On exact and optimal single-sampling plans by variables
We deal with sampling by variables with two-way protection in the case of a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$N\>(\mu ,\sigma ^2)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>N</mi> <mspace width="0.222222em"/> <mo stretchy="false">(</mo> <mi mathvariant="italic">μ</mi> <mo>,</mo> <msup> <mi mathvariant="italic">σ</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> distributed characteristic with unknown <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">σ</mi> </math> </EquationSource> </InlineEquation>. The LR sampling plan proposed by Lieberman and Resnikoff (JASA 50: 457<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${-}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mo>-</mo> </math> </EquationSource> </InlineEquation>516, <CitationRef CitationID="CR9">1955</CitationRef>) and the BSK sampling plan proposed by Bruhn-Suhr and Krumbholz (Stat. Papers 31: 195–207, <CitationRef CitationID="CR1">1990</CitationRef>) are based on the UMVU and the plug-in estimator, respectively. For given <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$p_1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>p</mi> <mn>1</mn> </msub> </math> </EquationSource> </InlineEquation> (AQL), <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$p_2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>p</mi> <mn>2</mn> </msub> </math> </EquationSource> </InlineEquation> (RQL) and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$\alpha ,\beta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">α</mi> <mo>,</mo> <mi mathvariant="italic">β</mi> </mrow> </math> </EquationSource> </InlineEquation> (type I and II errors) we present an algorithm allowing to determine the optimal LR and BSK plans having minimal sample size among all plans satisfying the corresponding two-point condition on the OC. An R (R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL <ExternalRef> <RefSource>http://www.R-project.org/</RefSource> <RefTarget Address="http://www.R-project.org/" TargetType="URL"/> </ExternalRef> <CitationRef CitationID="CR11">2012</CitationRef>) package, ExLiebeRes‘ (Krumbholz and Steuer ExLiebeRes: calculating exact LR- and BSK-plans, R-package version 0.9.9. <ExternalRef> <RefSource>http://exlieberes.r-forge.r-project.org</RefSource> <RefTarget Address="http://exlieberes.r-forge.r-project.org" TargetType="URL"/> </ExternalRef> <CitationRef CitationID="CR8">2012</CitationRef>) implementing that algorithm is provided to the public. Copyright Springer-Verlag Berlin Heidelberg 2014
