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

Corollary
For ρ 2 /ρ 1 > c 2 /c 1 there is only one real positive root for F (m) = 0. Note that this makes
the coefficients of m i < 0 for i = c 2 − 1, c 2 − 2, ..., c 2 − c 1 .
There are no ‘good’ C kind Plans
If we now set
ρ i+1 /ρ i = AQL i+1 /AQL i
and also try to ensure a reasonable producer’s risk α (say) then for each i, the value of
G(c i , n.AQL i ) ≥ (1 − α).
...(1.2.14)
For example we may calculate c i from G(c i , n.AQL i ) = 0.95. We get from Cornish-Fisher
expansion,
n.AQL i ≃ c i − 1.6449 √ c i + 1 + 1.5685 + 0.1962/ √ c i + 1.
It can be easily verified that for c i+1 ≥ c i in this case,
[ ] [ ]
n.AQLi+1 ci+1
>
n.AQL i c i
...(1.2.15)
...(1.2.16)
It, therefore, follows that in this case (ρ i+1 /ρ i ) > (c i+1 /c i ). Surely for some process
average this plan will fail to satisfy the condition Slope i ≥ Slope i+1 for all positive m as
evident from the corollary to theorem 1.2.1.
1.2.6 An alternative sampling scheme
As discussed the OC of C kind Plans do not possess in general the property to become more
sensitive (in the sense, defined ) to the changes in the process average of the attribute with
lower AQL. We now propose the following alternatives.
The A kind Plan
We take a sample of size n, observe the number of defectives or defects in the sample for the
i th attribute as x i for all i = 1, 2, ..., r and apply the following acceptance criterion: accept
if,
x 1 ≤ a 1 ,
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