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Introduction
Repetitive testing models for binary classification (i.e., accept or reject) have been studied extensively in the realm of semiconductor fabrication. In this context, devices may undergo numerous testing iterations before being accepted or ultimately scrapped [1, 8, 10, 11–12]. There are situations, however, where the number of tests conducted is limited, with the most prevalent instances occurring in quality control and reliability testing, particularly when the cost of testing is prohibitively high. Other situations with limited testing include high-throughput production, where time constraints are a limiting factor,forensic lab processing, where the identification of controlled substances necessitates two tests for evidentiary admissibility in court [2, 17], and medical diagnostics, where unexpected results may prompt physicians to repeat a test [15].
Scope and Objective
In this study, we examine the case where only two tests are conducted—an initial test followed by a second repetitive test. Our focus is on repetitive testing for purposes of binary classification of units/subjects. Repetitive testing, or retesting, is broadly defined herein as testing the same unit more than once, a concept elaborated upon in the Methods section.
The objective of this work is to determine the impact of two repetitive tests on classification accuracy, measured by the probability of correct sample classification, as compared to conducting only a single test. For example, let’s assume that we have a binary test with a 95% chance of classifying the unit correctly (i.e., the test accuracy is 95%). If we are permitted (or required) to run the test a second time, is it possible to use the two test results to obtain a greater than 95% chance of classifying the unit correctly? Despite the widespread application of repetitive testing in critical domains, this question has not been addressed in the existing literature.
While some may argue that focusing solely on cases involving two tests is overly simplistic, this work illustrates the nuances of this special case. Notably, accuracy is found to be highly contingent on how “ties” (conflicting test results) are classified. This is important because ties are more likely to occur in situations with limited testing.
Previous Work and Contributions
Greenberg and Stokes [12] and Ding et al. [10] have previously introduced repetitive testing models for binary classification. A notable limitation of these...