Book ChapterDOI
On the Robustness of the Shewhart Control Chart to Different Types of Dependencies in Data
Olgierd Hryniewicz
- pp 19-33
TLDR
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.read more
Citations
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Journal ArticleDOI
Some robust approaches based on copula for monitoring bivariate processes and component-wise assessment
TL;DR: The novelty of the proposed technique lies in the fact that it indigenously helps in identifying the component(s) responsible for the signal, which is not straightforward with the traditional schemes for surveillance of a bivariate process.
Journal ArticleDOI
Bivariate copulas on the Hotelling's T2 control chart
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.
Posted Content
A Control Chart Using Copula-Based Markov Chain Models
Ting-Hsuan Long,Takeshi Emura +1 more
TL;DR: This paper proposes to apply a copula-based Markov chain to perform statistical process control for correlated observations and shows that Joe’s parametric maximum likelihood method provides the most reliable estimates of the UCL and LCL compared to the other methods.
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Copula modelling for multivariate statistical process control: a review
Journal ArticleDOI
Bivariate copulas on the exponentially weighted moving average control chart
TL;DR: This paper proposes four types of copulas on the Exponentially Weighted Moving Average control chart when observations are from an exponential distribution using a Monte Carlo simulation approach and shows that the Normal copula can be used for almost all shifts.
References
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Book
An Introduction to Copulas
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Journal ArticleDOI
Statistical Inference Procedures for Bivariate Archimedean Copulas
TL;DR: In this paper, the authors examined the problem of selecting an Archimedean copula providing a suitable representation of the dependence structure between two variates X and Y in the light of a random sample (X 1, Y 1, X n, Y n ).
Journal ArticleDOI
The Joy of Copulas: Bivariate Distributions with Uniform Marginals
Christian Genest,Jock MacKay +1 more
TL;DR: This work shows how a class of bivariate distributions whose marginals are uniform on the unit interval can be used to illustrate the existence of distributions with singular components and to give a geometric interpretation to Kendall's tau.
Journal ArticleDOI
Time-Series Modeling for Statistical Process Control
Layth C. Alwan,Harry V. Roberts +1 more
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.