C. Caroni

Sequential application of Wilks's multivariate outlier test

A generalization of Wilkss single‐outlier test suitable for application to the many‐outlier problem of detecting from 1 to k outliers in a multivariate data set is proposed and appropriate critical values determined. The method used follows that suggested by Rosner employing sequential application of the generalized extreme Studentized deviate to univariate samples of reducing size, in which the type I error is controlled both under the hypothesis of no outliers and under the alternative hypothesis of 1, 2,. . ., k outliers. It is shown that critical values for the sequential application of Wilkss test to detect many outliers depend only on those for a single outlier test which may be approximated by percentage points from the F‐distributions as tabulated by Wilks. Relationships between Wilkss test statistic, the Mahalanobis distance between the ‘outlier’ and the mean vector, and Hotellings T2‐test between the outlier and the rest of the data, are used to reduce the amount of computation involved in applying the sequential procedure. Simulations are used to show that the method behaves well in detecting multiple outliers in samples larger than about 25. Finally, an example with three dimensions is used to illustrate how the method is applied.

The correct "ball bearings" data.

The famous data on fatigue failure times of ball bearings have been quoted incorrectly from Lieblein and Zelens original paper. The correct data include censored values, as well as non-fatigue failures that must be handled appropriately. They could be described by a mixture of Weibull distributions, corresponding to different modes of failure.

In-depth analysis of the causal factors of incidents reported in the Greek petrochemical industry

This paper presents a statistical analysis of all reported incidents in the Greek petrochemical industry from 1997 to 2003. A comprehensive database has been developed to include industrial accidents (fires, explosions and substance releases), occupational accidents, incidents without significant consequences and near misses. The study concentrates on identifying and analyzing the causal factors related to different consequences of incidents, in particular, injury, absence from work and material damage. Methods of analysis include logistic regression with one of these consequences as dependent variable. The causal factors that are considered cover four major categories related to organizational issues, equipment malfunctions, human errors (of commission or omission) and external causes. Further analyses aim to confirm the value of recording near misses by comparing their causal factors with those of more serious incidents. The statistical analysis highlights the connection between the human factor and the underlying causes of accidents or incidents.

Failure limited data and TTT-based trend tests in multiple repairable systems

Tests for trend in multiple repairable systems based on the total time on test (introduced by Kvaloy and Lindqvist) are valid for data that end at a failure time only if data collection was planned to continue until a predetermined number of failures had occurred. They are not valid for a commoner form of data that end with the last of a random number of failures within a predetermined observation period. The necessary modification to the analysis is given here and appropriate terminology is suggested.

Outlier detection by robust principal components analysis

The robust principal components analysis (RPCA) introduced by Campbell (Applied Statistics 1980, 29, 231–237) provides in addition to robust versions of the usual output of a principal components analysis, weights for the contribution of each point to the robust estimation of each component. Low weights may thus be used to indicate outliers. The present simulation study provides critical values for testing the kth smallest weight in the RPCA of a sample of n p-dimensional vectors, under the null hypothesis of a multivariate normal distribution. The cases p=2(2)10, 15, 20 for n=20, 30, 40, 50, 75, 100 subject to n≥p/2, are examined, with k≤√n.

Robust Detection of Multiple Outliers in Grouped Multivariate Data

Abstract Many methods have been developed for detecting multiple outliers in a single multivariate sample, but very few for the case where there may be groups in the data. We propose a method of simultaneously determining groups (as in cluster analysis) and detecting outliers, which are points that are distant from every group. Our method is an adaptation of the BACON algorithm proposed by Billor, Hadi and Velleman for the robust detection of multiple outliers in a single group of multivariate data. There are two versions of our method, depending on whether or not the groups can be assumed to have equal covariance matrices. The effectiveness of the method is illustrated by its application to two real data sets and further shown by a simulation study for different sample sizes and dimensions for 2 and 3 groups, with and without planted outliers in the data. When the number of groups is not known in advance, the algorithm could be used as a robust method of cluster analysis, by running it for various numbers of groups and choosing the best solution.

Proportional hazards models with discrete frailty

We extend proportional hazards frailty models for lifetime data to allow a negative binomial, Poisson, Geometric or other discrete distribution of the frailty variable. This might represent, for example, the unknown number of flaws in an item under test. Zero frailty corresponds to a limited failure model containing a proportion of units that never fail (long-term survivors). Ways of modifying the model to avoid this are discussed. The models are illustrated on a previously published set of data on failures of printed circuit boards and on new data on breaking strengths of samples of cord.

Detecting an innovative outlier in a set of time series

Abstract Tests for an innovative outlier affecting every member of a set of autoregressive time series at the same time point are developed. In one model, the outliers are represented as independent random effects; likelihood ratio tests are derived for this case and simulated critical values are tabulated. In a second model, assuming that the size of the outlier is the same in each series, a standard regression framework can be used and correlations between the series are introduced. Simulation studies show that approximate critical values obtained from the χ 1 2 distribution work well for heteroscedastic independent series and for the case of equal correlations between each pair of series.

Nuclear grade plus proliferation grading system for invasive ductal carcinoma of the breast: validation in a tertiary referral hospital cohort.

OBJECTIVES For patients with invasive breast cancer, management decisions are informed by tumor grade according to the Nottingham Grading System (NGS), either on its own or as part of the Nottingham Prognostic Index (NPI). A system retaining the nuclear grade element but substituting the two subjective components, mitosis count and tubule formation, of the NGS with a proliferation index based on Ki-67 (MIB-1) has been proposed (nuclear grade plus proliferation [N+P] grading). METHODS We validated the prognostic value of this grading system on a population of 322 women. RESULTS N+P grading resulted in more grade I tumors (47.9% vs 4.5%) and fewer grade II (32% vs 51.5%) and grade III (20.1% vs 44%) tumors compared with NGS. The NPI calculated based on N+P grade had a similar association with survival (P < .001; odds ratio, 1.729) as the NPI calculated on the basis of the NGS grade (P < .001; odds ratio, 1.668). CONCLUSIONS The N+P system seems equivalent to the NGS system.

Graduation and attrition of engineering students in Greece

Greek engineering Schools have a high status and attract good students. However, we show that in the leading institution, the National Technical University of Athens, only 27% of the students admitted in 1992–2003 graduated after the nominal five years study: the median graduation time was 73 months (reaching 93 months in one School) and 12% are predicted never to graduate at all, most without withdrawing officially. Results differ between Schools, between routes of admission and by gender (females being better than males). Systematic study of reasons for not completing or delay in completing studies is urgently needed. Overall, 4% of the students withdraw officially during their first year. The percentage of withdrawals by School is negatively correlated with the percentage that gave that School as first choice in the entrance procedure, indicating problems in the admission system.