Optimum Preventative Sampling

The situation envisaged is that in which a number of articles of varying value and liability to defect are sampled and inspected, the ultimate aim being not so much to detect defects as to discourage their arisal. General results are obtained (see “The General Equations”), of which the following specific result is typical, under certain circumstances the optimum sampling fraction for those articles having value v i is approximately \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$f_{i} = F + \frac{1}{C} \log (v_{i}/v_{G}).$$\end{document} Here F is the predetermined total sampling fraction, v G the geometric mean value of all articles, and C a coefficient measuring the deterrent effect of sampling on carelessness, etc. Under the same circumstances, the ratio of the expected total avoidable loss under optimum sampling to that under uniform sampling is approximately v G / v A , where v A is the arithmetic mean article value. The ratio v A / v G thus provides a measure of the advantage to be expected in using an optimum sampling scheme. Operations Research , ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.