Abstract
We deal with the double sampling plans by variables proposed by Bowker and Goode (Sampling Inspection by Variables, McGraw–Hill, New York, 1952) when the standard deviation is unknown. Using the procedure for the calculation of the OC given by Krumbholz and Rohr (Allg. Stat. Arch. 90:233–251, 2006), we present an optimization algorithm allowing to determine the ASN Minimax plan. This plan, among all double plans satisfying the classical two-point-condition on the OC, has the minimal ASN maximum.
Similar content being viewed by others
References
Bowker, A.H., Goode, H.P.: Sampling Inspection by Variables. McGraw–Hill, New York (1952)
Brooke, A., Kendrick, D., Meeraus, A., Raman, R.: GAMS—A Users Guide. GAMS Development Corporation, Washington (1998)
Bruhn-Suhr, M., Krumbholz, W.: Exact two-sided Lieberman–Resnikoff sampling plans. Stat. Pap. 32, 233–241 (1991)
Duarte, B.P.M., Saraiva, P.M.: An optimization-based framework for designing acceptance sampling plans by variables for nonconforming proportions. Technical Report, University of Coimbra (2009)
Eichwede, R., Krumbholz, W.: ASN-optimal double sampling plans for attributes. Allg. Stat. Arch. 85, 427–442 (2001)
Feldmann, B.: Zweifache und sequentielle Minimax-ASN-Variablenprüf- pläne mit exponential- und normalverteiltem Merkmal. Thesis. Universität der Bundeswehr Hamburg (1999)
Feldmann, B., Krumbholz, W.: ASN-minimax double sampling plans for variables. Stat. Pap. 43, 361–377 (2002)
Hilbert, M., Zweifache ASN-Minimax-Variablenprüfpläne für normalver- teiltes Merkmal bei unbekannten Parametern. Thesis. Universität der Bundeswehr Hamburg (2005)
Krumbholz, W., Rohr, A.: The operating characteristic of double sampling plans by variables when the standard deviation is unknown. Allg. Stat. Arch. 90, 233–251 (2006)
Lieberman, G.J., Resnikoff, G.J.: Sampling plans for inspection by variables. J. Am. Stat. Assoc. 50, 457–516 (1955)
Sommers, D.J.: Two point double variables sampling plans. J. Qual. Technol. 13, 25–30 (1981)
Author information
Authors and Affiliations
Corresponding author
Additional information
The authors wish to thank Yvonne Köllner and Eno Vangjeli for technical support.
Rights and permissions
About this article
Cite this article
Krumbholz, W., Rohr, A. Double ASN Minimax sampling plans by variables when the standard deviation is unknown. AStA Adv Stat Anal 93, 281–294 (2009). https://doi.org/10.1007/s10182-009-0111-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10182-009-0111-8