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

P (p (j) ) denotes the probability of acceptance at p (j) and Q(p (j) ) = 1 − P (p (j) ).
...(2.2.2)
For a q point prior distribution, the cost averaged over the prior become
q∑
K(N, n) = w j K(N, n, p (j) ).
j=1
...(2.2.3)
For r = 1 and q = 2, the model is identical to the cost model developed by Hald(1965)
for discrete prior distribution for the single attribute. As discussed in section 2.2.1, we
will consider the case q = 2 i.e. the situation where we can use a two point discrete prior
distribution.
2.2.4 The regret function for the two point prior.
Starting from (2.2.2), we introduce cost functions for j = 1, 2 and for i = 1, 2, ..., r
k s (p (j) ) = S 0 +
k a (p (j) ) = A 0 +
k r (p (j) ) = R 0 +
r∑
i=1
r∑
i=1
r∑
i=1
S i p (j)
i
A i p (j)
i
R i p (j)
i
...(2.2.4)
...(2.2.5)
...(2.2.6)
Let k a (p (1) ) < k r (p (1) ) and k a (p (2) ) > k r (p (2) ). [The assumption is obviously reasonable
and the rational, one is referred to Hald (1981) ]
We now define the function k m (p (j) ) which stands for the unavoidable (minimum) cost as
for j = 1 and
k m (p (j) ) = k a (p (j) )
k m (p (j) ) = k r (p (j) )
88