minimum aberration designs with two level and four level factors summary for optimal assignment of factors to columns of a 4 2 n design we consider extensions of the minimum aberration criterion for the 2 level designs minimum aberration 412n and 422n designs in 16 and 32 runs are obtained and tabulated some results on the wordlength patterns and design classification are obtained

multiparameter analysis of aero icing problems using proper orthogonal decomposition and multidimensional interpolation steady and unsteady three dimensional viscous turbulent aero icing simulations are computationally expensive especially for certification campaigns when broad parametric studies are needed to overcome the computational effort of such investigations a reduced order modeling approach based on proper orthogonal decomposition and kriging interpolation is proposed using a database of high fidelity numerical simulations experimental data or combinations of both the proposed technique allows approximating solutions by linear combination of a limited number of eigenfunctions bayesian kriging a recent variant is used to obtain the scalar coefficients for the expansion the accuracy of the proposed method is assessed against reference solutions from two and three dimensional aero icing simulations as well as against experimental data

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

regular fractional factorial designs with minimum aberration and maximum estimation capacity using the approach of finite projective geometry we make a systematic study of estimation capacity a criterion of model robustness under the absence of interactions involving three or more factors some general results providing designs with maximum estimation capacity are obtained in particular for two level factorials it is seen that constructing a design with maximum estimation capacity calls for choosing points from a finite projective geometry such that the number of lines is maximized and the distribution of these lines among the chosen points is as uniform as possible we also explore the connection with minimum aberration designs under which the sizes of the alias sets of two factor interactions which are not aliased with main effects are the most uniform possible

quarter fraction factorial designs constructed via quaternary codes submitted quarter fraction factorial designs constructed via quaternary codes by frederick k h phoa and hongquan xu university of california los angeles the research of developing a general methodology for the con struction of good nonregular designs has been very active in the last decade recent research by xu and wong 2007 suggested a new class of nonregular designs constructed from quaternary codes this paper explores the properties and uses of quaternary codes towards the construction of quarter fraction nonregular designs some theo retical results are obtained regarding the aliasing structure of such designs optimal designs are constructed under the maximum resolu tion minimum aberration and maximum projectivity criteria these designs often have larger generalized resolution and larger projectiv ity than regular designs of the same size it is further shown that some of these designs have generalized minimum aberration and maximum projectivity among all possible designs 1 introduction in many scienti c researches and investigations the interests lie in the study of e ects of many factors simultaneously frac tional factorial designs especially two level fractional factorial designs are the most commonly used experimental plans for this type of investigations designs that can be constructed through de ning relations among factors are called regular designs any two factorial e ects in a regular design are supported in part by nsf grant dms 05 05728 ams 2000 subject classi cations primary 62k15 keywords and phrases aliasing index fractional factorial design generalized minimum aberration generalized resolution nonregular design projectivity

clear two factor interactions and minimum aberration wu and hamada recommend selecting resolution iv designs with the maximum number of clear two factor interactions 2fis called maxc2 designs in this paper we develop a method by using graphical representations combinatorial and group theoretic arguments to prove if a given design is a maxc2 design in particular we show that all known minimum aberration designs with resolution iv are maxc2 designs except in six cases and that the second 2 9 4 2 13 7 2 16 10 and 2 17 11 designs given in wu and hamada are maxc2 designs the method also enables us to identify new maxc2 designs that are too large to be verified by computer search

a bayesian variable selection approach for analyzing designed experiments with complex aliasing experiments using designs with complex aliasing patterns are often performed for example twolevel nongeometric plackett burman designs multilevel and mixed level fractional factorial designs two level fractional factorial designs with hard to control factors and supersaturated designs hamada and wu proposed an iterative guided stepwise regression strategy for analyzing the data from such designs that allows entertainment of interactions their strategy provides a restricted search in a rather large model space however this article provides an efficient methodology based on a bayesian variable selection algorithm for searching the model space more thoroughly we show how the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models the proposed methodology is demonstrated with four examples three of which come from actual industrial experiments

