Trend-Free Designs in Blocked Factorial Experiments

Appropriate run orders can make all estimable effects free of some trends in blocked fractional factorial experiments. We need to design blocked experiments with effects free of trends in blocks. The generalized foldover scheme given by Coster (1993 Coster , D. C. ( 1993 ). Trend-free run orders of mixed-level fractional factorial designs . Ann. Statist. 21 : 2072 – 2086 .[Crossref], [Web of Science ®] , [Google Scholar]) can be used to obtain such designs. In this article, we propose an easy and better approach to deal with this issue when the same trends appear in blocks. We investigate block trend property of columns in the orthogonal plans in s ^k runs for assigning factors to obtain block-trend free designs in a trend-free order. We illustrate our approach with three examples.     

Clustering Effects in Unreplicated Factorial Experiments

The analysis of unreplicated factorial designs concentrates much attention since there are no degrees of freedom left to estimate the error variance. In this article, we propose clustering the factorial estimates in two groups, one containing the active effects and one containing the inactive effects. The powerfulness of the proposed method is revealed via a comparative simulation study.     

Some statistical issues in weather experimentation

A number of topics of statistical methodology in weather modification are discussed. The time sequence of unit definition, classification and randomization is shown to affect the types of units that can be used validly, and this casts doubt on the value of blocking. Re-randomization (permutation) tests are recommended as the only reliable method of confirmatory inference for weather experiments. Some aspects of such tests are examined, including a procedure for multiple comparisons. The plague of multiplicity of tests is discussed and warned against. Doubts about cumulative evaluations of "all" experiment's are expressed. A case is argued for examination of some non-randomized seeding operations. Consid¬ering the dearth of randomized data, it is argued that careful evaluation of seeding operations should be undertaken.     

Factorial experiments in the analysis of assembly systems

Assembly systems are a key tool for mass production and are increasingly being implemented in the manufacturing industry. Since the performance of such systems depends on the levels of many design variables, they are not well understood. In this paper, the performance of free transfer automatic assembly systems with closed inspection and repair loops is studied via factorial experiments of a simulated system. Five factors were identified that affect the throughput of the system: buffer size, number of pallets in the system, number of repair stations, repair time of jammed assembly machines, and subcomponent defect rate. Initially, two levels of each factor were considered, so that a full 2 5 factorial design of the experiment was used to study the system. Next, to develop a deeper understanding of the linear or non-linear effect of each factor, additional levels were investigated. Finally, a predictive model is proposed. Engineers and system designers can use this predictive model to estimate the performance of the system, given a combination of levels of each of the five factors that we studied.     

Split-plot designs for multistage experimentation

Most of today’s complex systems and processes involve several stages through which input or the raw material has to go before the final product is obtained. Also in many cases factors at different stages interact. Therefore, a holistic approach for experimentation that considers all stages at the same time will be more efficient. However, there have been only a few attempts in the literature to provide an adequate and easy-to-use approach for this problem. In this paper, we present a novel methodology for constructing two-level split-plot and multistage experiments. The methodology is based on the Kronecker product representation of orthogonal designs and can be used for any number of stages, for various numbers of subplots and for different number of subplots for each stage. The procedure is demonstrated on both regular and nonregular designs and provides the maximum number of factors that can be accommodated in each stage. Furthermore, split-plot designs for multistage experiments with good projective properties are also provided.     

A scenario for sequential experimentation

This tutorial emphasizes the role of differecnt types of experimental design in a multi–stage investigation. In the initial phase group–screeningo can reveal the really important factors among hundreds of factors. Resooulution III designs are useful immediately after the screening phase, to investigate firstorder effects, provided higher–order effects are unimportants, i.e., validation is necessary. Resulotion IV designs may explain why a first–order model is not valid, i.e., they may yield unbiased estimators of sums of interactions. Resolution V designs yield unbiased estimators of the individual two–factor interactions. They can be easily extended to central composite designs to estimate pure quadratic effects of quantitative factors. Smaller steps are also possible, e.g. one run at a time, for model discrimination and calibration.     

