Abstract
Investigations on acceptance sampling have attached rather few attention to defects inspection. As to sampling models and the corresponding operating characteristic (OC) function of single defects sampling plans, generally only typeB (process model) has been considered: sampling from a production process where the OC is conceived as a function of sample sizen, acceptance numberc, and process average number of defects per itemλ. For modern quality control, both the steadily increasing complexity of products and the need for differentiated cost calculation involve a clear demand for defects sampling in its practically most relevant form: lot-by-lot single sampling plans, where the OC (typeA, lot OC) is considered as a function of lot sizeN, sample sizen, acceptance numberc, number of defects in the lotK. The present paper develops two lot OC functions from suitable assumptions on the arrangements of the total numberK of defects over theN elements of the lot. Limiting theorems on these OC functions are used to justify to some extent the customary assumption that the Poisson process OC can serve as an approximation for typeA. The dependence of the OC functions on sample sizen, acceptance numberc, total number of defects in the lotK is described by simple formulae.
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References
Burr LW (1976) Statistical Quality Control Methods. Dekker, New York Basel
von Collani E (1990) Wirtschaftliche Qualitätskontrolle — eine Übersicht über einige neue Ergebnisse. OR Spektrum 12:123
Dodge HF (1969) Notes on the Evolution of Acceptance Sampling Plans. Parts I, II, III. J Qual Technol 1:77–88, 155–162, 225–232
Dodge HF, Romig HG (1959) Sampling Inspection Tables, 2nd Ed. Wiley, New York
Hald A (1981) Statistical Theory of Sampling Inspection by Attributes. Academic Press, London New York Toronto Sydney San Francisco
Johnson NL, Kotz S (1969) Discrete Distributions. Houghton Mifflin, Boston
Patel J, Kapadia CH, Owen DB (1976) Handbook of Statistical Distributions. Dekker, New York Basel
Rényi A (1970) Probability Theory. North-Holland, Amsterdam London
Schilling EG (1982) Acceptance Sampling in Quality Control. Dekker, New York Basel
Uhlmann W (1970) Kostenoptimale Prüfpläne, Tabellen, Praxis und Theorie eines Verfahrens der statistischen Qualitätskontrolle. Physica, Würzburg Wien
Uhlmann W (1982) Statistische Qualitätskontrolle, 2nd Ed. Teubner, Stuttgart
US Department of Defence (1963). Military Standard, Sampling Procedures and Tables for Inspection by Attributes (MIL-STD-105D). US Government Printing Office, Washington DC
Wetherill GB, Chiu WK (1975) A Review of Acceptance Sampling Schemes with Emphasis on the Economic Aspect. International Statistical Rev 43:191–209
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Göb, R. TypeA operating characteristic functions of defects sampling plans. Metrika 39, 139–153 (1992). https://doi.org/10.1007/BF02613993
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DOI: https://doi.org/10.1007/BF02613993