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I'm trying to work in the AOQ, AOQL, IOQ, RQL, LPTD, OC Curve, Dodge-Romings, when to use the ATI and AOQ curves, ASN and its curve, etc. into a one-stop-shopping, common-speak short notes that I can teach to my 9-year old. Over-simplifying is good.

I started it, but then found something that said that above AQL, the consumer will not accept defects. I was thinking that AQL is an acceptable level and that the "defects are too many for the consumer level" was RQL/LPTD/LQ. So its past the AQL that I'm getting wrapped around. The Dodge-Roming portion, ATI and ASN curve portion also needs help.

Here's my start if anyone can offer some assistance. (If there is already something like this out there, please let me know. Any progress is good.)


  • Manufacture stuff in batches (lots) that have anywhere from 2 items to 500,000+ in each lot.
  • We could inspect 100% every item, but that would take time, be costly, and if destructive tested, would destroy everything produced.
  • We could not inspect anything.
  • Bad ideas, so we do acceptance sampling.
  • Sampling for atttributes per z1.4 (MIL-STD-105 cancelled), or for variables via z1.9.
  • Using lot size and desired critical/major/minor quality level (based on customer data (some defects, no defects, etc.)), determine random sample size from each lot, and acceptance and rejection numbers.
  • Good history with few defects? Use General Inspection Level I. Bad history or critical items that demand more inspection? Use III. Mostly use II for a good mix of risk and cost.
  • For each lot, keep or reject based on one sample (single sampling), two samples (double sampling), more than two samples (multiple sampling), based on each item (sequential sampling), or a fraction of each lot (skip lot sampling).
  • OC curve plots what consumers will accept based on percentage of defects in a lot.
  • Some defects beyond the AQL passed to consumers.
  • Producer could reject an acceptable lot (left of AQL). This is Producer's Risk Point which is a Type I (Beta) error.
  • Can also be more defects than the AQL, but at some point, there will be too many for the customer will accept. That's the LTPD, the upper limit of how many defects in an individual lot the customer will tolerate. This is also called the Rejectable quality level (RQL) or limiting quality (LQ) point.
  • Customer may accept a lot that has too many defects (at or past the LTPD). Now, that risk has been passed on to them. (Consumer's Risk (alpha, Type I error).
  • The percentage of defects (quality level) between the AQL and LPTD is the Indifference Quality Level.
  • If the samples are from large lots, or streams of lots, then the OC curve (type B) will follow the binominal distribution.
  • If the samples are from an isolated lot of finite size, then the OC curve (type A) will follow the hypergeometric distribution
  • Dodg-Romig AOQL tables: When I sample, I have to determine what to do with the lots I reject. I can 100% inspect the lot and replace all the bad items with good (a rectifying inspection). Then the entire lot will have no defects. Since the rejected lots have been made perfect, it's just the accepted lots that have defects and are defining the quality. This is AOQ (Average Outgoing Quality) and if I plot this against the incoming lot quality percentage, the AOQL (Average Outgoing Quality Level) will be the highest point on the curve. For this same process (100% inpection of rejected lots), I can plot a Average Total Inspection (ATI).
  • Dodge-Romig LPTD tables:
  • ATI curve:
  • Average Sample Number (ASN):
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