Hyper-Graeco-Latin Squares and Fractional Factorial Designs

A Latin square of order s is an arrangement of the s letters in an s × s square so that every letter appears exactly once in every row and exactly once in every column. Copeland and Nelson (2000) used two examples to show that a Latin square can be chosen such that it corresponds to a fractional factorial design. In this article, we are going to study this topic more precisely. Furthermore, we will explore the relationship between fractional factorial designs and hyper-Graeco-Latin squares in general, where s is a prime or a power of a prime.     

Statistics in Latin America

Statistics is a relatively new discipline in Latin America. At present only sparse information is available about the state of the statistical profession in Latin America. We present and summarize the available information about the job market; training, education, and research; professional societies and their activities; and so forth. We also share our hopes, concerns, and suggestions for the future.     

Comparison of design for quadratic regression on cubes

Designs for quadratic regression are considered when the possible choices of the controllable variable are points x=(x₁,x₂,…,x_q) in the q-dimensional cube of side 2. The designs that are optimum with respect to such criteria as those of D-, A-, and E-optimality are compared in their performance relative to these and other criteria. Some of the results are developed algebraically; others, numerically. The possible supports of E-optimum designs are much more numerous than the D-optimum supports characterized earlier. The A-optimum design appears to be fairly robust in its efficiency, under variation of criterion.     

Improving a food process by experimentation

Like any other industry, the food industry continuously develops and improves its products and the processes that are used to make them, says Steven Gilmour. The customer is mainly interested in the sensory characteristics of the product: how does it taste; how does it smell; how does it look? However, commercial success also depends on whether or not the product can be produced economically, consistently and safely. Product development and improvement require research, which often means experimentation.     

Split-plot designs for robust product experimentation

Genichi Taguchi has emphasized the use of designed experiments in several novel and important applications. In this paper we focus on the use of statistical experimental designs in designingproducts to be robust to environmental conditions. The engineering concept of robust product design is very important because it is frequently impossible or prohibitively expensive to control or eliminate variation resulting from environmental conditions. Robust product design enablesthe experimenter to discover how to modify the design of the product to minimize the effect dueto variation from environmental sources. In experiments of this kind, Taguchi's total experimental arrangement consists of a cross-product of two experimental designs:an inner array containing the design factors and an outer array containing the environmental factors. Except in situations where both these arrays are small, this arrangement may involve a prohibitively large amount of experimental work. One of the objectives of this paper is to show how this amount of work can be reduced. In this paper we investigate the applicability of split-plot designs for thisparticular experimental situation. Consideration of the efficiency of split-plot designs and anexamination of several variants of split-plot designs indicates that experiments conductedin a split-plot mode can be of tremendous value in robust product design since they not only enable the contrasts of interest to be estimated efficiently but also the experiments can be considerably easier to conduct than the designs proposed by Taguchi.     

Factorial hypercube designs for spatial correlation regression

SUMMARY The problem of generating a good experimental design for spatial correlation regression is studied in this paper. The quality of fit generated by random designs, Latin hypercube designs and factorial designs is studied for a particular response surface that arises in inkjet printhead design. These studies indicate that the quality of fit generated by spatial correlation models is highly dependent on the choice of design. A design strategy that we call 'factorial hypercubes' is introduced as a new method. This method can be thought of as an example of a more general class of hybrid designs. The quality of fit generated by these designs is compared with those of other methods. These comparisons indicate a better fit and less numerical problems with factorial hypercubes.     

The treatment versus experimentation dilemma in dose finding studies

Phase I clinical trials are conducted in order to find the maximum tolerated dose (MTD) of a given drug from a finite set of doses. For ethical reasons, these studies are usually sequential, treating patients or groups of patients with the optimal dose according to the current knowledge, with the hope that this will lead to using the true MTD from some time on. However, the first result proved here is that this goal is infeasible, and that such designs, and, more generally, designs that concentrate on one dose from some time on, cannot provide consistent estimators for the MTD unless very strong parametric assumptions hold. Allowing some non-MTD treatment, we construct a randomized design that assigns the MTD with probability that approaches one as the size of the experiment goes to infinity and estimates the MTD consistently. We compare the suggested design with several methods by simulations, studying their performances in terms of correct estimation of the MTD and the proportion of individuals treated with the MTD.     

