Journal ArticleDOI
Robust multivariate control charts based on Birnbaum–Saunders distributions
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In this article, a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum-Saunders distributions and an adapted Hotelling statistic is proposed for Phases I and II of control charts.Abstract:
Multivariate control charts are powerful and simple visual tools for monitoring the quality of a process. This multivariate monitoring is carried out by considering simultaneously several correlated quality characteristics and by determining whether these characteristics are in control or out of control. In this paper, we propose a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum–Saunders distributions and an adapted Hotelling statistic. This methodology is constructed for Phases I and II of control charts. We estimate the corresponding parameters with the maximum likelihood method and use parametric bootstrapping to obtain the distribution of the adapted Hotelling statistic. In addition, we consider the Mahalanobis distance to detect multivariate outliers and use it to assess the adequacy of the distributional assumption. A Monte Carlo simulation study is conducted to evaluate the proposed methodology and to compare it with a standard method...read more
Citations
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Journal ArticleDOI
Economic Control of Quality of Manufactured Product.
A. R. Crathorne,W. A. Shewhart +1 more
Journal ArticleDOI
Birnbaum‐Saunders distribution: A review of models, analysis, and applications
TL;DR: In this article, the authors provide a detailed review of all these developments and at the same time indicate several open problems that could be considered for further research, while also providing a detailed discussion of some open problems.
Journal ArticleDOI
Birnbaum-Saunders spatial regression models: Diagnostics and application to chemical data
TL;DR: In this paper, the authors examined a Birnbaum-Saunders spatial regression model and derived global and local diagnostic methods to assess the influence of atypical observations on the maximum likelihood estimates of its parameters.
Posted Content
Birnbaum-Saunders Distribution: A Review of Models, Analysis and Applications
TL;DR: In this article, the authors provide a detailed review of all these developments and at the same time indicate several open problems that could be considered for further research, while also providing a detailed discussion of some open problems.
References
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TL;DR: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes
Journal ArticleDOI
Economic Control of Quality of Manufactured Product.
A. R. Crathorne,W. A. Shewhart +1 more
Book
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TL;DR: In this paper, the authors present a non-Edgeworth view of the Bootstrap and propose a method of importance sampling for estimating bias, variance, and skewness.
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