# Is it possible to make an educated decision using a very very small sample size?

#### ProblemChild

##### Starting to get Involved
When an inspection is complex and very costly. Is there a way to make an educated decision based on a very very very small sampling size?

For example, I have a population of 10,000 units. Based on the AQL table at level II, I suppose to inspect a lot size of 200 units.

What happens when an inspection becomes very costly. (due to complex inspections steps, high transportation cost, or inspection itself is destructive. )

Is there a "logical" way one can make an acceptance decision based on a single digit sample size in this case?

I know how it sounds, but inspecting 200 units is just impossible in this case.

Thanks

#### Mike S.

##### Happy to be Alive
Trusted Information Resource
Like another recent poster, you seem to want a treasure trove of data to be extracted from just a few samples. Don't we all! Unless you have valid reasons to believe that the homogeneity of the lot is exceptionally good, the answer is no.

Now, if your process controls are such that you do have valid reasons to believe that the lot is very homogenous, then small sample sizes can be said to be representative of the lot. I have had processes where I would use 2 samples to represent thousands of parts, and did so successfully, but only when my other process controls showed the process was in control.

Without knowing your process and process controls, we cannot answer that question.

#### Miner

##### Forum Moderator
Staff member
One thing to keep in mind is that most sampling plans were designed for binomial data (i.e., pass/fail). If you are able to collect variable data during your inspection, these sampling plans are not appropriate. You can either switch to a variable data sampling plan, or use other statistical methods designed for variable data. Either approach would reduce the sample size required.

#### Jim Wynne

Staff member
When an inspection is complex and very costly...
To complete the sentence, you need to do whatever you can in terms of process control to avoid expensive post-production inspection. Sampling is all about risk. No one here knows anything about the history of the product in question or the potential risks involved in reducing or eliminating lot acceptance sampling. You need to determine (or recognize) what bad things might happen if a given lot isn't inspected, or if a radically reduced sample size is used, and act accordingly.

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