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

indicator function and its application in two level factorial designs a two level factorial design can be uniquely represented by a polynomial indicator function therefore properties of factorial designs can be studied through their indicator functions this paper shows that the indicator function is an effective tool in studying two level factorial designs the indicator function is used to generalize the aberration criterion of a regular two level fractional factorial design to all two level factorial designs an important identity of generalized aberration is proved the connection between a uniformity measure and aberration is also extended to all two level factorial designs

expected total test time and bayesian estimation for generalized lindley distribution under progressively type ii censored sample where removals follow the beta binomial probability law in this paper we have proposed the progressive type ii censoring scheme which allows the removals of the live units from a life test with beta binomial probability law during the execution of the experiment to stablish the theory the generalized lindley distribution is considered for our proposed procedure the behaviour of the expected total test time has been investigated through the numerical study the classical as well as the bayesian procedures for the estimation of the unknown model parameters have also been developed under this censoring scheme further the discussion has been extended to the prediction of the future samples under bayesian paradigm finally a real data set has been analysed to illustrate the discussed methodology

blocked nonregular two level factorial designs this article discusses the optimal blocking criteria for nonregular two level designs we extend the optimal blocking criteria of cheng and wu to nonregular designs by adapting the g and g2 minimum aberration criteria discussed by tang and deng to define word length pattern for nonregular designs we extend the notion of word to nonregular designs through a polynomial representation of factorial designs we define treatment resolution and block resolution for evaluating the degrees of aliasing and confounding we propose four new criteria which we use to search for optimal blocking schemes of 12 run 16 run and 20 run two level orthogonal arrays

design of reduced order multirate output linear functional observer based compensators abstract often in control system design it is only necessary to estimate a single but prespecified linear function of the system s state for the purpose of implementing a feedback control law this can be achieved by a linear functional observer which may have order one less than the observability index of the plant but generically cannot have smaller order in this paper we explore the concept of multirate output sampling and show that a linear functional observer based compensator employing multirate sampling of the plant output can be designed with dimension much smaller than that of the linear functional observer based compensator employing single rate sampling of the plant output necessary and sufficient conditions for the existence of the single rate and multirate output linear functional observer based compensators are found design procedures for constructing these observer based compensators are also outlined furthermore both types of compensators are strictly causal and open loop stable for sufficiently small frame period t 0

multivariable multirate sampled data systems state space description transfer characteristics and nyquist criterion first a discrete time state space description is derived for multivariable multirate sampled data systems then the multirate impulse modulation mim and the symmetric coordinate multirate impulse modulation smim of a transfer matrix are defined and their relation to the discrete time state space description is clarified based on the above results four stability criteria are derived the contents of the paper will be useful to extend the modern results about continuous time and single rate sampled data control systems to the multirate sampled data case especially extensions of the ina method and of the robust stability conditions will be straightforward

data analytic tools for understanding random field regression models random field regression rfr models in which a response is treated as the realization of a random field have been advocated for modeling data from experiments in high signal to noise settings in particular rfr models have proven useful in analyzing data generated from computer simulations of complex processes they offer flexibility for smoothing these data and are able to interpolate the known values for factor settings tested on the simulator however these models lack the easy interpretability of standard regression estimators our purpose in this article is to demonstrate that there is actually much common ground between the rfr models and bayesian regression and to provide some simple data analytic tools that can help expose a regression model associated with an rfr model

geometric isomorphism and minimum aberration for factorial designs with quantitative factors factorial designs have broad applications in agricultural engineering and scientific studies in constructing and studying properties of factorial designs traditional design theory treats all factors as nominal however this is not appropriate for experiments that involve quantitative factors for designs with quantitative factors level permutation of one or more factors in a design matrix could result in different geometric structures and thus different design properties in this paper indicator functions are introduced to represent factorial designs a polynomial form of indicator functions is used to characterize the geometric structure of those designs geometric isomorphism is defined for classifying designs with quantitative factors based on indicator functions a new aberration criteria is proposed and some minimum aberration designs are presented

indicator functions and the algebra of the linear quadratic parameterization indicator functions are constructed under the linear quadratic parameterization for contrasts and applied to the study of partial aliasing properties for three level fractional factorial designs an algebraic operation is introduced for the calculation of indicator function coefficients this operation connects design construction methods to the analysis under the linear quadratic system and helps establish simple conditions for the estimability of interactions

