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

a shirt with a button missing or a shirt with a wrong button), or when defects are classified
in mutually exclusive classes e.g. critical, major or minor. It would therefore be necessary
to take care of both the situations.
As stated earlier that the primary focus of the present enquiry is to examine different alternative
acceptance criteria rather than to locate an optimal plan in a given set up and
to develop search alogorithm for the mentioned purpose. We make use of the cost models
developed by Majumdar(1980), Majumdar(1990) and Majumdar (1997). The cost models
mentioned along with some elementary results in the following chapter of the part have already
been published as noted here.
2.1.4 A generalized cost model for nondestructive testing
In our case we take a sample of size n and inspect each item for all the attributes. We
observe x i ; i = 1, 2, .., r. as the number of defectives on the i th attribute. We denote the
vector (x 1 , x 2 , ..., x r ) as x. We define set A as the set of x for which we declare the lot as
acceptable. Let Ā be the complementary set for which we reject the lot. Let X i; denotes the
number of defectives on i th characteristic in the lot, i = 1, 2, ..., r.
Let the costs be
when x ∈ A
r∑
r∑
C(x) = nS 0 + x i S i + (N − n)A 0 + (X i − x i )A i
i=1
i=1
... (2.1.1)
r∑
r∑
C(x) = nS 0 + x i S i + (N − n)R 0 + (X i − x i )R i
i=1
i=1
when x ∈ Ā ...(2.1.2)
The interpretations of cost parameters are as follows: S 0 is the common cost of inspection
i.e. sampling and testing cost per item in the sample for all the characterstics put together;
x i S i the cost proportional to the number of defectives of i th type in the sample which is
the additional cost for an inspected item containing defects of i th type.
The cost of acceptance is composed of two parts; (N − n)A 0 is cost proprtional to the
r∑
items in the remainder of the lot, and another part (X i − x i )A i where A i is the cost
of accepting an item containing defective for i th attribute.
i=1
We assume the loss due to
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