Sample Size for Rejected Units

V

veness

#1
Hi All,
In semiconductor industry, from the lot size of 12000 units, 600 units are rejected units in Test. Now I would like to draw sample from 600 rejected units for X-ray analysis. How many samples i should take for X-ray to conclude the defect mode in these rejected units? (Example: offpad wire bonding).

Pls advice.

Thanks and regards,
veness
 
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Statistical Steven

Statistician
Staff member
Super Moderator
#2
Hi All,
In semiconductor industry, from the lot size of 12000 units, 600 units are rejected units in Test. Now I would like to draw sample from 600 rejected units for X-ray analysis. How many samples i should take for X-ray to conclude the defect mode in these rejected units? (Example: offpad wire bonding).

Pls advice.

Thanks and regards,
veness
I am going to suggest three different approaches, with three different sample sizes. You need to assess which scenario fits you best.

Scenario #1

How many unique defect modes are there? If there are less than 10 modes, you can take 5 times the number of modes to estimate the percent of each mode in the defective tests. If the number of modes is higher, then you will need to test a substantial amount to ensure all modes are in the sample.

Scenario #2

You can use the square root of N+1 leading to a sample size of 26 using N=600. This would be used to test if all 26 had a defect. You can also use regular attribute sampling plans for different AQL and LTPD values if the purpose is to confirm the test with X-ray analysis.

Scenario #3

Would require doing X-ray on both the "good" and "bad" project to confirm the inprocess testing and X-ray are consistent. Since you have a 5% defective rate, you can take a sample if 50 "bad" and 50 "good" using a 2x2 contigency table. You will need to use a test like Fisher's Exact since the expected value in some of the cells will be less than 5.


Hope that helps some....
 
V

veness

#3
Hi Steven,
I seek for your further advice.

Scenario #1:

How many unique defect modes are there? If there are less than 10 modes, you can take 5 times the number of modes to estimate the percent of each mode in the defective tests. If the number of modes is higher, then you will need to test a substantial amount to ensure all modes are in the sample.
Question: How do you define "5 times the number of modes"? Any statistical theory behind?

Thanks...
 

Statistical Steven

Statistician
Staff member
Super Moderator
#4
Hi Steven,
I seek for your further advice.

Scenario #1:

How many unique defect modes are there? If there are less than 10 modes, you can take 5 times the number of modes to estimate the percent of each mode in the defective tests. If the number of modes is higher, then you will need to test a substantial amount to ensure all modes are in the sample.
Question: How do you define "5 times the number of modes"? Any statistical theory behind?

Thanks...
Veness

Failure modes are for example shorts, pits, missing components, etc. The idea of 5 times has no real statistical theory, but more a practical experience that shows for common defect modes, this works best to ensure all defects are captured in a sample. If you want a more statistically rigorous method, you can look at the probability of each defect mode and use a weighted sampling strategy.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#5
Steven's approach is very sound:

How many test failure modes are there in the 600? For each of these test failure modes, how many possible defects are there that can create the device level failure you have observed?

for each test failure mode, take 5-10 devices for each of the possible defects

then see what you get.


there really is no precise statistical formula for this. take some data, then if needed you can take more. Also ask yourself - willl a precise knwoledge of the defect type distribtuion change any action you will take to solve the problem? if not then all you need is a gross estimate that the defect occurs and a rough estimate of how frequently it occurs (often or not very often)
 
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