A comparative study of phase II robust multivariate control charts for individual observations

Use of Hotelling's T² charts with high breakdown robust estimates to monitor multivariate individual observations are the recent trend in the control chart methodology. Vargas (J. Qual. Tech. 2003; 35: 367‐376) introduced Hotelling's T² charts based on the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD) estimates to identify outliers in Phase I data. Studies carried out by Jensen et al. (Qual. Rel. Eng. Int. 2007; 23: 615‐629) indicated that the performance of these charts heavily depends on the sample size, amount of outliers and the dimensionality of the Phase I data. Chenouri et al. (J. Qual. Tech. 2009; 41: 259‐271) recently proposed robust Hotelling's T² control charts for monitoring Phase II data based on the reweighted MCD (RMCD) estimates of the mean vector and covariance matrix from Phase I. They showed that Phase II RMCD charts have better performance compared with Phase II standard Hotelling's T² charts based on outlier free Phase I data, where the outlier free Phase I data were obtained by applying MCD and MVE T² charts to historical data. Reweighted MVE (RMVE) and S‐estimators are two competitors of the RMCD estimators and it is a natural question whether the performance of Phase II Hotelling's T² charts with RMCD and RMVE estimates exhibits similar pattern observed by Jensen et al. (Qual. Rel. Eng. Int. 2007; 23: 615‐629) in the case of MCD and MVE‐based Phase I Hotelling's T² charts. In this paper, we conduct a comparative study to assess the performance of Hotelling's T² charts with RMCD, RMVE and S‐estimators using large number of Monte Carlo simulations by considering different data scenarios. Our results are generally in favor of the RMCD‐based charts irrespective of sample size, outliers and dimensionality of Phase I data. Copyright © 2010 John Wiley & Sons, Ltd.     

Phase I monitoring with nonparametric mixed‐effect models

In many real‐life applications, the quality of products from a process is monitored by a functional relationship between a response variable and one or more explanatory variables. In these applications, methodologies of profile monitoring are used to check the stability of this relationship over time. In phase I of profile monitoring, historical data points that can be represented by curves (or profiles) are collected. In this article, 2 procedures are proposed for detecting outlying profiles in phase I data, by incorporating the local linear kernel smoothing within the framework of nonparametric mixed‐effect models. We introduce a stepwise algorithm on the basis of the multiple testing viewpoint. Our simulation results for various linear and nonlinear profiles display the superior efficiency of our proposed monitoring procedures over some existing techniques in the literature. To illustrate the implementation of the proposed methods in phase I profile monitoring, we apply the methods on a vertical density profile dataset.     

Reducing the threat of in-transit derailments involving dangerous goods through effective placement along the train consist

Train derailments are important safety concerns, and they become increasingly so when dangerous goods (DG) are involved. One way to reduce the risk of DG derailments is through effective DG railway car placement along the train consist. This paper investigates the relationship between DG railway car placement and derailment for different route attributes and DG shipments. A model is presented for estimating the probability of derailment by position, based on the estimated point of derailment (POD) and the number of cars derailing. A DG placement model that considers in-transit derailment risk is shown to provide a sound scientific basis for effective DG marshalling in conventional rail hump yard operations.