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Book ChapterDOI

Sequential Signals on a Control Chart Based on Nonparametric Statistical Tests

01 Jan 2010-pp 99-117
TL;DR: A new control chart based on Kendall’s tau statistic is proposed which is nearly as good as a well known autocorrelation chart, but outperforms this chart when these basic assumptions are not fulfilled.
Abstract: The existence of dependencies between consecutive observations of a process makes the usage of SPC tools much more complicated. In order to avoid unnecessary costs we need to have simple tools for the discrimination between correlated and uncorrelated process data. In the paper we propose a new control chart based on Kendall’s tau statistic which can be used for this purpose. In case of normally distributed observations with dependence of an autoregressive type the proposed Kendall control chart is nearly as good as a well known autocorrelation chart, but outperforms this chart when these basic assumptions are not fulfilled.
Citations
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Journal ArticleDOI
TL;DR: The results show that the copula approach can be fitted the observation and it can be used as an option for application on Hotelling's T2 control chart.
Abstract: In this paper, we propose five types of copulas on the Hotelling's T2 control chart when observations are from exponential distribution and use the Monte Carlo simulation to compare the performance of the control chart, which is based on the Average Run Length (ARL) for each copula. Five types of copulas function for specifying dependence between random variables are used and measured by Kendall's tau. The results show that the copula approach can be fitted the observation and we can use copula as an option for application on Hotelling's T2 control chart.

17 citations


Cites background from "Sequential Signals on a Control Cha..."

  • ...Hryniewicz and Szediw (2010) have shown a new control chart based on nonparametric Kendall’s tau statistics by a bivariate normal distribution....

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Book ChapterDOI
01 Jan 2012
TL;DR: The concept of copulas is used to model dependencies of other types in classical control charts and the impact of type and strength of dependence in data on the value of the ARL of Shewhart control charts is investigated.
Abstract: Shewhart control charts were originally designed under the assumption of independence of consecutive observations. In the presence of dependence the authors usually assume dependencies in the form of autocorrelated and normally distributed data. However, there exist many other types of dependencies which are described by other mathematical models. The question arises then, how classical control charts are robust to different types of dependencies. This problem has been sufficiently well discussed for the case of autocorrelated and normal data. In the paper we use the concept of copulas to model dependencies of other types. We use Monte Carlo simulation experiments to investigate the impact of type and strength of dependence in data on the value of the ARL of Shewhart control charts.

15 citations


Cites background or methods from "Sequential Signals on a Control Cha..."

  • ...Other approaches are based on the concept of residuals (see the papers by Alwan and Roberts (1988) or by Montgomery and Mastrangelo (1991)) or on monitoring statistics related to autocorrelations (see the papers by Yourstone and Montgomery (1991) or by Jiang et al. (2000)). There also exist more sophisticated methods for dealing with SPC autocorrelated data. An overview of SPC methods used for autocorrelated data can be found in papers by Wardell et al. (1994), Lu and Reynolds (1999a) and Knoth et al....

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  • ...This can be done using the Kendall control chart proposed by Hryniewicz and Szediw (2010)....

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  • ...This problem was considered in the paper by Hryniewicz and Szediw (2010) who proposed a relatively simple and efficient nonparametric tool, named by them the Kendall control chart, for testing hypotheses about independence of SPC data....

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  • ...Other approaches are based on the concept of residuals (see the papers by Alwan and Roberts (1988) or by Montgomery and Mastrangelo (1991)) or on monitoring statistics related to autocorrelations (see the papers by Yourstone and Montgomery (1991) or by Jiang et al. (2000)). There also exist more sophisticated methods for dealing with SPC autocorrelated data. An overview of SPC methods used for autocorrelated data can be found in papers by Wardell et al. (1994), Lu and Reynolds (1999a) and Knoth et al. (2001). While dealing with correlated data we cannot rely, even in the case of classical control charts, on the methods used for the estimation of their parameters in case independent observations. Some corrections are necessary, as it was mentioned e.g. in the paper by Maragah and Woodall (1992). Another problem with the application of the procedures designed to control autocorrelated data is the knowledge of the structure of correlation....

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  • ...Other approaches are based on the concept of residuals (see the papers by Alwan and Roberts (1988) or by Montgomery and Mastrangelo (1991)) or on monitoring statistics related to autocorrelations (see the papers by Yourstone and Montgomery (1991) or by Jiang et al. (2000))....

    [...]

Journal ArticleDOI

13 citations


Cites background from "Sequential Signals on a Control Cha..."

  • ...Many researchers have developed the copula for use with control charts (Dokouhaki and Noorossana, 2013; Fatahi et al., 2011, 2012; Hryniewicz, 2012; Hryniewicz and Szediw, 2010; Kuvattana et al., 2016; Verdier, 2013)....

