# Alpha and Beta in the Sampling Plan for ISO 2859 & ISO 3951

#### ifserav

##### Involved In Discussions
Hi to everibody?

Do you know waht are the alpha and beta in the sampling plan for ISO 2859 and ISO 3951?

Sergio ?vila

#### ifserav

##### Involved In Discussions
alpha and beta in validation sampling plan

Hi to everibody?
I want to know if there is a requirement about apha and beta when you develpo a sampling plan for validation of a process?

Sergio ?vila

#### Bev D

##### Heretical Statistician
Super Moderator
Re: Alpha and beta for ISO 2859 & ISO 3951

First the referenced ISO standards are intended for acceptance sampling of material and are NOT appropriate for determining the sample sizes for validation of processes (or of products)

To answer your direct question in terms of acceptance sampling:
• alpha is 1-probability of rejecting a lot when it is at the acceptable defect rate (AQL); in other words it is the probability that the sample size will contain an unusually high number of defects resulting in the conclusion that the process is more defective than it actually is.
• beta is 1-probability of accepting a lot when it is at the rejectable defect rate (RQL - aslo called UQL or LQ); in other words it is the probability that the sample size will contain an unusually low number of defects resulting in the conclusion that the process is less defective than it actually is.

#### Statistical Steven

##### Statistician
Super Moderator
Re: Alpha and beta for ISO 2859 & ISO 3951

I believe AQL is at 95% so alpha=0.05 and LQ is at 10% or a beta of 0.10.

First the referenced ISO standards are intended for acceptance sampling of material and are NOT appropriate for determining the sample sizes for validation of processes (or of products)

To answer your direct question in terms of acceptance sampling:
• alpha is 1-probability of rejecting a lot when it is at the acceptable defect rate (AQL); in other words it is the probability that the sample size will contain an unusually high number of defects resulting in the conclusion that the process is more defective than it actually is.
• beta is 1-probability of accepting a lot when it is at the rejectable defect rate (RQL - aslo called UQL or LQ); in other words it is the probability that the sample size will contain an unusually low number of defects resulting in the conclusion that the process is less defective than it actually is.

#### ifserav

##### Involved In Discussions
Re: Alpha and beta for ISO 2859 & ISO 3951

Thank you so much, what i want to know is if are there any guidelines to stablish alpha and beta for a validation sampling plan and what are the values of alpha and beta in the ISO norms?

#### Bev D

##### Heretical Statistician
Super Moderator
Re: Alpha and beta for ISO 2859 & ISO 3951 I believe AQL is at 95% so alpha=0.05 and LQ is at 10% or a beta of 0.10.
This is the default level used since the Mil-Std was developed when AQL was deemed more important than RQL since producers wanted to be more biased towards accepting than rejecting. (yes the Mil-Std was as much a result of negotiation as it was statistics)

There is no need to stay at those levels. The severity of the effect of the defect and it's usage should drive the choice of alpha and beta...

#### Statistical Steven

##### Statistician
Super Moderator
Re: Alpha and beta for ISO 2859 & ISO 3951 This is the default level used since the Mil-Std was developed when AQL was deemed more important than RQL since producers wanted to be more biased towards accepting than rejecting. (yes the Mil-Std was as much a result of negotiation as it was statistics)

There is no need to stay at those levels. The severity of the effect of the defect and it's usage should drive the choice of alpha and beta...
Bev -

I am in violent agreement  Problem is that the standards (ISO, MIL-STD, etc.) are tabled for AQL at 95% and LQ at 10%. It kinda sticks!

#### Bev D

##### Heretical Statistician
Super Moderator
Re: Alpha and beta for ISO 2859 & ISO 3951

Thank you so much, what i want to know is if are there any guidelines to stablish alpha and beta for a validation sampling plan and what are the values of alpha and beta in the ISO norms?
So Steven answered the "ISO norms" for alpha (5%) and beta (10%). But many people are realizing that these 'defaults' or 'norms' aren't always useful for their application. The real choice depends on the severity of the effect. for example a defect that could kill someone should have a very low beta because even small defect rates are not acceptable.

HOWEVER, I must stress again that acceptance samplign methods are NOT applicable for validation of processes. the sample size will be much too small because the question that is being asked by the statistics is very different.

Acceptance sampling is intended to have only a few defects found in the sample to make a decision on whether the lot is most likely at or below (or above) a specified defect rate.

Validation testing is intended to determine with some precision the actual defect rate and that requires larger sample sizes so a different formula is used. You still need to determine alpha and beta risks, but these values go into a different formula.

Can you clarify / describe what you are trying to do?

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#### ifserav

##### Involved In Discussions
Re: Alpha and beta for ISO 2859 & ISO 3951

Thank you so much, how do you determine the actual defect rate?