stochastic polynomial interpolation for uncertainty quantification with computer experiments multivariate polynomials are increasingly being used to construct emulators of computer models for uncertainty quantification for deterministic computer codes interpolating polynomial metamodels should be used instead of noninterpolating ones for logical consistency and prediction accuracy however available methods for constructing interpolating polynomials only provide point predictions there is no known method that can provide probabilistic statements about the interpolation error furthermore there are few alternatives to grid designs and sparse grids for constructing multivariate interpolating polynomials a significant disadvantage of these designs is the large gaps between allowable design sizes this article proposes a stochastic interpolating polynomial sip that seeks to overcome the problems discussed above a bayesian approach in which interpolation uncertainty is quantified probabilistically through the posterior distribution of the output is employed this allows assessment of the effe

computer experiments with both qualitative and quantitative variables computer experiments have received a great deal of attention in many fields of science and technology most literature assumes that all the input variables are quantitative however researchers often encounter computer experiments involving both qualitative and quantitative variables bqqv in this article a new interface on design and analysis for computer experiments with bqqv is proposed the new designs are one kind of sliced latin hypercube designs with points clustered in the design region and possess good uniformity for each slice for computer experiments with bqqv such designs help to measure the similarities among responses of different level combinations in the qualitative variables an adaptive analysis strategy intended for the proposed designs is developed the proposed strategy allows us to automatically extract information from useful auxiliary responses to increase the precision of prediction for the target response the interface between the proposed design and the analysis strategy

space filling fractional factorial designs fractional factorial designs are widely used in various scientific investigations and industrial applications level permutation of factors could alter their geometrical structures and statistical properties this article studies space filling properties of fractional factorial designs under two commonly used space filling measures discrepancy and maximin distance when all possible level permutations are considered the average discrepancy is expressed as a linear combination of generalized word length pattern for fractional factorial designs with any number of levels and any discrepancy defined by a reproducing kernel generalized minimum aberration designs are shown to have good space filling properties on average in terms of both discrepancy and distance several novel relationships between distance distribution and generalized word length pattern are derived it is also shown that level permutations can improve space filling properties for many existing saturated designs a two step construction pro

periodically varying compensation of time invariant systems linear time invariant discrete time scalar systems under periodically varying output feedback and the associated problems of stabilization and arbitrary eigenvalue assignment are investigated the general form of the characteristic polynomial of the closed loop periodically varying system is obtained and some detailed results are provided for the second order case interesting research questions are pointed out

gaussian process models for computer experiments with qualitative and quantitative factors modeling experiments with qualitative and quantitative factors is an important issue in computer modeling we propose a framework for building gaussian process models that incorporate both types of factors the key to the development of these new models is an approach for constructing correlation functions with qualitative and quantitative factors an iterative estimation procedure is developed for the proposed models modern optimization techniques are used in the estimation to ensure the validity of the constructed correlation functions the proposed method is illustrated with an example involving a known function and a real example for modeling the thermal distribution of a data center

additive gaussian process for computer models with qualitative and quantitative factors abstractcomputer experiments with qualitative and quantitative factors occur frequently in various applications in science and engineering analysis of such experiments is not yet completely resolved in this work we propose an additive gaussian process model for computer experiments with qualitative and quantitative factors the proposed method considers an additive correlation structure for qualitative factors and assumes that the correlation function for each qualitative factor and the correlation function of quantitative factors are multiplicative it inherits the flexibility of unrestrictive correlation structure for qualitative factors by using the hypersphere decomposition embracing more flexibility in modeling the complex systems of computer experiments the merits of the proposed method are illustrated by several numerical examples and a real data application supplementary materials for this article are available online

analysis of computer experiments using penalized likelihood in gaussian kriging models kriging is a popular analysis approach for computer experiments for the purpose of creating a cheap to compute meta model as a surrogate to a computationally expensive engineering simulation model the maximum likelihood approach is used to estimate the parameters in the kriging model however the likelihood function near the optimum may be flat in some situations which leads to maximum likelihood estimates for the parameters in the covariance matrix that have very large variance to overcome this difficulty a penalized likelihood approach is proposed for the kriging model both theoretical analysis and empirical experience using real world data suggest that the proposed method is particularly important in the context of a computationally intensive simulation model where the number of simulation runs must be kept small because collection of a large sample set is prohibitive the proposed approach is applied to the reduction of piston slap an unwanted engine noise due to piston secondary motion issu

