Optimal Parallel Inspection for Finding the First Nonconforming Unit in a Batch--An Information Theoretic Approach

We consider the case of a batch of discrete units produced by a process subject to failures under a known probability distribution function, and apply information theory to the problem of finding the first nonconforming unit in the batch at minimum cost. Two distinct but related aspects of this prob...

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Bibliographic Details
Published inManagement science Vol. 46; no. 6; pp. 845 - 857
Main Authors Herer, Yale T, Raz, Tzvi
Format Journal Article
LanguageEnglish
Published Hanover, MD., etc INFORMS 01.06.2000
Institute for Operations Research and the Management Sciences
SeriesManagement Science
Subjects
Batch processing
Dynamic programming
Experiment design
Fixed costs
Heuristics
Information
Information economics
Information theory
inspection planning
Mathematical economics
Mathematical vectors
Minimization of cost
Probability
Programming
Statistical analysis
Studies
Theory
Total costs
Uncertainty
Unit costs
Variable costs
United States > US
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Summary:We consider the case of a batch of discrete units produced by a process subject to failures under a known probability distribution function, and apply information theory to the problem of finding the first nonconforming unit in the batch at minimum cost. Two distinct but related aspects of this problem were treated: determining which units should be inspected, and determining how many units should be sent for inspection at the same time. The solution is based on the principles of inspecting the product units that maximize the reduction in the uncertainty regarding the location of the first nonconforming unit, and of minimizing the cost per unit of uncertainty reduced. These principles are formalized by means of a series of theorems leading to an easy-to-implement algorithm for managing parallel inspection. This approach is successfully compared with the optimal solution obtained with dynamic programming and with other heuristics.
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ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.46.6.845.11933