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  • ...Hryniewicz and Szediw (2010) have shown a new control chart based on non-parametric Kendall’s tau statistics by a bivariate normal distribution....

    [...]

Journal ArticleDOI
TL;DR: Three families are proposed from elliptical and Archimedean copulas on the multivariate cumulative sum control chart when observations are draw from an exponential distribution and the numerical results indicate that the observations can be fitted and that the copula can be used on the MCUSUM for cases of small and large dependencies.
Abstract: The copula approach is a popular method for multivariate modeling applied in several fields; it defines non-parametric measures of dependence between random variables. In this paper, three families are proposed from elliptical and Archimedean copulas on the multivariate cumulative sum (MCUSUM) control chart when observations are draw from an exponential distribution. The performance of the control chart is based on the average run length (ARL)—via Monte Carlo simulations. A copula function for specifying the dependence between random variables is measured by Kendall’s tau. The numerical results indicate that the observations can be fitted and that the copula can be used on the MCUSUM for cases of small and large dependencies.

9 citations


Additional excerpts

  • ...…charts (see Dokouhaki & Noorossana, 2013; Fatahi, Dokouhaki, & Moghaddam, 2011; Fatahi, Noorossana, Dokouhaki, & Moghaddam, 2012; Hryniewicz, 2012; Hryniewicz & Szediw, 2010; Kuvattana, Sukparungsee, Busababodhin, & Areepong, 2016; Sukparungsee, Kuvattana, Busababodhin, & Areepong, in press;…...

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Book ChapterDOI
01 Jan 2019
TL;DR: This study shows that copulas may alternatively be used for getting the same or little wider acceptable region between upper and lower limits, which may help to decrease some of the negative effects of dependent data being monitored on charts for further studies.
Abstract: Copula is a distribution function on the unit hypercube with uniform margins. The margin is directly related to the stochastic behaviour of one variable, while joint distribution function covers the holistic character of more. In multivariate (and particularly bivariate) analysis, using copulas is an elegant way to solve the missing information problem between joint distribution function and the total of the margins. Hereby, the intention of this paper is twofold. Firstly, the paper intends to emphasize the advantages of copulas in practice. In order to encourage potential researchers to diversify their subject of work with these functions, authors give the essential introductory details for a clear understanding of copulas associated with their basic mathematical and statistical preliminaries. Secondly, the study exemplifies the practical usage of copulas in statistical process control area. In this context, process parameters are estimated in order to calculate the control limits of a typical Shewhart type control chart. Parameter estimation is performed by Maximum Likelihood Estimation (MLE) for the bivariate Clayton copula in univariate AR (1) time series with several different levels of high dependence. Since monitoring autocorrelated data in control charts is known as being one of the main causes of producing tighter control limits than required, false alarm rate may be increased and accordingly, the performance of control charts may be dramatically decreased. This study shows that copulas may alternatively be used for getting the same or little wider acceptable region between upper and lower limits. This recognition of the properness of copulas may help to decrease some of the negative effects of dependent data being monitored on charts for further studies.

4 citations

References
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Book
01 Jan 1970
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
Abstract: From the Publisher: This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application —forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.

19,748 citations

Journal ArticleDOI
TL;DR: This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application —forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.
Abstract: From the Publisher: This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application —forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.

12,650 citations

Journal ArticleDOI
TL;DR: This work proposes and illustrates statistical modeling and fitting of time-series effects and the application of standard control-chart procedures to the residuals from these fits.
Abstract: In statistical process control, a state of statistical control is identified with a process generating independent and identically distributed random variables. It is often difficult in practice to attain a state of statistical control in this strict sense; autocorrelations and other systematic time-series effects are often substantial. In the face of these effects, standard control-chart procedures can be seriously misleading. We propose and illustrate statistical modeling and fitting of time-series effects and the application of standard control-chart procedures to the residuals from these fits. The fitted values can be plotted separately to show estimates of the systematic effects.

676 citations

Journal ArticleDOI
TL;DR: Control charts are developed assuming that the sequence of process observations to which they are applied are uncorrelated, but the presence of autocorrelation has a serious impact on quality.
Abstract: Traditionally, control charts are developed assuming that the sequence of process observations to which they are applied are uncorrelated. Unfortunately, this assumption is frequently violated in practice. The presence of autocorrelation has a serious i..

611 citations

Journal ArticleDOI
TL;DR: In this paper, the authors examined the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent, which can be used to construct families of distributions whose marginals are arbitrary and which include the Frechet bounds as well as the distribution corresponding to independent variables.
Abstract: SUMMARY This paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent The proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the Frechet bounds as well as the distribution corresponding to independent variables Three nonparametric estimators of the association parameter are suggested and Monte Carlo experiments are used to compare their small-sample behaviour to that of the maximum likelihood estimate

416 citations