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Activity Number: 600
Type: Contributed
Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 AM
Sponsor: Quality and Productivity Section
Abstract - #307600
Title: Sorting Machine Correlation Paradox
Author(s): Emil Bashkansky*+ and Tamar Gadrich
Companies: ORT Braude College of Engineering and ORT Braude College of Engineering
Keywords: qualitative analysis ; sorting machine ; binary classification ; repeatability ; correlation coefficient ; joint probability distribution
Abstract:

Qualitative analysis is often used to determine whether or not a particular feature appears or is absent in tests. It is widely applied in quality control, identification scans, go/no go measurements and many other fields. Generally, such analysis classifies the analyzed property value into two comprehensive and exclusive classes/categories. The performance of such binary measurement systems (BMS) is usually assessed by false positive and false negative rates. We present an additional statistical aspect related to BMS: consistency/repeatability problem. This feature is examined with the help of the correlation coefficient between the random variables denoting the number of items that were classified as Type 1 (for example) in two sequential sorting processes. It is shown that some intuitively plausible at a first glance concepts such as hypotheses about the binomial distribution of test results or consistency testing by sequentially repeated sorting are wrong if the objective is to conduct a deep examination. The obtained paradoxical results lead to the conclusion that the usual measures are not suitable for estimating consistency and therefore, should be avoided.


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