Binary Data Sample Size

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• #44939

RP
Member

I’m using a gauge / no-go gauge to determine whether cavities within a product are acceptable to use or not.  Each product has 20 cavities.
My data is binary (pass/fail).  The samples will be randomly drawn from a population that is assumed to be normal.  Each of the 20 cavitieswithin each part are also assumed to be equivalent .
Is there a formula or rule of thumb that I can apply to testing these samples that will give a statistical representation of the population of whether or not they will be acceptable.

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#145164

I AM SMART
Participant

Pick at least 2, but no more than 100.

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#145464

Fontanilla
Participant

It’s not quite clear from your description of the problem what you will be doing here.  Are you implying that some sort of reject level is acceptable?  I.e. a “fail” of an individual cavity within the 20-cavity part doesn’t necessarily “fail” the entire part?  Or, are you saying that you have a 20-cavity tool that produces 20 individual parts per cycle?
There are numerous examples of acceptance sampling.  When selecting a plan, you determine your AQL or, “Acceptable Quality Level.”  There are tables you can use to determine your sample size given an AQL and lot size.  One common, but dated, table is the ABC-STD-105. In general, the rule of thumb is that the absolute size of a random sample is more important than its relative size compared to the size of the lot.  For example, if you take 5 samples out of a lot of 50 (10%) which has 4% defects, you will accept the lot of 50 about 81% of the time.   If you take 100 samples from a lot of 1000 (still 10%) which has 4% defects, you will accept the lot less than 2% of the time.
You can look up the values in a table in Quality Control textbooks or, you can use Minitab to create the probability of acceptance for you.  Model your situation based on the hypergeometric distribution if your trials are not independent and mutually exclusive or the binomial distribution if they are.
Good luck!

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#145545

Jonathon Andell
Participant

There are some statistics that can be done with discrete data like pass/fail. However, I strongly encourage you to investigate whether you can replace a go/no-go gauge with anything that shoots for the underlying continuous data. For instance, if your dimension is a diameter, consider using a tapered tube with readable markings.This will give you a number of benefits:1. You can anticipate and avert impending failures.2. You get more process information when continuous measurements are charted through time, than by counting passes and fails. This is true every time.Of course you will need to verify that your new measurement system is capable through an R&R study. However, what is gained almost always exceeds the investment.

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