QUADRATIC ADMISSIBLE ESTIMATE OF COVARIANCE IN PSEUDO-ELLIPTICAL CONTOURED DISTRIBUTION

This article mainly discusses the admissibility of quadratic estimate of covariance in pseudoelliptical distribution. Under the quadratic loss function, the necessary and sufficient conditions that a quadratic estimator is an admissible estimator of covariance in the class of quadratic estimators are obtained. A complete class of the quadratic estimator class is also given.

The Minimax Estimator of Stochastic Regression Coefficients and Parameters in the Class of All Estimators

In this paper, the authors address the problem of the minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general normal linear model with random effects. Under a quadratic loss function, the minimax property of linear estimators is investigated. In the class of all estimators, the minimax estimator of estimable functions, which is unique with probability 1, is obtained under a multivariate normal distribution.

Simultaneous determination of manufacturer’s process mean and production run length,and retailer’s order quantity

In Chen and Liu’s optimum profit model with a traditional production system,they did not consider the effect of product quality on the customer’s demand order quantity,and also ignored the used cost of customers for product.In fact,the customer’s demand quantity is always seriously related to product quality.Hence,in the present paper,we modify Chen and Liu’s model to address the determination of the optimal process parameters by employing the idea of quality loss and single sampling rectifying inspection plan.Assuming that the quality characteristic of the product is normally distributed,Taguchi’s symmetric quadratic quality loss function is applied in evaluating the product quality.Three decision variables,i.e.,the mean of the process characteristic,the production run length of the product and the retailer’s order quantity,are jointly determined in our modified model to maximize the expected total profit of society,which includes both the manufacturer and the retailer.A heuristic solution procedure is developed for this optimization problem,and a numerical example is provided for illustration.From the numerical results,it can be seen that both the sale price per unit and the intercept of the mean demand of the customer are two major(or significant)parameters in the model and should be more accurately estimated in practice.Finally,the quality investment policy is provided to compare its effect on the optimum profit model with quality improvement.

Simultaneous settings of order quantity,wholesale price,production run length,process mean,and warranty period

In this article,the authors propose a modified version of S.L.Chen and Liu’s model with a two-stage production system.Assume that the retailer’s order quantity is concerned with the manufacturer’s selling price and the warranty period of product.The used cost of the customer is measured under the Taguchi’s quadratic quality loss function and concluded in the retailer’s profit function.The quality of the lot for the manufacturer is determined by adopting a two-stage single sampling rectifying inspection plan.The modified economic manufacturing quantity(EMQ)model is addressed in formulating the manufacturer’s expected profit.The retailer’s order quantity,manufacturer’s wholesale price,production run length,process mean,and warranty period of product will be jointly determined by maximizing the total expected profit of the supply chain system including the manufacturer and the retailer.Finally,the quality investment policy is introduced to illustrate the profit improvement for the supply chain system.