Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Dual response surface optimization: A fuzzy modeling approach

In modern quality engineering, dual response surface methodology is a powerful tool. In this paper, we introduce a fuzzy modeling approach to optimize the dual response system. We demonstrate our approach in two examples and show the advantages of our method by comparing it with existing methods.X11104sciescopu

Optimization of multiple responses considering both location and dispersion effects

An integrated modeling approach to simultaneously optimizing both the location and dispersion effects of multiple responses is proposed. The proposed approach aims to identify the setting of input variables to maximize the overall minimal satisfaction level with respect to both location and dispersion of all the responses. The proposed approach overcomes the common limitation of the existing multiresponse approaches, which typically ignore the dispersion effect of the responses. Several possible variations of the proposed model are also discussed. Properties of the proposed approach are revealed via examples. (c) 2004 Elsevier B.V. All rights reserved.X1166sciescopu

Bayesian Analysis for Weighted Mean-squared Error in Dual Response Surface Optimization

Dual response surface optimization considers the mean and the variation simultaneously. The minimization of mean-squared error (MSE) is an effective approach in dual response surface optimization. Weighted MSE (WMSE) is formed by imposing the relative weights, (lambda, 1-lambda), on the squared bias and variance components of MSE. To date, a few methods have been proposed for determining lambda. The resulting lambda from these methods is either a single value or an interval. This paper aims at developing a systematic method to choose a lambda value when an interval of lambda is given. Specifically, this paper proposes a Bayesian approach to construct a probability distribution of lambda. Once the distribution of lambda is constructed, the expected value of lambda can be used to form WMSE. Copyright (C) 2009 John Wiley & Sons, Ltd.X111012sciescopu

Two-Resource Stochastic Capacity Planning Employing a Bayesian Methodology

We examine a stochastic capacity-planning problem with two resources that can satisfy demand for two services. One of the resources can only satisfy demand for a specific service, whereas the other resource can provide both services. We formulate the problem of choosing the capacity levels of each resource to maximize expected profits. In addition, we provide analytic, easy-to-interpret optimal solutions, as well as perform a comparative statics analysis. As applying the optimal solutions effectively requires good estimates of the unknown demand parameters, we also examine Bayesian estimates of the demand parameters derived via a class of conjugate priors. We compare the optimal expected profits when demands for the two services follow independent distributions with informative and non-informative priors, and demonstrate that using good informative priors on demand can significantly improve performance

Application of uniform design in the formation of cement mixtures

As products and processes become more and more complex, there is an increasing need in the industry to perform experiments with a large number of factors and a large number of levels for each factor. For such experiments, application of traditional designs such as factorial designs or orthogonal arrays is impractical because of the large number of runs required. As an alternative, a type of design, called the uniform design, can be used to solve such problems. The uniform design has been intensively studied by theoreticians for several decades and has many successful examples of application in industry. In this article, we report a successful application of uniform design in product formation in the cement manufacturing industry. Specifically, we investigate the effects of additives on bleeding and compressive strength of a cement mixture. This example illustrates how an experiment of 16 runs was performed to study three factors with 16 levels, 8 levels, and 8 levels, respectively.link_to_subscribed_fulltex

Cumulative probability control charts for geometric and exponential process characteristics

A statistical process control chart called the cumulative probability control chart (CPC-chart) is proposed. The CPC-chart is motivated from two existing statistical control charts, the cumulative count control chart (CCC-chart) and the cumulative quantity control chart (CQC-chart). The CCC- and CQC-charts are effective in monitoring production processes when the defect rate is low and the traditional p- and c-charts do not perform well. In a CPC-chart, the cumulative probability of the geometric or exponential random variable is plotted against the sample number, and hence the actual cumulative probability is indicated on the charts, Apart from maintaining all the favorable features of the CCC- and CQC-charts, the CPC-chart is more flexible and it can resolve a technical plotting inconvenience of the CCC- and CQC-charts.link_to_subscribed_fulltex