Reconciling the Integral Equation and Markov Chain Approaches for Computing EWMA Average Run Lengths

DOI10.1081/SAC-120017508zbMath1075.62659OpenAlexW2006191377MaRDI QIDQ4707025

Stephen M. Scariano, M. E. Calzada

Publication date: 4 June 2003

Published in: Communications in Statistics - Simulation and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/sac-120017508

zbMATH Keywords

EWMA charts, Average run lengths, Integral equations, Markov chain

Mathematics Subject Classification ID

Applications of statistics in engineering and industry; control charts (62P30) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20)

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Evaluation of exponentially weighted moving variance control chart subject to linear drifts ⋮ Computation of the ARL for CUSUM-\(S^2\) schemes ⋮ Computation of the run-length percentiles of CUSUM control charts under changes in variances ⋮ Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL ⋮ The optimization design of EWMA charts for monitoring environmental performance

Cites Work

• Linear integral equations.
• A Simple Method for Studying Run-Length Distributions of Exponentially Weighted Moving Average Charts
• Average Run Lengths of Geometric Moving Average Charts by Numerical Methods
• The Numerical Solution of Integral Equations of the Second Kind
• Robustness to non-normality and autocorrelation of individuals control charts
• Exponentially weighted moving average control charts with reflecting boundaries
• An approach to the probability distribution of cusum run length
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