Multiattribute acceptance sampling plans - Library(ISI Kolkata ...

We take this case and the case of the finished garment verification cited as an example
in chapter 1.1, where the inspection is done at the producer’s end before shipment of the
product. We attempt to adopt the MIL-STD-105D for both the cases. The sampling plans
employed using MIL-STD-105D inspection level II for normal inspection for a typical lot size
are worked out as given in the following table.
Table 1.2.2 Sampling plans using MIL-STD-105D (normal inspection,
inspection level II )
Product Lot Size Sample Size Defect category
Critical Major Minor
AQL c AQL c AQL c
Plastic container 15,000 315 0.15% 1 1.0% 7 4% 21
Garment 50,000 500 0.1% 1 1% 10 2.5% 21
The Producer’s Risk
As applicable to multiattribute case, the consumer wants to make reasonably sure that
the product of satisfactory quality is accepted and he therefore chooses an AQL as p =
(p 1 , p 2 , ..., p r ) say, and a small risk Q(p ) = α, where Q(p ) denotes the probability of
rejection at p. Since the lot is accepted only when the acceptance criterion is satisfied for
all the attributes independently, the producer’s risk will always be more than the target
producer’s risk for the individual characteristics in the MIL-STD-105D. In these examples,
we compute the overall producer’s risk as more than 10.5% for the first set of plans (plastic
container) and around 22% for the second set of plans (garment). It would appear that we
are asking for the moon from the producer.
The OC performance
Secondly, we thought it reasonable to expect that the OC function should be more sensitive
to the changes in the defect level of more important attributes, particularly, where unsatisfactory
defect level occurs due to more serious type of defects. Suppose that the defect on i
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