• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.195-208
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• 2009

A conventional single design optimality criterion has been used to select an efficient experimental design. But, since an experimental design is constructed with respect to an optimality criterion pre specified by investigators, an experimental design obtained from one optimality criterion which is superior to other designs may perform poorly when the design is evaluated by another optimality criterion. In other words, none of these is entirely satisfactory and even there is no guarantee that a design which is constructed from using a certain design optimality criterion is also optimal to the other design optimality criteria. Thus, it is necessary to develop certain special types of experimental designs that satisfy multiple design optimality criteria simultaneously because these multi-optimal designs (MODs) reflect the needs of the experimenters more adequately. In this article, we present a heuristic approach to construct second-order response surface designs which are more flexible and potentially very useful than the designs generated from a single design optimality criterion in many real experimental situations when several competing design optimality criteria are of interest. In this paper, over cuboidal design region for $3\;{\leq}\;k\;{\leq}\;5$ variables, we construct multi-optimal designs (MODs) that might moderately satisfy two famous alphabetic design optimality criteria, G- and IV-optimality criteria using a GA which considers a certain amount of randomness. The minimum, average and maximum scaled prediction variances for the generated response surface designs are provided. Based on the average and maximum scaled prediction variances for k = 3, 4 and 5 design variables, the MODs from a genetic algorithm (GA) have better statistical property than does the theoretically optimal designs and the MODs are more flexible and useful than single-criterion optimal designs.

• Journal of Korean Society for Quality Management
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• v.21 no.2
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• pp.140-155
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• 1993

The characteristics of $I_{\lambda}$-optimality, one of the linear criteria suggested by Fedorov (1972) are investigated with respect to the D-and heteroscedastic G-optimality in case of non-constant variance function. Though having limited results obtained from simple models, we may conclude that $I_{\lambda}$-optimality is sometimes preferred to the heteroscedastic G-optimality suggested newly bv Wong and Cook (1992) in the sense that the experimenter's belief in weighting function exists in $I_{\lambda}$-optimality criterion, not to mention its computational simplicity.

• Journal of Korean Society for Quality Management
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• v.32 no.3
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• pp.234-243
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• 2004

In this paper, we study the optimality of 2-level resolution V minimal fractional factorial designs which can be constructed by using a partially balanced array. Moreover the relative efficiencies of such designs are compared in the sense of three optimality criteria such as determinant(D)-optimality, trace(A)-optimality, and eigenvalue(E) -optimality criterion.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.55-63
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• 1995

The characteristics of $I{\lambda}$-optimality are investigated with repsect to other experimental design's criteria, D-and G-optimality. The comparisons are based on D- and G-, and $I{\lambda}$-efficiencies using the Beta(p, q) distribution as a weighting function for $I{\lambda}$-optimality. Results indicate that serious consideration should be given to the $I{\lambda}$-optimality criterion especially when the error variance function is not homogeneous.

• International Journal of Reliability and Applications
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• v.17 no.1
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• pp.21-49
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• 2016

Many mechanical, electrical and electronic products have more than one performance characteristics (PCs). For example the performance degradation of rubidium discharge lamps can be characterized by the rubidium consumption or the decreasing intensity the lamp. The product may degrade due to all the PCs which may be independent or dependent. This paper deals with the design of optimal bivariate step-stress partially accelerated degradation test (PADT) with degradation paths modelled by gamma process. The dependency between PCs has been modelled through Frank copula function. In partial step-stress loading, the unit is tested at usual stress for some time, and then the stress is accelerated. This helps in preventing over-stressing of the test specimens. Failure occurs when the performance characteristic crosses the critical value the first time. Under the constraint of total experimental cost, the optimal test duration and the optimal number of inspections at each intermediate stress level are obtained using variance optimality criterion.

• International Journal of Reliability and Applications
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• v.18 no.2
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• pp.45-63
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• 2017

In this paper, we have formulated optimum Accelerated Life Test (ALT) plan for a parallel system with two independent components using masked data with ramp-stress loading scheme and Type-I censoring. Consider a system of two independent and non-identical components connected in parallel. Such a system fails whenever all of its components has failed. The exact component that causes the system to fail is often unknown due to cost and time constraint. For each parallel system at test, we observe its system's failure time and a set of component that includes the component actually causing the system to fail. The stress-life relationship is modelled using inverse power law, and cumulative exposure model is assumed to model the effect of changing stress. The optimal plan consists in finding out the optimum stress rate using D-optimality criterion. The method developed has been explained using a numerical example and sensitivity analysis carried out.

• The Korean Journal of Applied Statistics
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• v.27 no.7
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• pp.1269-1278
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• 2014

Despite the D-optimality criterion becomes very popular in designing an experiment for nonlinear models because of theoretical foundations it provides, it is very critical that the criterion depends on the unknown parameters of the nonlinear model. But some nonlinear models turned out to be partially nonlinear in sense that the optimal design depends on the subset of parameters only. It was a strong belief that the maximin approach to find a robust design to protect against the uncertainty of parameters is not guaranteed to be successful in nonlinear models. But the maximin approach could be a success for the partial nonlinear model, because often the optimal design depends on only one unknown value of parameter, easier to handle than the full parameters. We deal with maximin approach for Michaelis-Menten model with respect to D- and $D_s$-optimality.

• Communications for Statistical Applications and Methods
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• v.15 no.1
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• pp.95-104
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• 2008

This paper addresses issues of robustness in Bayesian optimal design. We may have difficulty applying Bayesian optimal design principles because of the uncertainty of prior distribution. When there are several plausible prior distributions and the efficiency of a design depends on the unknown prior distribution, robustness with respect to misspecification of prior distribution is required. We suggest a new optimal design criterion which has relatively high efficiencies across the class of plausible prior distributions. The criterion is applied to the problem of estimating the turning point of a quadratic regression, and both analytic and numerical results are shown to demonstrate its robustness.

• The Korean Journal of Applied Statistics
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• v.25 no.3
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• pp.485-501
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• 2012

This research is to find a design D that minimizes forecast variance in d dimensions over the candidate space ${\chi}$. We want a robust design since we may not know the specific covariance structure. We seek a design that minimizes a coverage criterion and hope that this design will provide a small forecast variance even if the covariance structure is unobservable. The details of an exchange or swapping algorithm and several properties of the parameters of coverage criterion with the unknown correlation structures are discussed.

• International Journal of Quality Innovation
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• v.1 no.1
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• pp.32-37
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• 2000

In an industrial process, the proper objective is to find the optimal operating conditions with minimum process variability around the target. Vining and Myers(1990) suggest to use the separate model for the mean response and the process varian linear predictor ${\tau}_i={\log}\;{\sigma}^2_i$ is unknown and should be estimated. Noting that the variance of $\hat{{\tau}_i}$ is heterogeneous, another appropriate D-optimality criterion $D_3$ based on the method of generalized least squares is proposed in this paper.