multivariate control chart I am trying to build a multivariate control chart but I did not find any good explanation of how to do that. 
Starting with $x_0$ a part of the samples that are in control I compute $\mu_0$ and $\Sigma_0$ the mean and the covariance matrix. 
Now with new data $x_n$ I compute $d= (\bar{x}_n-\mu_0)\Sigma^{-1}(\bar{x}_n-\mu_0)$ . 
After this step I do not really know how to go further.
The best answer will be a theoretical explanation and an R or python code. 
 A: I'm not sure, if you're still interested in the topic, but I will provide a brief answer for you and other people that are interested in working with quality control charts (QCC), using R language. For a theoretical introduction to the topic, I would suggest reviewing the corresponding section of StatSoft's nice electronic textbook: http://www.uta.edu/faculty/sawasthi/Statistics/stquacon.html. For much more advanced treatment of the topic, I'd suggest this relevant thesis, titled "An investigation of some characteristics of univariate and multivariate control charts" (see links to PDF chapters).
Traditionally, R ecosystem offers a wide variety of packages to choose from for a specific domain. This applies to the QCC analysis as well. Most frequently used package for QCC analysis is qcc (Quality Control Charts), however there many other packages with varying ranges of functionality:


*

*IQCC: Improved Quality Control Charts

*MSQC: Multivariate Statistical Quality Control

*qcr: Quality control and reliability

*qualityTools: Statistical Methods for Quality Science

*SPCadjust: Functions for calibrating control charts

*CMPControl: Control Charts for Conway-Maxwell-Poisson Distribution

*edcc: Economic Design of Control Charts

*MetaQC: Objective Quality Control and Inclusion/Exclusion Criteria for Genomic Meta-Analysis

*graphicsQC: Quality Control for Graphics in R

*QCGWAS: Quality Control of Genome Wide Association Study results

*GWAtoolbox: GWAS Quality Control

*qAnalyst (removed from CRAN)

*SixSigma: Six Sigma Tools for Quality and Process Improvement

*qicharts: Quality Improvement Charts


For qcc there is a hard-to-find vignette by Luca Scrucca, which can be complemented by this blog post. For those, considering using QCC in educational setting, there is an interesting paper, describing the process (no code, though). Finally, anyone, interested in using QCC in a larger context of SixSigma and in R environment, the book "Six Sigma with R: Statistical engineering for process improvement", published by Springer, might be helpful.
