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Chapter 15: B. Sampling 153
Acceptance Sampling by Attributes
Acceptance sampling by attributes is generally used for two purposes: 1) protection
against accepting lots from a continuing process whose average quality deteriorates
beyond an acceptable quality level, and 2) protection against isolated lots
that may have levels of nonconformances greater than can be considered acceptable.
The most commonly used form of acceptance sampling plan is sampling by
attributes. The most widely used standard of all attribute plans, although not necessarily
the best, is ANSI/ASQ Z1.4-2003. The following sections provide more
detail on the characteristics of acceptance sampling and a discussion of military
standards in acceptance sampling.
Acceptance Quality Limit
Acceptance quality limit (AQL) is defined as the quality level that is the worst tolerable
process average when a continuing series of lots is submitted for acceptance
sampling. This means that a lot that has a fraction defective equal to the AQL has
a high probability (generally in the area of 0.95, although it may vary) of being
accepted. As a result, plans that are based on AQL, such as ANSI/ASQ Z1.4-2003,
favor the producer in getting lots accepted that are in the general neighborhood of
the AQL for fraction defective in a lot.
Lot Tolerance Percent Defective
The lot tolerance percent defective (LTPD), expressed in percent defective, is the
poorest quality in an individual lot that should be accepted. The LTPD has a
low probability of acceptance. In many sampling plans, the LTPD is the percent
defective having a 10 percent probability of acceptance.
Part III.B
Producer’s and Consumer’s Risks
There are risks involved in using acceptance sampling plans. The risks involved
in acceptance sampling are 1) producer’s risk and 2) consumer’s risk. These risks
correspond with type 1 and type 2 errors in hypothesis testing. The definitions of
producer’s and consumer’s risks are:
Producer’s Risk (`). The producer’s risk for any given sampling plan is the
probability of rejecting a lot that is within the acceptable quality level (ASQ 2005).
This means that the producer faces the possibility (at level of significance a) of
having a lot rejected even though the lot has met the requirements stipulated by
the AQL level.
Consumer’s Risk (a). The consumer’s risk for any given sampling plan is the
probability of acceptance (usually 10 percent) for a designated numerical value of
relatively poor submitted quality (ASQ 2005). The consumer’s risk, therefore, is
the probability of accepting a lot that has a quality level equal to the LTPD.