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Optimal Design for Experiments with Potentially Failing TrialsHackl, Peter January 1994 (has links) (PDF)
We discuss the problem of optimal allocation of the design points of an experiment for the case where the trials may fail with non-zero probability. Numerical results for D-optimal designs are given for estimating the coefficients of a polynomial regression. For small sample sizes these designs may deviate substantially from the corresponding designs in the case of certain response. They can be less efficient, but are less affected by failing trials. (author's abstract) / Series: Forschungsberichte / Institut für Statistik
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Optimal Design for Variogram EstimationMüller, Werner, Zimmerman, Dale L. January 1997 (has links) (PDF)
The variogram plays a central role in the analysis of geostatistical data. A valid variogram model is selected and the parameters of that model are estimated before kriging (spatial prediction) is performed. These inference procedures are generally based upon examination of the empirical variogram, which consists of average squared differences of data taken at sites lagged the same distance apart in the same direction. The ability of the analyst to estimate variogram parameters efficiently is affected significantly by the sampling design, i.e., the spatial configuration of sites where measurements are taken. In this paper, we propose design criteria that, in contrast to some previously proposed criteria oriented towards kriging with a known variogram, emphasize the accurate estimation of the variogram. These criteria are modifications of design criteria that are popular in the context of (nonlinear) regression models. The two main distinguishing features of the present context are that the addition of a single site to the design produces as many new lags as there are existing sites and hence also produces that many new squared differences from which the variograrn is estimated. Secondly, those squared differences are generally correlated, which inhibits the use of many standard design methods that rest upon the assumption of uncorrelated errors. Several approaches to design construction which account for these features are described and illustrated with two examples. We compare their efficiency to simple random sampling and regular and space-filling designs and find considerable improvements. (author's abstract) / Series: Forschungsberichte / Institut für Statistik
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Optimal coordinate sensor placements for estimating mean and variance components of variation sourcesLiu, Qinyan 29 August 2005 (has links)
In-process Optical Coordinate Measuring Machine (OCMM) offers the potential of diagnosing in a timely manner variation sources that are responsible for product quality defects. Such a sensor system can help manufacturers improve product quality and reduce process downtime. Effective use of sensory data in diagnosing variation sources depends on the optimal design of a sensor system, which is often known as the problem of sensor placements. This thesis addresses coordinate sensor placement in diagnosing dimensional variation sources in assembly processes. Sensitivity indices of detecting process mean and variance components are defined as the design criteria and are derived in terms of process layout and sensor deployment information. Exchange algorithms, originally developed in the research of optimal experiment deign, are employed and revised to maximize the detection sensitivity. A sort-and-cut procedure is used, which remarkably improve the algorithm efficiency of the current exchange routine. The resulting optimal sensor layouts and its implications are illustrated in the specific context of a panel assembly process.
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Further aspects on an example of D-optimal designs in the case of correlated errorsStehlik, Milan January 2004 (has links) (PDF)
The aim of this paper is discussion on particular aspects of the extension of a classic example in the design of experiments under the presence of correlated errors. Such extension allows us to study the effect of the correlation range on the design. We discuss the dependence of the information gained by the D-optimum design on the covariance bandwidth and also we concentrate to some technical aspects that occurs in such settings. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics
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Some properties of D-optimal designs for random fields with different variogramsStehlik, Milan January 2004 (has links) (PDF)
The aim of this paper is discussion on particular properties of D-optimal designs under isotropic and intrinsically stationary correlation structures. We show that design points can collapse under the presence of some covariance structures. This enables to include so called nugget effect by natural way. Some numerical examples are also included. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics
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Optimal coordinate sensor placements for estimating mean and variance components of variation sourcesLiu, Qinyan 29 August 2005 (has links)
In-process Optical Coordinate Measuring Machine (OCMM) offers the potential of diagnosing in a timely manner variation sources that are responsible for product quality defects. Such a sensor system can help manufacturers improve product quality and reduce process downtime. Effective use of sensory data in diagnosing variation sources depends on the optimal design of a sensor system, which is often known as the problem of sensor placements. This thesis addresses coordinate sensor placement in diagnosing dimensional variation sources in assembly processes. Sensitivity indices of detecting process mean and variance components are defined as the design criteria and are derived in terms of process layout and sensor deployment information. Exchange algorithms, originally developed in the research of optimal experiment deign, are employed and revised to maximize the detection sensitivity. A sort-and-cut procedure is used, which remarkably improve the algorithm efficiency of the current exchange routine. The resulting optimal sensor layouts and its implications are illustrated in the specific context of a panel assembly process.
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Optimal Design of Experiments for Dual-Response SystemsJanuary 2016 (has links)
abstract: The majority of research in experimental design has, to date, been focused on designs when there is only one type of response variable under consideration. In a decision-making process, however, relying on only one objective or criterion can lead to oversimplified, sub-optimal decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical during the decision-making process in order to balance the tradeoffs of all potential solutions. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest does not have a clear answer, particularly when the response variables have different distributions. Responses with different distributions have different requirements of the design.
Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work.
The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016
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Locally D-optimal Designs for Generalized Linear ModelsJanuary 2018 (has links)
abstract: Generalized Linear Models (GLMs) are widely used for modeling responses with non-normal error distributions. When the values of the covariates in such models are controllable, finding an optimal (or at least efficient) design could greatly facilitate the work of collecting and analyzing data. In fact, many theoretical results are obtained on a case-by-case basis, while in other situations, researchers also rely heavily on computational tools for design selection.
Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem. / Dissertation/Thesis / Doctoral Dissertation Statistics 2018
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Regularities in the Augmentation of Fractional Factorial DesignsKessel, Lisa 03 May 2013 (has links)
Two-level factorial experiments are widely used in experimental design because they are simple to construct and interpret while also being efficient. However, full factorial designs for many factors can quickly become inefficient, time consuming, or expensive and therefore fractional factorial designs are sometimes preferable since they provide information on effects of interest and can be performed in fewer experimental runs. The disadvantage of using these designs is that when using fewer experimental runs, information about effects of interest is sometimes lost. Although there are methods for selecting fractional designs so that the number of runs is minimized while the amount of information provided is maximized, sometimes the design must be augmented with a follow-up experiment to resolve ambiguities. Using a fractional factorial design augmented with an optimal follow-up design allows for many factors to be studied using only a small number of additional experimental runs, compared to the full factorial design, without a loss in the amount of information that can be gained about the effects of interest. This thesis looks at discovering regularities in the number of follow-up runs that are needed to estimate all aliased effects in the model of interest for 4-, 5-, 6-, and 7-factor resolution III and IV fractional factorial experiments. From this research it was determined that for all of the resolution IV designs, four or fewer (typically three) augmented runs would estimate all of the aliased effects in the model of interest. In comparison, all of the resolution III designs required seven or eight follow-up runs to estimate all of the aliased effects of interest. It was determined that D-optimal follow-up experiments were significantly better with respect to run size economy versus fold-over and semi-foldover designs for (i) resolution IV designs and (ii) designs with larger run sizes.
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Exact D-optimal Designs for First-order Trigonometric Regression Models on a Partial CircleSun, Yi-Ying 24 June 2011 (has links)
Recently, various approximate design problems for low-degree trigonometric regression models on a partial circle have been solved. In this paper we consider approximate and exact optimal design problems for first-order trigonometric regression models without intercept on a partial circle. We investigate the intricate geometry of the non-convex exact trigonometric moment set and provide characterizations of its boundary. Building on these results we obtain a complete solution of the exact D-optimal design problem. It is shown that the structure of the optimal designs depends on both the length of the design interval and the number of observations.
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