs
2 samples to detect the shift.
If the sampling interval is 1 hr,
Average Time to Signal (ATS)
or exposure is 2 hrs typically.

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#### supreecha

Ex. II: Management has the following concerns with
regards to implementing control charts at the shop floor:

1.False Alarm:
Not more than 1 false alarm for every 240 hrs of production.
2.Exposure:
Not more than 3 hrs exposure if process has shifted.
Allowable Shift:
From historical data, Cp ? 2.2.
Min customer requirement, Cpk ? 1.33

Design an appropriate X bar-R chart to meet the above constraints.

Ex. III:

After some time, the factory decides to switch to 12 hrs of production per day.

Tolerable false alarm:
Average 1 false alarm per month (30 days)

What changes do you need to make to the charts you have designed in Example 2 ?

#### Bev D

##### Heretical Statistician
Super Moderator
OK let's try a simple approach first; plot your data in a multi-vari chart.
I always start with a plot of the data as it tell me so much more than any statistical analysis.

I have attached a plot for you to review.

Now we don't have all of the six months of data just 3 lots BUT those 3 lots are pretty capable. The first real observation I have is that the process is not homogenous (within unit variation is NOT representative of the between unit variation) so traditional SPC is NOT appropriate.

I do have a viable solution for you but I need to take some time and work with the data a bit. I will get back to this on Monday.

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#### Murphys Law

Aileen - take a big step backwards and think about what you are controlling here. Your ball shear test assures your solder ball attach process.

Go back and look at the amount of failures, you've had and I'll bet you never had any or if it was, it was special cause such as units that have a fine solder ball pitch. Even if your spec limit is 10gF, I bet your min readings are 2x your spec limit.

Your ball attach process is going to be influenced by your reflow process, your substrate lot and solder ball lot. Your substrate lot should come with a CoC (Certificate of Conformance) that assures pad finish, pad plating thickness, warpage etc, Your solder ball attach profile should be under SPC control and your solder ball supplier should also assure the ball diameter and alloy %'s.

Solder ball shear per assembly lot has redundancy especially as 10 - 30 assembly lots will all use the same supplier substrate lot and go through the the same reflow process + solder ball type. Thus, already you can start to reduce the amount of sampling by doing it on a per substrate lot basis instead of a per assembly lot run.

Carry on going with your research and I would be sure that if the package technology is mature and has a good track record of ball off, you can group this by BGA family / substrate supplier and you can start to get coverage by smarter sampling on a family basis. - device x,y and z that use same substrat supplier and design rule can be grouped together. It is quite acceptable to control SBS (Solder ball shear test) on a package family basis where SBS is sampled per day, per shift or whatever.

Be aware in too much generality as there will be some devices more susceptable than others - For example, larger BGAs could be susceptable to warpage and cause a ball off issue.

You need to pay attention to solder ball - SnPb solder balls have lower solder temperatures than SAC solder ball types. Even SAC balls can have different amounts of silver in them that could require slightly different solder profiles. Pitch of the solder ball is also important - smaller ones could be more susceptable to ball off.

Plan into your sampling special cases such as low volume runner devices where your substrates may be old. If not controlled, the finish could be oxidized that could result in sub-standard ball adhesion. You may get around this if you have plasma clean but if not, old substrates should be deemed as risky if not stored appropriately.

Plan a SBS test if you shut your reflow oven down for maintenance or if you are changing it, a repeat of SBS on a larger basis.

Finally, if you are reducing blind SBS testing to a family control basis, I strongly recommened you consider SBS test as a reaction plan to your final Visual inspection. If you are seeing unacceptable amount of ball off at VM or other logpoints such as test, then it could be that your have damaged them at a back end of the lines operation that use connectors to the solder balls. Even doing a SBS in your line may not catch this as your SBS test could be done while your BGAs are still in strip format.

In summary, you have excellent opportunity to move to a predictive sampling instead of random sampling especially as in most cases, the solder ball strength will be assured earlier steps.