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

2.1 General cost models
2.1.1 Scope
So far we have discussed the comparative features of A kind, C kind and D kind multiattribute
acceptance sampling schemes based on OC function. We now attempt to do this on
the basis of economic considerations. We first review the various cost models for dealing simultaneously
with more than one attribute. We further develop a generalized cost model as
appropriate to compare the costs of different sampling schemes proposed by us, under the assumptions
of independence of defect occurrences and also under the assumption of mutually
exclusive occurrences of defect in a lot/sample. We do this under Poisson conditions.
2.1.2 Existing cost models for multiattribute acceptance sampling
Hald [ See Chapter 0.2.7 ] has been the major contributor in the field of economic design
of acceptance sampling plans. He obtained general solutions for linear cost models under
discrete and continuous prior distribution of process average for single attribute. Hald’s
major emphasis has been on finding asymptotic relationships between n and c, and between
N and n for a single attribute single sampling plan.
The economic design of multiattribute sampling scheme was considered by Schimdt and
Bennett(1972), and further by Case, Schimdt and Bennett(1975), Ailor, Schimdt and Bennet(1975),
Majumdar(1980), Moskowitz, Plante, Tang and Ravindran(1984), Tang, Plante
and Mokowitz(1986), and Majumdar(1997). We discuss some of them and examine their
relevance in the context of our enquiries.
i) Case, Schimdt and Bennett(1975)
This model is developed under following assumptions:
(a) Each attribute is assumed to have its own sample size n i and an acceptance number c i
for i = 1, 2, ..., r; r being the number of attributes.
(b) Any item inspected on one attribute may be inspected on all other attributes thus resulting
in the total member of items sampled being maximum of (n 1 , n 2 , ..., n r ). Acceptance
is realized only if and only if x i ≤ c i ; i = 1, 2, ..., r
(c) The number of items inspected for the i th attribute is without exception n i . No screening/sorting
is made on the rejected lots.
(d) Irrespective of the lot size a rejected lot is ‘scrapped’ at a fixed cost.
(e) The sampled items are replaced in the lot by additional items and are taken from a lot
of the same overall quality as the sampled lots.
78