An Integrative Loss Function Approach to Multi‐Response Optimization

Loss function approach is effective for multi‐response optimization. However, previous loss function approaches ignore the dispersion performance of squared error loss and model uncertainty. In this paper, a weighted loss function is proposed to simultaneously consider the location and dispersion performances of squared error loss to optimize correlated multiple responses with model uncertainty. We propose an approach to minimize the weighted loss function under the constraint that the confidence intervals of future predictions for the multiple responses should be contained in specification limits of the responses. An example is illustrated to verify the effectiveness of the proposed method. The results show that the proposed method can achieve reliable optimal operating condition under model uncertainty. Copyright © 2013 John Wiley & Sons, Ltd.     

Using Fuzzy Cost‐Based FMEA,GRA and Profitability Theory for Minimizing Failures at a Healthcare Diagnosis Service

This paper proposes an integrated approach to identify, evaluate and improve the potential failures in a service setting. This integrated approach combines Fuzzy cost‐based service‐specific FMEA (FCS‐FMEA), Grey Relational Analysis (GRA) and profitability theory for better prioritization of the service failures by considering cost as an important issue and using the profitability theory in a way that the corrective actions costs are taken into account. Considering profitability with FCS‐FMEA and GRA reduces the losses caused by failure occurrence. Besides, a maximization linear mathematical problem is used to select the best mix of failures to be repaired. We apply our approach to an academic example concerning the potential failures diagnosis of the Internal Medicine service of a hospital located in Seoul, Korea. We applied our approach and solved the associated maximization problem by a commercial solver, producing an optimal solution which indicates the most convenient mix of failures to be repaired by considering available budget. Copyright © 2013 John Wiley & Sons, Ltd.     

Visualization Approaches for Evaluating Ridge Regression Estimators in Mixture and Mixture‐Process Experiments

When the component proportions in mixture experiments are restricted by lower and upper bounds, the input space of a designed experiment space can become an irregular region that can induce multicollinearity problems when estimating the component proportion parameters. Thus, ridge regression provides a beneficial means of stabilizing the coefficient estimates in the fitted model. Previous research has focused on using prediction variance as a metric for determining an appropriate value of the ridge constant, k. We use visualization techniques to illustrate and evaluate ridge regression estimators and the robustness of estimation with respect to the variance and the bias. The addition of bias allows better balancing between the stability of the estimators and minimally changing the estimates. We illustrate the graphical methods with mixture and mixture‐process examples from the literature. Copyright © 2014 John Wiley & Sons, Ltd.