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A Study on Overestimating a Given Fraction Defective by an Imperfect Inspector
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-09-15
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
It has been believed that even an imperfect inspector with nonzero inspection errors could either overestimate or underestimate a given FD (fraction defective) with a 50 : 50 chance.
What happens to the existing inspection plans, if an imperfect inspector overestimates a known FD, when it is very low? We deal with this fundamental question, by constructing four mathematical models, under the assumptions that an infinite sequence of items with a known FD is given to an imperfect inspector with nonzero inspection errors, which can be constant and/or randomly distributed with a uniform distribution.
We derive four analytical formulas for computing the probability of overestimation (POE) and prove that an imperfect inspector overestimates a given FD with more than 50%, if the FD is less than a value termed as a critical FD.
Our mathematical proof indicates that the POE approaches one when FD approaches zero under our assumptions.
Hence, if a given FD is very low, commercial inspection plans should be revised with the POE concept in the near future, for the fairness of commercial trades.
American Psychological Association (APA)
Yang, Moon Hee& Chang, Kyung. 2014. A Study on Overestimating a Given Fraction Defective by an Imperfect Inspector. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1044396
Modern Language Association (MLA)
Yang, Moon Hee& Chang, Kyung. A Study on Overestimating a Given Fraction Defective by an Imperfect Inspector. Mathematical Problems in Engineering No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-1044396
American Medical Association (AMA)
Yang, Moon Hee& Chang, Kyung. A Study on Overestimating a Given Fraction Defective by an Imperfect Inspector. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1044396
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1044396