Profile control charts based on nonparametric LL-1 regression methods

Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric $L$-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by three individual metrics. The proposed approach is applied to the previously analyzed vertical density profile data, leading to some interesting insights.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS501 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Univariate And Multivariate Synthetic Control Charts For Monitoring The Process Mean Of Skewed Distributions

Alat yang paling berkuasa dalam Kawalan Kualiti Berstatistik (SQC) ialah carta kawalan. The most powerful tool in Statistical Quality Control (SQC) is the control chart. Control charts are now widely accepted and used in industries

Profile Monitoring of Probability Density Functions via Simplicial Functional PCA with application to Image Data

The advance of sensor and information technologies is leading to data-rich industrial environments, where large amounts of data are potentially available. This study focuses on industrial applications where image data are used more and more for quality inspection and statistical process monitoring. In many cases of interest, acquired images consist of several and similar features that are randomly distributed within a given region. Examples are pores in parts obtained via casting or additive manufacturing, voids in metal foams and light-weight components, grains in metallographic analysis, etc. The proposed approach summarizes the random occurrences of the observed features via their (empirical) probability density functions (PDFs). In particular, a novel approach for PDF monitoring is proposed. It is based on simplicial functional principal component analysis (SFPCA), which is performed within the space of density functions, that is, the Bayes space B2. A simulation study shows the enhanced monitoring performances provided by SFPCA-based profile monitoring against other competitors proposed in the literature. Finally, a real case study dealing with the quality control of foamed material production is discussed, to highlight a practical use of the proposed methodology. Supplementary materials for the article are available online

A New SVDD-Based Multivariate Non-parametric Process Capability Index

Process capability index (PCI) is a commonly used statistic to measure ability of a process to operate within the given specifications or to produce products which meet the required quality specifications. PCI can be univariate or multivariate depending upon the number of process specifications or quality characteristics of interest. Most PCIs make distributional assumptions which are often unrealistic in practice. This paper proposes a new multivariate non-parametric process capability index. This index can be used when distribution of the process or quality parameters is either unknown or does not follow commonly used distributions such as multivariate normal