Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

Long-term optical variability of PKS 2155-304

Aims: The optical variability of the blazar PKS 2155-304 is investigated to characterise the red noise behaviour at largely different time scales from 20 days to O(>10 yrs). Methods: The long-term optical light curve of PKS 2155-304 is assembled from archival data as well as from so-far unpublished observations mostly carried out with the ROTSE-III and the ASAS robotic telescopes. A forward folding technique is used to determine the best-fit parameters for a model of a power law with a break in the power spectral density function (PSD). The best-fit parameters are estimated using a maximum-likelihood method with simulated light curves in conjunction with the Lomb Scargle Periodogram (LSP) and the first-order Structure Function (SF). In addition, a new approach based upon the so-called Multiple Fragments Variance Function (MFVF) is introduced and compared to the other methods. Simulated light curves have been used to confirm the reliability of these methods as well as to estimate the uncertainties of the best-fit parameters. Results: The light curve is consistent with the assumed broken power-law PSD. All three methods agree within the estimated uncertainties with the MFVF providing the most accurate results. The red-noise behaviour of the PSD in frequency f follows a power law with f^-{\beta}, {\beta}=1.8 +0.1/-0.2 and a break towards f^0 at frequencies lower than f_min=(2.7 +2.2/-1.6 yrs)^-1.Comment: 10 pages, 8 figures, the ROTSE-light curve can be downloaded from http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/A+A/531/A12

A Methodology for the Diagnostic of Aircraft Engine Based on Indicators Aggregation

Aircraft engine manufacturers collect large amount of engine related data during flights. These data are used to detect anomalies in the engines in order to help companies optimize their maintenance costs. This article introduces and studies a generic methodology that allows one to build automatic early signs of anomaly detection in a way that is understandable by human operators who make the final maintenance decision. The main idea of the method is to generate a very large number of binary indicators based on parametric anomaly scores designed by experts, complemented by simple aggregations of those scores. The best indicators are selected via a classical forward scheme, leading to a much reduced number of indicators that are tuned to a data set. We illustrate the interest of the method on simulated data which contain realistic early signs of anomalies.Comment: Proceedings of the 14th Industrial Conference, ICDM 2014, St. Petersburg : Russian Federation (2014