Hostname: page-component-669899f699-chc8l Total loading time: 0 Render date: 2025-04-26T12:32:31.831Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Bonett, D.G. (1988). Estimating the number of defects under imperfect inspection. Journal of Applied Statistics 15: 63–67.CrossRefGoogle Scholar
2.Bonett, D.G. & Woodward, J.A. (1994). Sequential defect removal sampling. Management Science 40: 898–902.CrossRefGoogle Scholar
3.Briand, L.C., El Emam, K., Freimut, B.G., & Laitenberger, O. (2000). A comprehensive evaluation of capture–recapture models for estimating software defect content. IEEE Transactions on Software Engineering 26: 518–540.CrossRefGoogle Scholar
4.Chao, A. (2001). An overview of closed capture–recapture models. Journal of Agricultural, Biological, and Environmental Statistics 6: 158–175.CrossRefGoogle Scholar
5.Chun, Y.H. (2005). Serial inspection plan in the presence of inspection errors: maximum likelihood and maximum entropy approaches. Quality Engineering 17: 627–632.CrossRefGoogle Scholar
6.Grubbs, F.E. (1948). On estimating precision of measuring instruments and product variability. Journal of the American Statistical Association 43: 243–264.CrossRefGoogle Scholar
7.Grubbs, F.E. (1973). Errors of measurement, precision, accuracy and the statistical comparison of measuring instruments. Technometrics 15: 53–66.CrossRefGoogle Scholar
8.Haff, R.P. & Toyofuku, N. (2008). X-ray detection of defects and contaminants in the food industry. Sensing and Instrumentation for Food Quality and Safety 2: 262–273.CrossRefGoogle Scholar
9.Holgate, P. (1964). Estimation for the bivariate Poisson distribution. Biometrika 51: 241–287.CrossRefGoogle Scholar
10.Huang, S.H. & Pan, Y.C. (2015). Automated visual inspection in the semiconductor industry: a survey. Computers in Industry 66: 1–10.CrossRefGoogle Scholar
11.Johnson, N.L., Kotz, S. & Balakrishnan, N. (1997). Discrete multivariate distributions. New York: Wiley.Google Scholar
12.Kocherlakota, S. & Kocherlakota, K. (2004). Bivariate discrete distributions. Encyclopedia of Statistical Sciences 1, New York: Marcel Dekker.Google Scholar
13.Kotz, S. & Johnson, N.L. (1984). Effects of false and incomplete identification of defective items on the reliability of acceptance sampling. Operations Research 32: 575–583.CrossRefGoogle Scholar
14.Lehmann, E.L. & Casella, G. (2006). Theory of point estimation. New York: Springer.Google Scholar
15.Lombard, F. & Potgieter, C.J. (2012). Another look at the Grubbs estimators. Chemometrics and Intelligent Laboratory Systems 110: 74–80.CrossRefGoogle Scholar
16.McCrea, R.S. & Morgan, B.J.T. (2014). Analysis of capture–recapture data. Boca Raton: CRC Press.CrossRefGoogle Scholar
17.Montgomery, D.C. (2009). Statistical quality control. New York: Wiley.Google Scholar
18.Mood, G., Graybill, F., & Boes, D.C. (1974). Introduction to the theory of statistics. New York: McGraw-Hill.Google Scholar
19.Petersson, H., Thelin, T., Runeson, P., & Wohlin, C. (2004). Capture–recapture in software inspections after 10 years research—theory, evaluation and application. Journal of Systems and Software 72: 249–264.CrossRefGoogle Scholar
20.See, J.E. (2012). Visual inspection: a review of the literature. Albuquerque, New Mexico: Sandia National Laboratories.CrossRefGoogle Scholar
Supplementary material: PDF

Gadrich and Katriel supplementary material

Gadrich and Katriel supplementary material

Download Gadrich and Katriel supplementary material(PDF)
PDF 314.2 KB