Projection bounds on expectations of record statistics from restricted families

The projection method is applied to derive sharp moment bounds for the expectations of record statistics based on independent samples from two families of life distributions: the ones with decreasing failure probability and rate.     

MINIMAX ESTIMATION OF A MULTIVARIATE NORMAL MEAN UNDER A CONVEX LOSS FUNCTION

Let X = (X₁, - X_p)prime; ˜ N_p (μ, Σ) where μ= (μ₁, -, μ_p)' and Σ= diag (Σ²₁, -, Σ²_p) are both unknown and p3. Let (n_i - 2) w_i/Σ²_i! X²_ni, independent. of w_i (I ≠ j = 1, -, p). Assume that (w₁, -, w_p) and X are independent. Define W = diag (w₁, -, w_p) and ¶ X ¶²_w= X'W^-1Q^-1W^-1X where Q = diag (q₁, -,n q_p), q_i > 0, i = 1, -, p. In this paper, the minimax estimator of Berger & Bock (1976), given by δ (X, W) = [I_p - r(X, W) ¶ X ¶^-2_w Q^-1W^-1] X, is shown to be minimax relative to the convex loss (δ - μ)'[αQ + (1 - α) Σ^-1] δ - μ)/C, where C =α tr (Σ) + (1 - α)p and 0 α 1, under certain conditions on r(X, W). This generalizes the above mentioned result of Berger & Bock.     

Partner selection for reverse logistics centres in green supply chains: a fuzzy artificial immune optimisation approach

The design of reverse logistics networks has now emerged as a major issue for manufacturers, not only in developed countries where legislation and societal pressures are strong, but also in developing countries where the adoption of reverse logistics practices may offer a competitive advantage. This paper presents a new model for partner selection for reverse logistic centres in green supply chains. The model offers three advantages. Firstly, it enables economic, environment and social factors to be considered simultaneously. Secondly, by integrating fuzzy set theory and artificial immune optimisation technology, it enables both quantitative and qualitative criteria to be considered simultaneously throughout the whole decision-making process. Thirdly, it extends the flat criteria structure for partner selection evaluation for reverse logistics centres to the more suitable hierarchy structure. The applicability of the model is demonstrated by means of an empirical application based on data from a Chinese electronic equipment and instruments manufacturing company.     

Line balance analyses for system assembly lines in an electronic plant

This research analysed and optimised the assembly line balance of notebook computer system production lines in a major computer plant. The research developed a mathematical model for balancing assembly lines of a specific notebook computer system. Precedence relationship charts were created to enforce the required sequences and ILOG CPLEX software was used to obtain the optimal solution of the task assignments to the workstations. The new task assignments were simulated to verify the improvement recommendations and predict the potential benefits.The estimated improvements include: (1) 5.9% increase in average daily production; (2) 29% decrease in average daily WIP; (3) 67.9% reduction in cycle time; (4) 16.7% reduction in operator headcount over the whole system assembly area. The contributions of this research include: (1) Establishing line balancing mathematical model suitable for notebook computer factories; (2) Optimising the system assembly lines for the subject company; (3) Transferring the line balance modelling and optimisation techniques for company use.     

A note on the common location parameter of several exponential populations

The problem of estimation of an unknown common location parameter of several exponential populations with unknown and possibly unequal scale parameters is considered. A wide class of estimators, including both a modified maximum likelihood estimator (MLE), and the uniformly minimum variance unbiased estimator (Umvue) proposed by ghosh and razmpour(1984), is obtained under a class of convex loss functions.     

Projection Mean–Variance Bounds on Expectations of kth Record Values from Restricted Families

We present sharp mean–variance bounds for expectations of kth record values based on distributions coming from restricted families of distributions. These families are defined in terms of convex or star ordering with respect to generalized Pareto distribution. The bounds for expectations of kth record values from DD, DFR, DDA, and DFRA families are special cases of our results. The bounds are derived by application of the projection method.     

Bounds for Expectations of Differences of Generalized Order Statistics Based on General and Life Distributions

Let X _? ^(r), r ≥ 1, denote generalized order statistics based on an arbitrary distribution function F with finite pth absolute moment for some 1 ≤ p ≤ ∞. We present sharp upper bounds on E(X _? ^(s) ? X _? ^(r)), 1 ≤ r < s, for F being either general or life distribution. The bounds are expressed in various scale units generated by pth central absolute or raw moments of F, respectively. The distributions achieving the bounds are specified.     

On Maximum Likelihood Estimation for the Two Parameter Burr XII Distribution

This article considers three related aspects of maximum likelihood estimation of parameters in the two-parameter Burr XII distribution. Specifically, we first provide further clarification to some limiting results in Wingo (1993 Wingo , D. R. ( 1993 ). Maximum likelihood estimation of Burr XII distribution parameters under Type II censoring . Microelectron. Reliab. 33 : 1251 – 1257 .[Crossref], [Web of Science ®] , [Google Scholar]). We then focus on details in a proof of the uniqueness of the maximum likelihood estimators. Finally, we consider using the likelihood approach for data which does not satisfy Wingo's criterion, and show that this results in fitting either a Pareto distribution or an intuitively sensible degenerate distribution to the data. The discussion here is completely general, and not restricted to data obtained under Type II censoring.     

Mixtures of Farlie-Gumbel-Morgenstern Copulas

Some modifications of bivariate Farlie-Gumbel-Morgenstern (FGM) copulas are going to be explained in this article. These modifications are generated by using mixtures of bivariate FGM copula functions. The main goal of this study is to determine both the ranges of association parameter and the rate of correlation, and also observe the changes in local dependence function. An application, which is related with simulated data, is conducted and results are illustrated.     

Using Convex Combination of Copulas and EM Algorithm for Credibility

In this article, using longitudinal data, we develop the theory of credibility by copula model. The convex combination of copulas is used to describe the dependencies among claims. Finally, for comparing with the results of a single copula, using EM algorithm, some simulations of Massachusetts automobile claims are presented.