• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.16 no.1
• /
• pp.97-105
• /
• 2015

Multiresponse optimization (MRO) seeks to find the setting of input variables, which optimizes the multiple responses simultaneously. The approach of weighted mean squared error (WMSE) minimization for MRO imposes a different weight on the squared bias and variance, which are the two components of the mean squared error (MSE). To date, a weighted sum-based method has been proposed for WMSE minimization. On the other hand, this method has a limitation in that it cannot find the most preferred solution located in a nonconvex region in objective function space. This paper proposes a Tchebycheff metric-based method to overcome the limitations of the weighted sum-based method.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.14 no.2
• /
• pp.625-633
• /
• 2013

Multiple response surface optimization (MRSO) aims at finding a setting of input variables which simultaneously optimizes multiple responses. The minimization of mean squared error (MSE), which consists of the squared bias and variance terms, is an effective way to consider the location and dispersion effects of the responses in MRSO. This approach basically assumes that both the terms have an equal weight. However, they need to be weighted differently depending on a problem situation, for example, in case that they are not of the same importance. This paper proposes to use the weighted MSE (WMSE) criterion instead of the MSE criterion in MRSO to consider an unequal weight situation.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.2
• /
• pp.535-545
• /
• 2015

In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.

• Journal of the Korean Data and Information Science Society
• /
• v.16 no.2
• /
• pp.371-382
• /
• 2005

The paper compares the performance of some widely used Bayesian estimators such as Bayes estimator, empirical Bayes estimator, constrained Bayes estimator and constrained Bayes estimator by means of a new measurement under squared error loss function for the typical normal-normal situation. The proposed measurement is a weighted sum of the precisions of first and second moments. As a result, one can gets the criterion according to the size of prior variance against the population variance.

• Journal of Korean Society for Quality Management
• /
• v.42 no.4
• /
• pp.685-700
• /
• 2014

Purpose: The purpose of this paper is to develop a systematic weighting procedure based on process capability indices method applying weighted mean squared error minimization (WMSE) approach to dual response surface optimization. Methods: The proposed procedure consists of 5 steps. Step 1 is to prepare the alternative vectors. Step 2 is to rank the vectors based on process capability indices in a pairwise manner. Step 3 is to transform the pairwise rankings into the inequalities between the corresponding WMSE values. Step 4 is to obtain the weight value by calculating the inequalities. Or, step 5 is to obtain the weight value by minimizing the total violation amount, in case there is no weight value in step 4. Results: The typical 4 process capability indices, namely, $C_p$, $C_{pk}$, $C_{pm}$, $C_{pmk}$ are utilized for the proposed procedure. Conclusion: The proposed procedure can provide a weight value in WMSE based on the objective quality performance criteria, not on the decision maker's subjective judgments or experiences.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.16 no.10
• /
• pp.7061-7070
• /
• 2015

Multi-Response Surface Optimization aims at finding the optimal setting of input variables considering multiple responses simultaneously. The Weighted Mean Squared Error (WMSE) minimization approach, which imposes a different weight on the two components of mean squared error, squared bias and variance, first obtains WMSE for each response and then minimizes all the WMSEs at once. Most of the methods proposed for the WMSE minimization approach to date are classified into the prior preference articulation approach, which requires that a decision maker (DM) provides his/her preference information a priori. However, it is quite difficult for the DM to provide such information in advance, because he/she cannot experience the relationships or conflicts among the responses. To overcome this limitation, this paper proposes a posterior preference articulation method to the WMSE minimization approach. The proposed method first generates all (or most) of the nondominated solutions without the DM's preference information. Then, the DM selects the best one from the set of nondominated solutions a posteriori. Its advantage is that it provides an opportunity for the DM to understand the tradeoffs in the entire set of nondominated solutions and effectively obtains the most preferred solution suitable for his/her preference structure.

• Proceedings of the Korean Association for Survey Research Conference
• /
• 2002.11a
• /
• pp.255-274
• /
• 2002

We classify rotation sampling designs into two classes. The first class replaces sample units within the same rotation group while the second class replaces sample units between different rotation groups. The first class is specified by the three-way balanced design which is a multi-level version of previous balanced designs. We introduce an extended generalized composite estimator (EGCE) and derive its variance and mean squared error for each of the two classes of design, cooperating two types of correlations and three types of biases. Unbiased estimators are derived for difference between interview time biases, between recall time biases, and between rotation group biases. Using the variance and mean squared error, since any rotation design belongs to one of the two classes and the EGCE is a most general estimator for rotation design, we evaluate the efficiency of EGCE to simple weighted estimator and the effects of levels, design gaps, and rotation patterns on variance and mean squared error.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2012.05a
• /
• pp.623-625
• /
• 2012

The restoration of an image corrupted by Gaussian noise is an important task in image processing. There are many kinds of filters are proposed to remove Gaussian noise such as Gaussian filter, mean filter, weighted filter, etc. However, they perform not good enough for denoising and edge preservation. Hence, in this paper we proposed an adaptive weighted filter which considers spatial distance and the estimated variance of noise. We also compared the proposed method with existing methods through the simulation and used MSE(mean squared error) as the standard of judgement of improvement effect.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.38 no.3
• /
• pp.159-168
• /
• 2015

Aggregate Production Planning determines levels of production, human resources, inventory to maximize company's profits and fulfill customer's demands based on demand forecasts. Since performance of aggregate production planning heavily depends on accuracy of given forecasting demands, choosing an accurate forecasting method should be antecedent for achieving a good aggregate production planning. Generally, typical forecasting error metrics such as MSE (Mean Squared Error), MAD (Mean Absolute Deviation), MAPE (Mean Absolute Percentage Error), and CFE (Cumulated Forecast Error) are utilized to choose a proper forecasting method for an aggregate production planning. However, these metrics are designed only to measure a difference between real and forecast demands and they are not able to consider any results such as increasing cost or decreasing profit caused by forecasting error. Consequently, the traditional metrics fail to give enough explanation to select a good forecasting method in aggregate production planning. To overcome this limitation of typical metrics for forecasting method this study suggests a new metric, WACFE (Weighted Absolute and Cumulative Forecast Error), to evaluate forecasting methods. Basically, the WACFE is designed to consider not only forecasting errors but also costs which the errors might cause in for Aggregate Production Planning. The WACFE is a product sum of cumulative forecasting error and weight factors for backorder and inventory costs. We demonstrate the effectiveness of the proposed metric by conducting intensive experiments with demand data sets from M3-competition. Finally, we showed that the WACFE provides a higher correlation with the total cost than other metrics and, consequently, is a better performance in selection of forecasting methods for aggregate production planning.

• Communications for Statistical Applications and Methods
• /
• v.3 no.2
• /
• pp.205-216
• /
• 1996

Consider the problem of estimating a multivariate normal mean with an unknown covarience matrix under a weighted sum of squared error losses. We first provide hierarchical Bayes estimators which shrink the usual (maximum liklihood, uniformly minimum variance unbiased) estimator towards a regression surface and then prove the admissibility of these estimators using Blyth's (1951) method.