Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series B, Pt. 1, 96-107

IS SAMPLING BY VARIABLES WORSE THAN SAMPLING BY ATTRIBUTES ? A DECISION THEORETIC ANALYSIS AND A NEW MIXED STRATEGY FOR INSPECTING INDIVIDUAL LOTS

By

WILFRIED SEIDEL, Universität der Bundeswehr Hamburg

 

SUMMARY. In fundamental critique, v. Collani argued that acceptance sampling by variables is appropriate, if one is interested in the fraction nonconforming in incoming batches. We analyse this critique from a decision theoretic point of view, using a superpopulation model and loss structures that depend on the realization of individual lots. For important cost models, sampling by variables is always optimal. For other cost models it is compared to sampling by attributes; for a suitable choice of parameters, it behaves like variables sampling for large batches and automatically includes more elements of attributes sampling for small ones.

AMS (1990) subject classification. 62P30, 62N10, 62C99

Key words and phrases. Acceptance sampling, fraction nonconforming, operating characteristic, risk function, superpopulation model.

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