Limit theorems for runs containing two types of contaminations. Paper with detailed proofs

2023/09/20 by István Fazekas, Fazekas, István, Borbála Fazekas +3
Decision Sciences · Mathematics · #60C05 60F05 #Advanced Statistical Process Monitoring #FOS: Mathematics #Optimal Experimental Design Methods #Probability (math.PR) #Statistical Methods in Clinical Trials

paper · pdf · doi:10.48550/arxiv.2309.11602

openalex publication_date 2023/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, sequences of trials having three outcomes are studied. The outcomes are labelled as success, failure of type I and failure of type II. A run is called at most 1+1 contaminated, if it contains at most 1 failure of type I and at most 1 failure of type II. The limiting distribution of the first hitting time and the accompanying distribution for the length of the longest at most 1+1 contaminated run are obtained. This paper contains the detailed mathematical proofs. Simulation results supporting the theorems are also presented.

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