Accept/Reject (Ac/Re) Numbers (ISO 2859-1) Confusion

Mark Meer

Trusted Information Resource
Hi Everyone,

Just looking over ISO 2859-1, and according to 11.1.1 (Single sampling plan), the criteria for acceptance is:
"...If the number of nonconforming units found in the sample is equal to or less than the acceptance number, the lot shall be considered acceptable."

and criteria for rejection is:
"...If the number of nonconforming units is equal to or greater than the rejection number, the lot shall be considered not acceptable."

Why the two values (acceptance number, Ac, and rejection number, Re)?
Shouldn't a single number suffice, because a lot cannot be both accepted and rejected (i.e. if it meets acceptance criteria it is, by definition, not rejected (and vice versa)).

This is confusing me in those cases where there is a gap > 1 between the Ac and Re values.
For example, from the single-sampling, reduced inspection table (Table II-C), under AQL=4.0, Sample-size code = G, the Ac/Re is listed as 1/4.

In this example, what happens if the number of nonconforming units is found to be 2. In this case:
- The acceptance criteria has not been met (#NC units > Ac)
- The rejection criteria has not been met (#NC units < Re)

So how are you intended to proceed in this case?
 

Bev D

Heretical Statistician
Leader
Super Moderator
A single sampling plan requires that the reject number is the accept number + 1.

If there is a gap between Ac and Re you do not have a single sample plan. When the defect count is between Ac and Re you must sample again...
 

Statistical Steven

Statistician
Leader
Super Moderator
Hi Everyone,

Just looking over ISO 2859-1, and according to 11.1.1 (Single sampling plan), the criteria for acceptance is:
"...If the number of nonconforming units found in the sample is equal to or less than the acceptance number, the lot shall be considered acceptable."

and criteria for rejection is:
"...If the number of nonconforming units is equal to or greater than the rejection number, the lot shall be considered not acceptable."

Why the two values (acceptance number, Ac, and rejection number, Re)?
Shouldn't a single number suffice, because a lot cannot be both accepted and rejected (i.e. if it meets acceptance criteria it is, by definition, not rejected (and vice versa)).

This is confusing me in those cases where there is a gap > 1 between the Ac and Re values.
For example, from the single-sampling, reduced inspection table (Table II-C), under AQL=4.0, Sample-size code = G, the Ac/Re is listed as 1/4.

In this example, what happens if the number of nonconforming units is found to be 2. In this case:
- The acceptance criteria has not been met (#NC units > Ac)
- The rejection criteria has not been met (#NC units < Re)

So how are you intended to proceed in this case?

For reduced sampling, there is a footnote (dagger) at the bottom of the table that states "If the acceptance number has been exceeded, but the rejection number has not been reached, accept the lot, but reinstate normal inspection (see 10.1.4)"

Hope this helps
 

Mark Meer

Trusted Information Resource
For reduced sampling, there is a footnote (dagger) at the bottom of the table that states "If the acceptance number has been exceeded, but the rejection number has not been reached, accept the lot, but reinstate normal inspection (see 10.1.4)"

Thanks Steven! Missed the footnote.

I checked the other tables, and indeed any Re - Ac > 1 differences are only present in the reduced inspection table, which makes perfect sense given this explanation. The >1 difference acts as an additional switching rule - cool!

:agree1:
 
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