The EWMA sign chart revisited: performance and alternatives without and with ties

The EWMA Sign control chart is an efficient tool for monitoring shifts in a process regardless the observations' underlying distribution. Recent studies have shown that, for nonparametric control charts, due to the discrete nature of the statistics being used (such as the Sign statistic), it is...

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Bibliographic Details
Published inJournal of applied statistics Vol. 50; no. 1; pp. 170 - 194
Main Authors Perdikis, Theodoros, Psarakis, Stelios, Castagliola, Philippe, Rakitzis, Athanasios C., Maravelakis, Petros E.
Format Journal Article
LanguageEnglish
Published England Taylor & Francis 2023
Taylor & Francis Ltd
Taylor & Francis (Routledge)
Subjects
Control charts
EWMA control chart
Integral equations
Markov analysis
Markov chain
Markov chains
Nonparametric control chart
Nonparametric statistics
rounding-off errors
sign statistic
Statistical methods
Statistics
Markov chain
sign statistic
EWMA control chart
Nonparametric control chart
rounding-off errors
Sign statistic
Rounding-off errors
Nonparametric control chart Sign statistic Markov chain EWMA control chart Rounding-off errors
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Summary:The EWMA Sign control chart is an efficient tool for monitoring shifts in a process regardless the observations' underlying distribution. Recent studies have shown that, for nonparametric control charts, due to the discrete nature of the statistics being used (such as the Sign statistic), it is impossible to accurately compute their Run Length properties using Markov chain or integral equation methods. In this work, a modified nonparametric Phase II EWMA chart based on the Sign statistic is proposed and its exact Run Length properties are discussed. A continuous transformation of the Sign statistic, combined with the classical Markov Chain method, is used for the determination of the chart's in- and out-of-control Run Length properties. Additionally, we show that when ties occur due to measurement rounding-off errors, the EWMA Sign control chart is no longer distribution-free and a Bernoulli trial approach is discussed to handle the occurrence of ties and makes the proposed chart almost distribution-free. Finally, an illustrative example is provided to show the practical implementation of our proposed chart.
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ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2021.1982879