Stochastic Modelling of Times to Temperature for Furnaces Supplying Titanium Blooms to a Rolling Mill at TIMET

In conjunction with TIMET at Waunarlwydd (Swansea, UK) a model has been developed that will optimise the scheduling of various blooms to their eight furnaces so as to minimise the time taken to roll these blooms into the finished mill products. This production scheduling model requires reliable data on times taken for the various furnaces that heat the slabs and blooms to reach the temperatures required for rolling. These times to temperature are stochastic in nature and this paper identifies the distributional form for these times using the generalised F distribution as a modelling framework. The times to temperature were found to be similarly distributed over all furnaces. The identified distributional forms were incorporated into the scheduling model to optimise a particular campaign that was run at TIMET Swansea. Amongst other conclusion it was found that, compared to the actual campaign, the model produced a schedule that reduced the makespan by some 35%.     

Estimating ordered parameters by linear programming

There are many models that require the estimation of a set of ordered parameters. For example, multivariate analysis of variance often is formulated as testing for the equality of the parameters versus an ordered alternative. This problem, referred to as isotonic inference, constrained inference, or isotonic regression, has led to the development of general solutions, not often easy to apply in special models. In this expository paper, we study the special case of a separable convex quadratic programming problem for which the optimality conditions lead to a readily solved linear complementarity problem in the Lagrange multipliers, and subsequently to an equivalent linear programming problem, whose solution can be used to recover the solution of the original isotonic problem. The method can be applied to estimating ordered correlations, ordered binomial probabilities, ordered Poisson parameters, ordered exponential scale parameters, or ordered risk differences.     

A graphical summary of disparities in health care and related summary measures

In order to assess the effectiveness of government programs designed to reduce disparities in the health care minority groups receive relative to the majority white population, a proper statistical measure should be used. This article proposes a measure of and its accompanying graph, which is readily interpretable and is not affected by the number of minority subgroups examined.     

Estimating the distribution function using k-tuple ranked set samples

The basic assumption underlying the concept of ranked set sampling is that actual measurement of units is expensive, whereas ranking is cheap. This may not be true in reality in certain cases where ranking may be moderately expensive. In such situations, based on total cost considerations, k-tuple ranked set sampling is known to be a viable alternative, where one selects k units (instead of one) from each ranked set. In this article, we consider estimation of the distribution function based on k-tuple ranked set samples when the cost of selecting and ranking units is not ignorable. We investigate estimation both in the balanced and unbalanced data case. Properties of the estimation procedure in the presence of ranking error are also investigated. Results of simulation studies as well as an application to a real data set are presented to illustrate some of the theoretical findings.     

Nonparametric estimation of the conditional distribution function in a semiparametric censorship model

In this paper we propose a new nonparametric estimator of the conditional distribution function under a semiparametric censorship model. We establish an asymptotic representation of the estimator as a sum of iid random variables, balanced by some kernel weights. This representation is used for obtaining large sample results such as the rate of uniform convergence of the estimator, or its limit distributional law. We prove that the new estimator outperforms the conditional Kaplan–Meier estimator for censored data, in the sense that it exhibits lower asymptotic variance. Illustration through real data analysis is provided.     

Bayesian analysis of outlier problems using divergence measures

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.     

关于有效促进社会公正的几个问题

本文认为:(1)为了顺利地推进改革,为了中国社会经济持续、有效和健康的发展,就必须适应新的历史条件,顺应民意、顺应现代社会的基本趋势,把社会公正放到一个突出的位置。(2)在中国现阶段应当开始建立一个初级的社会公平保障体系。初级社会公平保障体系的基本特征是低水准、广覆盖、有实效。对于国家来说,近期需要做的事情可以分为两大块,一是国家的直接投入,二是国家的立法、监督、执行和引导。(3)有一些根深蒂固的观念在妨碍着我们重视社会公正问题。这些观念主要包括:“原始积累不可避免”,“国家财力不足”,“重视公正便会妨碍效率”,因此我们必须对这些观念进行一番必要的反思。(4)要想构建一个公正而和谐的社会,就必须培育一个庞大的中等收入者人群,形成一个“两头小,中间大”的橄榄型的社会结构,那么社会就会变得越来越稳定了。     

Two point priors and Γ-minimax estimating in families of uniform distributions

It is shown that when a parameter lying in a sufficiently small interval is to be estimated in a family of uniform distributions, a two point prior is least favourable under squared error loss. The unique Bayes estimator with respect to this prior is minimax. The Γ-minimax estimator is derived for sets Γ of priors consisting of all priors that give fixed probabilities to two specified subintervals of the parameter space if a two point prior is least favourable in Γ.     

A probablistic analysis for an optimal screening problem

Summary We consider a lotL formed byN apparently similar unitsW ₁,…,W _N, where each of theW _i may come from one of two different populationsP ₁ andP ₂;T ₁,…,T _N denote the corresponding lifetimes. The units fromP _i undergo a failure of kindi and their survival function isS _i (t). We assume that the failure rate function are known and that the units fromP ₁ are ?substandard?: λ ₁ (t)≥λ ₂ (t), ∀t≥0. We want to putW ₁,…,W _N under a pre-operational test (burn-in test) in order to eliminate at least a great part of the substandard units and we face the problem of obtaining a rule for stopping the test under the assumption that, with the failure of a unit, it is possible to recognize the population from which the unit comes. Such a problem will be formalized as an optimal stopping problem for a suitably defined Markov process. Our study shall evidentiate some fundamental aspects of the problem and the role of the prior distribution of the (random) numberM ₀ of those units inL coming fromP ₁ (substandard). The latter distribution has a great influence on the form of the solution. This research was supported by the C.N.R. Project ?Statistica Bayesiana e Simulazione in Affidalità e Modellistica Biologica?.     

Reliability analysis of systems with components having two dependent subcomponents

In this article, a system that consists of n independent components each having two dependent subcomponents (A_i, B_i), i = 1, …, n is considered. The system is assumed to compose of components that have two correlated subcomponents (A_i, B_i), and functions iff both systems of subcomponents A₁, A₂, …, A_n and B₁, B₂, …, B_n work under certain structural rules. The expressions for reliability and mean time to failure of such systems are obtained. A sufficient condition to compare two systems of bivariate components in terms of stochastic ordering is also presented.