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Stopping rules for proofreading

Published online by Cambridge University Press:  14 July 2016

T. S. Ferguson  and
J. P. Hardwick
T. S. Ferguson*
Affiliation:
University of California, Los Angeles
J. P. Hardwick*
Affiliation:
University of Michigan
*
∗ Postal address: Department of Mathematics, UCLA, Los Angeles, CA 90024, USA.
∗∗ Postal address: Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA.
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Abstract

A manuscript with an unknown random number M of misprints is subjected to a series of proofreadings in an effort to detect and correct the misprints. On the nthproofreading, each remaining misprint is detected independently with probability pn– 1. Each proofreading costs an amount CP > 0, and if one stops after n proofreadings, each misprint overlooked costs an amount cn > 0. Two models are treated based on the distribution of M. In the Poisson model, the optimal stopping rule is seen to be a fixed sample size rule. In the binomial model, the myopic rule is optimal in many important cases. A generalization is made to problems in which individual misprints may have distinct probabilities of detection and distinct overlook costs.

Keywords

OPTIMAL STOPPINGMYOPIC RULEMONOTONICITYDEBUGGING
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 304 - 313
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Partial support provided by NSF Grant DMS 8413452. Research begun at UCLA on NIMH Grant 37188.

References

Chow, Y. S., Robbins, H. and Siegmund, D. (1972) Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston.Google Scholar
Chow, C.-W. and Schechner, Z. (1985) On stopping rules in proofreading. J. Appl. Prob. 22, 971–977.CrossRefGoogle Scholar
Feller, W. (1968) An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edn, Wiley, New York.Google Scholar
Forman, E. H. and Singpurwalla, N. D. (1977) An empirical stopping rule for debugging and testing computer software. J. Amer. Statist. Assoc. 72, 750–757.Google Scholar
Joe, H. and Reid, N. (1985) Estimating the number of faults in a system. J. Amer. Statist. Assoc. 80, 222–226.CrossRefGoogle Scholar
Parunak, H. Van Dyke (1981) Quality-controlled proofreading of machine-readable texts. ALLC Journal 2, 51–54.Google Scholar
Pólya, G. (1976) Probabilities in proofreading. Amer. Math. Monthly 83, 42.CrossRefGoogle Scholar
Siegrist, K. (1985) Estimation and optimal stopping in a debugging model. J. Appl. Prob. 22, 336–345.CrossRefGoogle Scholar
Tierney, L. (1983) The hazards of optimal proofreading. Adv. Appl. Prob. 15, 892–893.CrossRefGoogle Scholar
White, G. C., Anderson, D. R., Barnham, K. P. and Otis, D. L. (1982) Capture-Recapture and Removal Methods for Sampling Closed Populations. LA-8787-NERP, Los Alamos National Laboratory, Los Alamos, New Mexico.Google Scholar
Wilks, S. S. (1962) Mathematical Statistics, Wiley. New York.Google Scholar
Yang, M. C. K., Wackerly, D. and Rosalsky, A. (1982) Optimal stopping rules in proofreading. J. Appl. Prob. 19, 723–729.CrossRefGoogle Scholar