Principal component analysis-based control charts for multivariate nonnormal distributions

Phaladiganon, Poovich; Kim, Seoung Bum; Chen, Victoria C. P.; Jiang, Wei

doi:10.1016/j.eswa.2012.12.020

Cited by 72 publications

(39 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The second alternative allows to compute with few variables the Mahalanobis distance by means of the Hotelling's T 2 ; for this reason, this last statistic is often called the D 2 ‐statistic . Hotelling's T 2 measures the variation in each sample within the PCA model . The expression to be applied is:

\begin{matrix} T^{2} Hotelling (M_{x}, M_{0}) & = n (M_{normalx} - M_{0}) \times Cov {((),, M_{normalx}, M_{0})}^{- 1} \\ \times {((), M_{x} - M_{0})}^{normalT} \end{matrix}

…”

Section: Fundamentalsmentioning

confidence: 99%

Multivariate approaches for stability control of the olive oil reference materials for sensory analysis – part I: framework and fundamentals

et al. 2018

View full text Add to dashboard Cite

show abstract

\begin{matrix} T^{2} Hotelling (M_{x}, M_{0}) & = n (M_{normalx} - M_{0}) \times Cov {((),, M_{normalx}, M_{0})}^{- 1} \\ \times {((), M_{x} - M_{0})}^{normalT} \end{matrix}

…”

Section: Fundamentalsmentioning

confidence: 99%

Multivariate approaches for stability control of the olive oil reference materials for sensory analysis – part I: framework and fundamentals

et al. 2018

View full text Add to dashboard Cite

show abstract

“…They are often addressed either by the model-based process monitoring and diagnosis technique [1, 2], observer schemes [4,5] or by the data-driven techniques [3, 6,7]. Rolling process plays an important role in steel manufacturing, which can yield different scales of steel plate.…”

Section: Introductionmentioning

confidence: 99%

New kernel independent and principal components analysis‐based process monitoring approach with application to hot strip mill process

Peng

Zhang

et al. 2014

IET Control Theory & Applications

View full text Add to dashboard Cite

In this article, a new kernel independent and principal components analysis (kernel ICA-PCA) based process monitoring approach is proposed for hot strip mill process (HSMP). HSMP appears widely in iron and steel industry, which runs in an environment with significant nonlinearity, non-Gaussianity and some other uncertainties. The present method, namely kernel ICA-PCA, firstly addresses the nonlinearity via the popular kernel trick, then applies kernel ICA model to isolate the non-Gaussian independent information, finally, utilises kernel PCA model to account for the uncertain part and extract the principal components. To avoid the disadvantage of the original fault detection statistics, a k nearest neighbour data description-based technique is employed into the kernel ICA-PCA for monitoring the variations occurring in the independent and principal components, whereas traditional Q statistic is employed to reflect the disturbance in the residuals. All of their thresholds will be determined by a new emerging bootstrap-based technique. The applicability of the new scheme is represented via hot strip mill process dataset recorded in the iron and steel company.

show abstract

“…Chatterjee and Qiu presented a cumulative sum control chart with the limits obtained by bootstrap method. A bootstrap‐based Hotelling T 2 control chart for a process mean with subgroup size of one was first suggested by Phaladiganon et al They were also able to use bootstrap method in the multivariate control chart for principal component analysis based on non‐normal distributions when subgroup size was one (Phaladiganon et al). Gandy and Kvaloy proposed guaranteed conditional performance of control charts via bootstrap methods.…”

Section: Introductionmentioning

confidence: 99%

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Mostajeran

Iranpanah

Noorossana

2017

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.

show abstract

Principal component analysis-based control charts for multivariate nonnormal distributions

Cited by 72 publications

References 21 publications

Multivariate approaches for stability control of the olive oil reference materials for sensory analysis – part I: framework and fundamentals

Multivariate approaches for stability control of the olive oil reference materials for sensory analysis – part I: framework and fundamentals

New kernel independent and principal components analysis‐based process monitoring approach with application to hot strip mill process

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Contact Info

Product

Resources

About