a bayesian approach to the design and analysis of fractionated experiments specifying a prior distribution for the large number of parameters in the statistical model is a critical step in a bayesian approach to the design and analysis of experiments this article shows that the prior distribution can be induced from a functional prior on the underlying transfer function the functional prior requires specification of only a few hyperparameters and thus can be easily implemented in practice the usefulness of the approach is demonstrated through the analysis of some experiments the article also proposes a new class of design criteria and establishes their connections with the minimum aberration criterion

permuting regular fractional factorial designs for screening quantitative factors fractional factorial designs are widely used in screening experiments they are often chosen by the minimum aberration criterion which regards factor levels as symbols for designs with quantitative factors however permuting the levels for one or more factors could alter their geometrical structures and statistical properties we provide a justification of the minimum aberration criterion for quantitative factors and study level permutations for regular fractional factorial designs in order to improve their efficiency for screening quantitative factors we show how regular designs can be linearly permuted to reduce contamination of nonnegligible interactions on the estimation of linear effects without increasing the run size we further show that such linear permutations are unique under the minimum aberration criterion and the best level permutations can be determined without an exhaustive search we establish additional theoretical results for three level designs and obtain the best level permutations for regular designs with 27 and 81 runs we illustrate the practical benefits of level permutation with an antiviral drug combination experiment

variable selection with the strong heredity constraint and its oracle property in this paper we extend the lasso method tibshirani 1996 for simultaneously fitting a regression model and identifying important interaction terms unlike most of the existing variable selection methods our method automatically enforces the heredity constraint that is an interaction term can be included in the model only if the corresponding main terms are also included in the model furthermore we extend our method to generalized linear models and show that it performs as well as if the true model were given in advance that is the oracle property as in fan and li 2001 and fan and peng 2004 the proof of the oracle property is given in online supplemental materials numerical results on both simulation data and real data indicate that our method tends to remove irrelevant variables more effectively and provide better prediction performance than previous work yuan joseph and lin 2007 and zhao rocha and yu 2009 as well as the classical lasso method

functionally induced priors for the analysis of experiments this work develops the idea of using functional priors for the design and analysis of three level and higher level experiments developing a prior distribution for model parameters is challenging because a factor can be qualitative or quantitative we propose appropriate correlation functions and coding schemes so that the prior distribution is simple and the results are interpretable the prior incorporates well known principles such as effect hierarchy and effect heredity which helps resolve the aliasing problems in fractional designs almost automatically the usefulness of the new approach is illustrated through the analysis of some real experiments

minimum aberration and model robustness for two level fractional factorial designs summary the performance of minimum aberration two level fractional factorial designs is studied under two criteria of model robustness simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived it is also shown that a minimum aberration design of resolution ilil or higher maximizes the number of two factor interactions which are not aliases of main effects and subject to that condition minimizes the sum of squares of the sizes of alias sets of two factor interactions this roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform it follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here examples are given to show that minimum aberration designs are indeed highly efficient

generalized minimum aberration for asymmetrical fractional factorial designs by studying treatment contrasts and anova models we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs the criterion is independent of the choice of treatment contrasts and thus model free it works for symmetrical and asymmetrical designs regular and nonregular designs in particular it reduces to the minimum aberration criterion for regular designs and the minimum g 2 aberration criterion for two level nonregular designs in addition by exploring the connection between factorial design theory and coding theory we develop a complementary design theory for general symmetrical designs which covers many existing results as special cases

interval estimation of parameters of life from progressively censored data a conditional method of inference is used to derive exact confidence intervals for several life characteristics such as location scale quantiles and reliability when the data are type ii progressively censored the method is shown to be feasible and practical although a computer program may be required for its implementation the method is applied for the purpose of illustration to the extreme value and the one and two parameter exponential models prediction limits for the lifelength of future units are also discussed an example consisting of data from an accelerated test on insulating fluid reported by nelson is used for illustration and comparison

a general criterion for factorial designs under model uncertainty motivated by two industrial experiments in which rather extreme prior knowledge was used to choose the design we show that the qb criterion which aims to improve the estimation in as many models as possible by incorporating experimenters prior knowledge along with an approximation to the as criterion is more general and has a better statistical interpretation than many standard criteria the generalization and application of the criterion to different types of designs are presented the relationships between qb and other criteria for different situations are explored it is shown that the e s2 criterion is a special case of qb and several aberration type criteria are limiting cases of our criterion so that qb provides a bridge between alphabetic optimality and aberration the two case studies illustrate the potential benefits of the qb criterion r programs for calculating qb are available online as supplemental materials

