**Question**

I am trying to determine the sampling size using my ANSI/ASQ Z1.4 table and I wanted to get some clarification. If I am using Table II A and my Sample Size Code letter is D, what would be my sample size? If it falls on an arrow does it mean that I have to change to the next sample size based on where the arrow points?

**Answers **

From Charlie Cianfrani:

If you are using Z1.4, your sample size is selected based on your lot size. You would pick the AQL you need based on the risk you are willing to take for the process average of percent defective. It is important to understand what you are doing when using sampling plans, what they are and the protection you are trying to ensure. Thus, the important step is to determine the AQL. Then you select the sample size to provide the level of protection you are striving to ensure. It is more important to understand the theory behind the tables than to mechanically use the tables.

From Fred Schenkelberg:

Use the sample size where the arrow points. In the 2008 and 2013 versions it explains this in section 9.4, “When no sampling plan is available for a given combination of AQL and code letter, the tables direct the user to a different letter. The sample size to be used is given by the new code letter, not by the original letter.”

From Steven Walfish:

The standard sample size for Code Letter D from IIA is a sample size of 8. But depending on your AQL, a sample size of 8 would be inappropriate, so the standard has arrows to delineate alternative sample sizes to reach the target AQL. So, you sample size and accept/reject values are changed. For example, at an AQL of 0.25, you would move down to a sample size of 50, with an accept/reject of 0/1. If the lot size is less than 50, you would need to do 100% inspection. In other words, there is no sampling plan that can give an AQL of 0.25 without a minimum sample size of 50.

From James Werner:

Yes. When using Z1.4 two items need to be known, lot size and the AQL (Acceptance Quality Limit). You use Table I –* Sample size code letters* to determine the Sample size code letter based on the Lot or batch size. In the question below that was determined to be “D”. Next step is to use Table II-A to find the sample size related to the sample size code letter – D and the AQL. On Table II-A go across the table’s row for letter D until it intersect the given AQL column heading. If an arrow is in that intersection point, follow the arrow then go back to the sample size code letter column to find the actual sample size (if a up/down arrow is in there then you choose).

Example 1. Code letter is D (as in the question below). Let’s say the AQL is 0.25. Starting at code letter D, move across that row until you intersect at the AQL 0.25 column. There’s a down arrow this row/column intersection. Follow the arrow downward until the “Ac Re” reads ” 0 1″. Staying on this row go back to the Sample size code letter column and find Code Letter H and Sample size = 50. This means for the lot size with code letter D and with an AQL of 0.25 the sample size = 50 and accept the entire lot if no nonconformances were found else reject the entire lot if 1 or more nonconformance were found in the sample.

Example 2. Let’s say the Sample size code letter was determine from Table I to be “F”. Looking at Table II-A; If the AQL = 0.65, then the sample size would be 20 and the lot would be accepted zero nonconformance. But if the AQL = 0.15 then the sample size would be 80.

For more information on this topic, please visit ASQ’s website.

Yes, the Z1.4 is indexed by AQL. But we should recognize that the AQL risk is the risk experienced by the producer: the chance that a truly passing lot will fail the sampling plan. The LTPD is the risk experienced by the customer. Two distinct risks. Therefore both producer and customer should jointly understand the risks associated with selecting both AQL and LTPD.