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

ma β (a 1 , a 2 , ρ) = m ′ ...(1.3.14)
construction of fixed risk C kind plans for r =2 as demonstrared is simple. No attempts are
made to investigate the case r > 2. The approach will be similar in essence, but numerically
the problem is sure to turn clumsy for r > 2
1.3.4 Construction of A kind plans of given strength
In this case we want to satisfy the equations :
P A(a 1 , a 2 ; np 1 , np 2 ) = 1 − α
P A(a 1 , a 2 ; np ′ 1, np ′ 2) = β
Restricting to the situation where p 1 /(p 1 + p 2 ) = p ′ 1/(p ′ 1 + p ′ 2) = ρ , for a given ρ we define
ma P (a 1 , a 2 , ρ) as the value of m satisfying the equation P A(a 1 , a 2 ; mρ, m(1 − ρ)) = P.
We must have n, a 1 , a 2 such that,
ma 1−α (a 1 , a 2 , ρ) = m
Introducing the auxiliary function Ra(a 1 , a 2 , ρ, α, β) = ma β (a 1 , a 2 , ρ)/ma 1−α (a 1 , a 2 , ρ),
we note that ma P (a 1 , a 2 , ρ) is an increasing function of a 1 and a 2 , Ra(a 1 , a 2 , α, β, ρ) is a
decreasing function of a 1 and a 2 and We obtain the smallest a 2 = a ∗ 2 for which,
then find a ∗ 1 such that
Ra (0, a ∗ 2 − 1, ρ, α, β) > p ′ /p ≥ Ra(a ∗ 2, a ∗ 2, ρ, α, β)
...(1.3.15)
Ra(a ∗ 1 − 1, a ∗ 2, ρ, α, β) > p ′ /p ≥ Ra(a ∗ 1, a ∗ 2, ρ, α, β)
...(1.3.16)[5pt]
To facilitate the above tasks we may construct a table containing
a 1 , a 2 , ma β (a 1 , a 2 , ρ), ma 1−α (a 1 , a 2 , ρ) arranged in descending order of Ra(a 1 , a 2 , ρ, α, β) for
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