# Sampling Plan

Six Sigma – iSixSigma Forums Old Forums General Sampling Plan

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• #35990

Brenda Gomez
Participant

Greetings,
We are planning introduce a sampling plan for failure analysis. We have an electrical tester that sorts 100%  the product.  However, we need to do a failure analysis to determine the type of failure (Poison). This analysis needs to be done using a sample because there is not enough resource. We have a failure rate of 6% that represents about 400 defective pieces.
Could you please help to determine how calculate the sample size?

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#102542

Cone
Participant

What is the capability of the available resource?
A more important question would be which failures to look at. If you have a known failure mode vs a new failure mode, which would you prefer to have analyzed?

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#102545

Brenda Gomez
Participant

Currently,  we are analizing around 50 pieces for this product. The technician takes 50 pieces and classifies them within the well-known defects. , if he finds a new defect, it should be included in the classification list.

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#102556

Gabriel
Participant

You are not providing enough information to answer your question.
If I tell you “take 2” you will say “not enugh” and if I say “inspect all” you will say “too much”.
So, what condotions do you need met to say that the sample size is big enough?

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#102585

Brenda Gomez
Participant

My concern is that I need to get a representative sample for attribute data. For example, what is the chance that the percentage of those pieces that had the defect “A” does not match the percentage in the entire population?
I know that the more pieces we analyze, the more likely we are to get a representative sample. However, we have limited resources so we need to determine exactly which will be a confidence sample size.
As additional information : The electrical tester sorts 100% of the product and we take a sample to make the failure classification. We have 5 different categories for defects.

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#102586

Brett Allen
Participant

You could use the formula for sample size:
np>5
where n = sample size to inspect
p = probability of (in you case finding a failure) = 0.06
Therefore n > 5/p
n> 5/(0.06) = 84 samples.
Brett.

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#102590

Gabriel
Participant

This number will work (together with a p or np chart) if you want to see if the overall defectives rate is significantly different from the usual rate, but not to see if each of the defect types remains as usual.
To do so, I would use the same formula (np>5) but using the p of the least frequent defect you want to follow.
For example, if the least frequent defect you want to follow-up hapens in 2% of the parts, then you would take 5/0.02=250.
Sample sizes are too big for attribute inspection because attribute data provides little information (compared with variable), specially when the defect you want to follow has few occurrences. If this number is too big you may want to try another approach:
You can make an initial large investigation to analyze what the “usual” number of defects of each type is. For that you need to make “parallel” p or np charts for each defect type, and also a p or np chart for the total defectives (you’ll see why). You will need a large sample for each group of parallel points (250 in my previous example) and you will need to collect at least 10 subgroups. Then you can plot the control limits for each defect type. It will be hard work, but it is an investment that you do only once.
Then you can keep only the p chart of the total defectives rate (regardless of the defect type) with subgroups of let’s say 100 individuals (i.e. every 100 individuals inspected in the 100% check you draw a point), and make no sampling as long as the defectives rate ramins in control. This will be not a great deal: You already have the 100% chck, you only need to fraw the points in the control chart for the total defectives rate for which you already defined the limits in the previous step. Only in those cases where you see that the defectives rate is out of control you would make further investigation, taking all rejected parts and analyzing the distribution of the defect types, and comparing each rate for each defect with the control limits for it. More than sure you will find at least one type of defective that show out-of-control in its specific chart, and that will be the one that caused the out-of-control signal in the chart of the overall defectives rate. Then you would go and investigate why this specific defect increased to an unusual level, find the causes, eliminate them, and enjoy never suffering the same problem again. Well, that’s at least in theory. It is harder to do than to write it.
These are all just ideas. Do not take them as the magic soution without an anlaysis to see if they fit your needs and your scenario.

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