Performance measures of M/G/1 retrial queues with recurrent customers,breakdowns, and general delays

In this paper, an M/G/1 retrial system with two classes of customers: transit and recurrent customers is studied. After service completion, recurrent customers always return to the orbit and transit customers leave the system forever. The server is subject to breakdowns and delayed repairs. The customer whose service is interrupted stays in the service, waiting for delay and repair of the server. After repair this customer completes his service. The study of the system concerns the joint generating function of the server state and the queue length in steady state. Some performance measures of the system are then derived and some numerical results are presented to illustrate the effect of the system parameters on the developed performance measures.     

Optimal maintenance intervals for a multi-component system

In the manufacturing industry, preventive maintenance (PM) is carried out to minimise the probability of plant unexpected breakdown. Planned PM is preferred as disruption to operation is then minimised. Suggested PM intervals are normally prepared by the original equipment manufacturers (OEMs), however due to the multifaceted relationship between operating context and production requirement for different plants, it is unlikely that these suggested intervals as prescribed by the OEMs are optimal. Reliability, budget and breakdown outages cost are some of the critical factors that will affect the calculation of optimal maintenance intervals. Maintenance managers are required to determine optimal maintenance intervals with the above different requirements set by management. In this paper three models are proposed to calculate optimal maintenance intervals for multi-component system in a factory subjected to minimum required reliability, maximum allowable budget and minimum total cost. Numerical examples are provided to illustrate the application and usefulness of the proposed models.     

A weighted spatial median for clustered data

A weighted spatial median is proposed for the multivariate one-sample location problem with clustered data. Its limiting distribution is derived under mild conditions (no moment assumptions) and it is shown to be multivariate normal. Asymptotic as well as finite sample efficiencies and breakdown properties are considered, and the theoretical results are supplied with illustrative examples. It turns out that there is a potential for meaningful gains in estimation efficiency: the weighted spatial median has superior efficiency to the unweighted spatial median particularly when the cluster sizes are widely disparate and in the presence of strong intracluster correlation. The unweighted spatial median for clustered data was considered earlier by Nevalainen et al. (Can J Statist, in press, 2007). The proposed weighted estimators provide companion estimates to the weighted affine invariant sign test proposed recently by Larocque et al. (Biometrika, in press, 2007). An affine equivariant weighted spatial median is discussed in parallel.     

Regression with outlier shrinkage

We propose a robust regression method called regression with outlier shrinkage (ROS) for the traditional n>p$n>p$ cases. It improves over the other robust regression methods such as least trimmed squares (LTS) in the sense that it can achieve maximum breakdown value and full asymptotic efficiency simultaneously. Moreover, its computational complexity is no more than that of LTS. We also propose a sparse estimator, called sparse regression with outlier shrinkage (SROS), for robust variable selection and estimation. It is proven that SROS can not only give consistent selection but also estimate the nonzero coefficients with full asymptotic efficiency under the normal model. In addition, we introduce a concept of nearly regression equivariant estimator for understanding the breakdown properties of sparse estimators, and prove that SROS achieves the maximum breakdown value of nearly regression equivariant estimators. Numerical examples are presented to illustrate our methods.     

Robust Regression Using Data Partitioning and M-Estimation

We propose a new robust regression estimator using data partition technique and M estimation (DPM). The data partition technique is designed to define a small fixed number of subsets of the partitioned data set and to produce corresponding ordinary least square (OLS) fits in each subset, contrary to the resampling technique of existing robust estimators such as the least trimmed squares estimator. The proposed estimator shares a common strategy with the median ball algorithm estimator that is obtained from the OLS trial fits only on a fixed number of subsets of the data. We examine performance of the DPM estimator in the eleven challenging data sets and simulation studies. We also compare the DPM with the five commonly used robust estimators using empirical convergence rates relative to the OLS for clean data, robustness through mean squared error and bias, masking and swamping probabilities, the ability of detecting the known outliers, and the regression and affine equivariances.     

Robust estimators based on generalization of trimmed mean

In this article, we propose new estimators of location. These estimators select a robust set around the geometric median, enlarge it, and compute the (iterative) weighted mean from it. By doing so, we obtain a robust estimator in the sense of the breakdown point, which uses more observations than standard estimators. We apply our approach on the concepts of boxplot and bagplot. We work in a general normed vector space and allow multi-valued estimators.     

Robust online scale estimation in time series: A model-free approach

This paper presents variance extraction procedures for univariate time series. The volatility of a times series is monitored allowing for non-linearities, jumps and outliers in the level. The volatility is measured using the height of triangles formed by consecutive observations of the time series. This idea was proposed by Rousseeuw and Hubert [1996. Regression-free and robust estimation of scale for bivariate data. Comput. Statist. Data Anal. 21, 67–85] in the bivariate setting. This paper extends their procedure to apply for online scale estimation in time series analysis. The statistical properties of the new methods are derived and finite sample properties are given. A financial and a medical application illustrate the use of the procedures.     

Robust linear regression: A review and comparison

Ordinary least-square (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article aims to review and describe some available and popular robust techniques, including some recent developed ones, and compare them in terms of breakdown point and efficiency. In addition, we also use a simulation study and a real data application to compare the performance of existing robust methods under different scenarios.     

Finite sample tail behaviour of hodges-lehmann type estimators

The tail behavior of Hodges-Lehmann type location estimators is studied with respect to a tail performance measure. The result obtained here generalizes and complements the corresponding work on R-estimators of JurecKova (1981a). The connection between the tail behavior and the breakdown point discovered in He, Jureckova Koenker and Portnoy (1990) for regression and monotone location estimators is extended to Hodges-Lehmann type location estimators, confirming the important role of the tail behavior as a measure of robustness of estimators.     

Robust Multivariate Outlier Labeling

A criterion for robust estimation of location and covariance matrix is considered, and its application in outlier labeling is discussed. This method, unlike the methods based on MVE and MCD, is applicable to large and high-dimension data sets. The method proposed here is also robust and has the same breakdown point as the MVE- and MCD-based methods. Furthermore, the computational complexity of the proposed method is significantly smaller than that of other methods.