# Sampling Plan - Testing by Attributes

##### Registered
I am curious if anyone can clarify terms used in Attribute C=0 testing?
I am using an acceptance sampling plan based on Attribute C=0 testing to receive medical device lots into inventory.
The terms in question are TEST and DEVICE.
I have a single attribute TEST required to demonstrate that my DEVICE is acceptable.
As example, I pull 5 DEVICES randomly from the lot and perform the attribute TEST on all 5 DEVICES.
May I alternatively repeat the attribute TEST 5 times on a single random DEVICE?

##### Involved In Discussions
with no other information, the answer is no.

Imagine a bag of 100 balls with 10 white and 90 black. A sampling plan for receiving this product is to test 5 devices. This plan is intended to have confidence that the number of white balls is less than 5%. You pull one ball out, it happens to be black. After verifying the ball is black you put it back in the bag but don't let go of it and pull it back out. At this point you'd say you pulled two balls out and both were black. You repeat this 3 more times and get a result that 'you pulled 5 balls and 0 were white' and we have the necessary confidence the defect rate of the batch meets expectations (i.e. is below a certain level). Hopefully you can see why this is not the right way to classify the batch.

Instead what should happen is you remove the first ball, it happens to be black. You do not replace that ball, you put your empty hand back in the bag and pull a new ball. Repeat until you have removed 5 balls from the bag and count the number of white balls. If its 0 (i.e. c=0) the batch can be considered conforming.

The sampling plan is designed that after you pull 5 different balls (without replacing them) and see 0 white balls, you can have a certain level of confidence the number of white balls in the batch is less than X.

In this example, the Device = Ball, Test = assessment of the color.

#### Bev D

##### Heretical Statistician
Super Moderator
D_addams is correct. Think of these things as being the same:
Test (electrical, mechanical, chemical…), inspection (visual, go/no-go gage, microscope, optical comparator…), measurement (CMM, calipers, ruler, ph meter…), etc. you are doing something to assess the acceptability of something
Device, unit, thing, part, item, object.

The sample size n, of an attributes ‘test’ is the number of things (devices, units, parts, objects) to be tested. One thing - one test per thing.

##### Registered
Very clear - well described.
For context, the reason I asked is we typically evaluate small lot sizes ~10 devices at a time.
We used to test a "rule of thumb 10%" but now use a Zero Acceptance Number Sampling Plan.
So, we now test 5 devices per lot instead of 1.
It was suggested that repeating the Attribute test 5 times on the 1 device would suffice.
Much appreciated for the clarification!

#### Bev D

##### Heretical Statistician
Super Moderator
Are these devices that are functionally tested such that failures may be intermittent? Otherwise I can so no logic for testing a single device 5 times.

##### Registered
Correct Bev. The Attribute TEST performed on the DEVICE is to take a sample reading. As example, if you were to turn on an Infrared Thermometer and take a non-contact dermal temperature reading.

#### Bev D

##### Heretical Statistician
Super Moderator
OK just for clarity and completeness if you have a known or highly suspect potential for intermittent failures you can use a ‘nested’ sample size. The first sample size (n1) is based on the intermittency rate. This will be the number of times each individual device is tested. The second sample size (n2) is the number of devices to be tested n1 times. The formulas for the two sample sizes are the same - only the RQL (or AQL if you must) is probably different. So the acc/rej numbers may be also different

For example you may test 10 devices (n2) 5 times each (n1).

N1 and n2 are independent. There is statistical foundation for combining or mixing the sample sizes.

It doesn’t sound like this is the case for you.