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ESTIMATING THE RATE OF DEFECTS UNDER IMPERFECT SAMPLING INSPECTION—A NEW APPROACH

Part of: Applications Parametric inference

Published online by Cambridge University Press:  28 October 2019

Tamar Gadrich Open the ORCID record for Tamar Gadrich [Opens in a new window]  and
Guy Katriel
Tamar Gadrich
Affiliation:
Department of Industrial Engineering and Management, ORT Braude College, Karmiel, Israel E-mail: tamarg@braude.ac.il
Guy Katriel
Affiliation:
Department of Mathematics, ORT Braude College, Karmiel, Israel E-mail: katriel@braude.ac.il
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Abstract

We consider the problem of estimating the rate of defects (mean number of defects per item), given the counts of defects detected by two independent imperfect inspectors on one sample of items. In contrast with the setting for the well-known method of Capture–Recapture, we do not have information regarding the number of defects jointly detected by both inspectors. We solve this problem by constructing two types of estimators—a simple moment-type estimator, and a complicated maximum-likelihood (ML) estimator. The performance of these estimators is studied analytically and by means of simulations. It is shown that the ML estimator is superior to the moment-type estimator. A systematic comparison with the Capture–Recapture method is also made.

Keywords

applied probabilityestimationdefectsmultiple inspection

MSC classification

Primary: 62F10: Point estimation
Secondary: 62P30: Applications in engineering and industry
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 2 , April 2021 , pp. 242 - 257
Copyright
Copyright © Cambridge University Press 2019

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