Factorial Experiments In Resolvable Generalized Cyclic Designs

It is shown that the class of generalized cyclic designs provides resolvable designs which are efficient for estimating factorial effects. A practical problem is discussed and useful designs for two-factors experiments are listed.     

Balanced Factorial Designs for cDNA Microarray Experiments

Balanced factorial designs are introduced for cDNA microarray experiments. Single replicate designs obtained using the classical method of confounding are shown to be particularly useful for deriving suitable balanced designs for cDNA microarrays. Classical factorial designs obtained using methods other than the method of confounding are also shown to be useful. The paper provides a systematic method of deriving designs for microarray experiments as opposed to algorithmic and ad-hoc methods and generalizes several of the microarray designs given recently in the literature.     

D-optimal Factorial Designs under Generalized Linear Models

Generalized linear models (GLMs) have been used widely for modeling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013 Yang, J., Mandal, A., Majumdar, D. (2013). Optimal designs for 2^k factorial experiments with binary response. Technical Report, Available at: http://arxiv.org/pdf/1109.5320v4.pdf. [Google Scholar]) considered full factorial and fractional factorial locally D-optimal designs for binary response and two-level experimental factors. In this article, we extend their results to a general setup with response belonging to a single-parameter exponential family and for multilevel predictors.     

Three Parallel Flats Designs for Two-level Factorial Experiments

This paper investigates the properties of the class of three parallel flats designs for two-level factorial experiments. It shows that the designs constructed from this class of designs can have a very simple correlation structure. The correlation of any pair of best linear unbiased estimators of factorial effects is 0, ⅓ or ¼. Furthermore, the designs obtained also have high D-efficiency. Finally, a class of designs is generated with run-size N = 12 to illustrate the use of the theorem.     

Missing values in replicated Latin squares

Designs based on any number of replicated Latin squares are examined for their robustness against the loss of up to three observations randomly scattered throughout the design. The information matrix for the treatment effects is used to evaluate the average variances of the treatment differences for each design in terms of the number of missing values and the size of the design. The resulting average variances are used to assess the overall robustness of the designs. In general, there are 16 different situations for the case of three missing values when there are at least three Latin square replicates in the design. Algebraic expressions may be determined for all possible configurations, but here the best and worst cases are given in detail. Numerical illustrations are provided for the average variances, relative efficiencies, minimum and maximum variances and the frequency counts, showing the effects of the missing values for a range of design sizes and levels of replication.     

网络测验中可靠性控制变量的完全因素不变性检验

网络测验相对于传统测验最重要的问题是对被试答题时的情境与条件无法控制。通过对网络测验中被试是否有急事处理(无vs.有)、测试时的情绪体验(积极情绪vs.消极情绪)、噪音影响(无影响vs.有影响)以及测试场所(学校vs.其他地方)等情境变量进行完全因素不变性检验,实现网络测验可靠性控制的目的。以主观健康量表(SHC)为例,针对3 667名青少年(年龄14²6岁,M±SD=19.31±1.62),进行上述情境变量不同组别的SHC完全因素不变性检验。结果表明:是否有急事需要处理、答题时情绪体验、噪音影响、答题场所等完全因素不变性都在一定程度上不能成立,说明上述指标可以作为网络测验中可靠性控制变量。     

On the Use of Semi-folding in Regular Blocked Two-level Factorial Designs

In this article, we consider experimental situations where a blocked regular two-level fractional factorial initial design is used. We investigate the use of the semi-fold technique as a follow-up strategy for de-aliasing effects that are confounded in the initial design as well as an alternative method for constructing blocked fractional factorial designs. A construction method is suggested based on the full foldover technique and sufficient conditions are obtained when the semi-fold yields as many estimable effects as the full foldover.