# Attribute MSA-AIAG 4th How to calculate sample size

##### Starting to get Involved
Hello guys,

For Attribute GRR according to AIAG 4th edition, they mention the sample size determination as follows (pages 140, 141):
// Sample Size:
The question always arises: “How many samples should be used in the study?” To the dismay of most people, the answer is “enough”. The purpose
of any measurement study (variables or attribute) is to understand the properties of the measurement system.. A sufficient number of samples should be selected to cover the expected operating range (see also Chapter II Section C). With attribute measurement systems, the area of interest are the Type II areas (see Chapter I, Section B). If the inherent process capability is good (i.e., large Cp, Cpk or Pp, Ppk) then a small random sample may not have many (or any) samples in this area. This means that as the process capability improves , the required random sample for the attribute study should become larger).
In the example above, the indices were Pp, Ppk = 0.5 (i.e. an expected process performance of approximately 13% nonconformance), the sample selected was 50.

An alternate approach to large samples is a “salted sample” where parts are selected specifically from the Type II areas to augment a random sample to ensure that the effect of appraiser variability is seen.
//

Can anyone explain the way they calculate 50 samples from ppk =0.5?
And in the alternate approach, what is "salted sample", how they select sample size with this?

##### Starting to get Involved
Hello, can anyone answer the above question?
Thank you very much!

#### Bev D

##### Heretical Statistician
Super Moderator
Sorry for the late response. I thought @Miner would respond as he is an expert in the AIAG manuals. I am not, having burned them in a Wiccan ceremony upon leaving the automotive industry A few decades ago.

I really don’t know how they calculated a sample size of 50, my guess is that they used the formula for estimating a %defective of a process using a random sample with a target defect rate of 13%. Although I have no idea how they got a defect rate of 13% from a Ppk of 0.5

What I do for standard attribute inspection is to use a 2 phase - or more - approach. First I create a sample set of parts that are clearly good and bad and parts that are marginally good and bad to test teh ability of the inspector to make correct calls. If they are struggle with the marginal parts I will investigate why and try to improve the inspection conditions. (Lighting, time to view, training on what to look for, sample prep if involved, etc.) This sample size is usually fairly moderate for attribute samples as it is important to increase the number of clearly good units and marginal units such that the inspector isn’t always looking for bad units. As teh standard says this is really about usign ‘enough’. There is no real sample size calculation here. And I don’t use random samples - which is probably what the sample size of 50 is about. (Randomly collect 50 units hoping that you wil get a decent collection of good, marginal, and bad samples. I refer to not leave this to chance). Once I am confident that the inspectors have good conditions, I may create another sample set that is much larger and contains roughly the same number of good, marginal and bad units as normal production. I will have the inspectors inspect this sample set twice (3 times is overkill) under normal speed and conditions and then assess the results. If the defect is new this all might happen concurrent with startup of the inspection. I also assess the number of false rejections and passes against the severity of the defect and what I am able to tolerate.

#### Bev D

##### Heretical Statistician
Super Moderator
I almost forgot the ‘chicken and egg’ dilemma: how do you know what the process capability is if you don’t know how much error is in your inspection? MSA is intended to be an iterative engineering task, not a statistical mathematics exercise…

#### Miner

##### Forum Moderator
@Bev D Funny, as I was waiting for you to respond as you are more of an expert in the Attribute MSAs.

The answer lies in the Concerns section, item 1), of page 141, which states "There are no theory-based decision criteria on acceptable risk. The above guidelines are heuristic and developed on individual "beliefs" about what will pass as "acceptable". This is a subject matter decision - not a statistical one. (Emphasis mine)

Heuristic, or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, short-term goal or approximation (Wikipedia).

In other words, AIAG cannot justify the sample size statistically, but believes that it is sufficient for this purpose.

#### Bev D

##### Heretical Statistician
Super Moderator
@Bev D Funny, as I was waiting for you to respond as you are more of an expert in the Attribute MSAs.

The answer lies in the Concerns section, item 1), of page 141, which states "There are no theory-based decision criteria on acceptable risk. The above guidelines are heuristic and developed on individual "beliefs" about what will pass as "acceptable". This is a subject matter decision - not a statistical one. (Emphasis mine)

Heuristic, or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, short-term goal or approximation (Wikipedia).

In other words, AIAG cannot justify the sample size statistically, but believes that it is sufficient for this purpose.
If only I could like this a thousand times!

#### MValdes

##### Starting to get Involved
Thank you Miner and Bev, saying this and if the nonacceptable part is detected as bad part for the go no go gage, the sample size for the MSA can be smaller?

#### Jim Wynne

Thank you Miner and Bev, saying this and if the nonacceptable part is detected as bad part for the go no go gage, the sample size for the MSA can be smaller?
If you've already done the study and found that there is 100% agreement between the operators, why would you need to change the sample size after the fact?