A unified Markov chain approach for computing the run length distribution in control charts with simple or compound rules.

DOI10.1016/J.SPL.2003.10.004zbMath1116.62438OpenAlexW1975931298MaRDI QIDQ1423069

James C. Fu, Galit Shmueli, Yung-Ming Chang

Publication date: 14 February 2004

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2003.10.004

zbMATH Keywords

Markov chainDiscretizationControl chartsTransition matrix

Mathematics Subject Classification ID

Applications of statistics in engineering and industry; control charts (62P30) Numerical analysis or methods applied to Markov chains (65C40)

Related Items (13)

Statistical process control using Shewhart control charts with supplementary runs rules ⋮ Improving the performance of the chi-square control chart via runs rules ⋮ Recursive equations in finite Markov chain imbedding ⋮ Nonparametric tests and nested sequential sampling plans for change-point detection ⋮ Reliability analysis of \(k\)-out-of-\(n\):F balanced systems with multiple functional sectors ⋮ On distribution and average run length of a two-stage control process ⋮ On the individuals chart with supplementary runs rules under serial dependence ⋮ Distribution of runs in a sequence of exchangeable multi-state trials ⋮ On average run lengths of control charts for autocorrelated processes ⋮ Run rules based phase IIcandnpcharts when process parameters are unknown ⋮ The computation of average run length and average time to signal: an overview ⋮ Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL ⋮ Run Statistics Defined on the Multicolor URN Model

Cites Work

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• Non-negative matrices and Markov chains. 2nd ed
• On the average run lengths of quality control schemes using a Markov chain approach
• Exact Results for Shewhart Control Charts with Supplementary Runs Rules
• Average Run Lengths of Geometric Moving Average Charts by Numerical Methods
• Robust cusum: a robustness study for cusum quality control schemes
• An approach to the probability distribution of cusum run length

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