Exact Determination of the Run Length Distribution of a One-Sided CUSUM Procedure Applied on an Ordinary Poisson Process

DOI10.1081/SQA-120034107zbMath1057.60039OpenAlexW2010735735MaRDI QIDQ3155685

Shelemyahu Zacks

Publication date: 18 January 2005

Published in: Sequential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/sqa-120034107

zbMATH Keywords

detection of change pointscumulative sums controldistribution of run lengthstopping times with linear boundaries

Mathematics Subject Classification ID

Applications of statistics in engineering and industry; control charts (62P30) Sums of independent random variables; random walks (60G50) Stopping times; optimal stopping problems; gambling theory (60G40) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (9)

Review of some functionals of compound Poisson processes and related stopping times ⋮ Performance comparison of some likelihood ratio-based statistical surveillance methods ⋮ Discussion on ``Detection of intrusions in information systems by sequential change-point methods by Tartakovsky, Rozovskii, Blažek, and Kim ⋮ A note on optimal stopping for possible change in the intensity of an ordinary Poisson process ⋮ Distributional Properties of CUSUM Stopping Times and Stopped Processes ⋮ CUSUM Hypothesis Tests and Alternative Response Probabilities for Finite Poisson Trials ⋮ Exact Risks of Sequential Point Estimators of the Exponential Parameter ⋮ Detecting Changes in a Poisson Process Monitored at Unequal Discrete Time Intervals ⋮ Discussion on “Is Average Run Length to False Alarm Always an Informative Criterion?” by Yajun Mei

Cites Work

• Sequential analysis. Tests and confidence intervals
• Wald's approximations to the average run length in cusum procedures
• The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables
• Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed
• Distributions of stopping times for poisson processes with linear boundaries
• Detection of Failure Rate Increases
• Procedures for Reacting to a Change in Distribution
• An approach to the probability distribution of cusum run length
• CONTINUOUS INSPECTION SCHEMES
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