mle and the estimated expected test time for the two parameter gompertz distribution under progressive censoring with binomial removals this study considers the estimation of two parameter gompertz distribution under type ii progressive censoring with random removals where the number of units removed at each failure time follows a binomial or a uniform distribution the maximum likelihood estimates of two parameters and their asymptotic distribution are derived the expected termination point to complete the censoring test is computed and analyzed for different censoring schemes for binomial removals the effect of various p on the expected termination point under progressive censoring and the relative expected termination point over the complete sample reet1 are investigated in this article for random removals pcr the expected termination point is computed and the relative expected termination point over the complete sample reet2 are also investigated

practical issues in multirate output controllers multirate output controllers are a new type of controller which detect the ith output of the plant n i times and change the plant input once during a period t 0 important features of this type of controller include equivalent realization of state feedback and strong stabilization above all they distinguish themselves from multirate input controllers in that they appear more suitable for industrial application nevertheless there are some potential problems that can degrade the operation of the controller in this paper these problems are highlighted and approaches to avoid them are provided

an efficient variable selection approach for analyzing designed experiments the analysis of experiments in which numerous potential variables are examined is driven by the principles of effect sparsity effect hierarchy and effect heredity we propose an efficient variable selection strategy to specifically address the unique challenges faced by such analysis the proposed methods are natural extensions of the lars general purpose variable selection algorithm they can be computed very rapidly and can find sparse models that better satisfy the goals of experiments simulations and real examples are used to illustrate the wide applicability of the proposed methods

a simple approach to emulation for computer models with qualitative and quantitative factors we propose a flexible yet computationally efficient approach for building gaussian process models for computer experiments with both qualitative and quantitative factors this approach uses the hypersphere parameterization to model the correlations of the qualitative factors thus avoiding the need of directly solving optimization problems with positive definite constraints the effectiveness of the proposed method is successfully illustrated by several examples

bayesian inspired minimum aberration two and four level designs summary motivated by a bayesian framework we propose a new minimum aberration type criterion for designing experiments with two and four level factors the bayesian approach helps in overcoming the ad hoc nature of effect ordering in the existing minimum aberration type criteria the approach is also capable of distinguishing between qualitative and quantitative factors numerous examples are given to demonstrate its advantages

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

bayes optimal designs for two and three level factorial experiments abstract two and three level factorial designs are often used for exploratory experiments with many independent variables the purpose of such experiments is to estimate the effects of all active independent variables and their interactions for reasons of economy or other constraints only a fraction of the full number of experimental settings of the independent variables may be run precluding the separate data based estimation of all the effects in this situation of relatively sparse data and many unknown parameters the benefits of reliable prior information used in the estimation and experimental design can be especially significant in this article exact bayes optimal designs of two and three level fractional factorial experiments and of blocked two and three level factorial experiments are derived the optimality criteria used in this process are versions of the bayes criterion introduced by duncan and degroot it is shown that the classical fractional factorial designs for the 2k experime

performance study of multi rate output controllers under noise disturbances this paper presents a comparative study of the performance of a multi rate output controller mroc with a linear quadratic gaussian lqg controller in the presence of noise disturbances and anti aliasing filters the basis of comparison is to apply an lqg law with a one step ahead prediction type kalman filter hereafter called lqg law i and an lqg law with a current estimation type kalman filter hereafter called lqg law ii to a linear time invariant continuous time plant model with a white gaussian process and measurement noise and compute a linear quadratic performance index for the discretized plant equivalent noise matrices for using the mroc law are derived and the same quadratic performance index computed in order to have a fair comparison the cut off frequency of the anti aliasing filter used to remove high frequency noise components prior to sampling is also kept the same when applying both laws application of both laws in typical situations shows that the performance of the mroc law is w

generalized resolution for orthogonal arrays the generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion xu and wu 2001 we provide a statistical interpretation for the number of shortest words of an orthogonal array in terms of sums of r values based on orthogonal coding or sums of squared canonical correlations based on arbitrary coding directly related to these results we derive two versions of generalized resolution for qualitative factors both of which are generalizations of the generalized resolution by deng and tang 1999 and tang and deng 1999 we provide a sufficient condition for one of these to attain its upper bound and we provide explicit upper bounds for two classes of symmetric designs factor wise generalized resolution values provide useful additional detail