Minimum Aberration Regular Two-Level Designs in the Presence of Dispersion Factors

In practice, the variance of the response variable may change as some specific factors change from one setting to another in a factorial experiment. These factors affecting the variation of the response are called dispersion factors, which can violate the usual assumption of variance homogeneity. In this study, we modify the conventional minimum aberration criterion to take the impact of dispersion factors into account. The situations of one or two dispersion factors are investigated. As a result, we present regular 2^{n ? p} designs with run sizes equal to 16 and 32 using the modified minimum aberration criterion.     

On Exact K-optimal Designs Minimizing the Condition Number

A new design criterion based on the condition number of an information matrix is proposed to construct optimal designs for linear models, and the resulting designs are called K-optimal designs. The relationship between exact and asymptotic K-optimal designs is derived. Since it is usually hard to find exact optimal designs analytically, we apply a simulated annealing algorithm to compute K-optimal design points on continuous design spaces. Specific issues are addressed to make the algorithm effective. Through exact designs, we can examine some properties of the K-optimal designs such as symmetry and the number of support points. Examples and results are given for polynomial regression models and linear models for fractional factorial experiments. In addition, K-optimal designs are compared with A-optimal and D-optimal designs for polynomial regression models, showing that K-optimal designs are quite similar to A-optimal designs.     

The Economic Design of the MSE Control Chart

In this article, an economic design model of the MSE control chart is proposed. The formulated cost function includes the cost incurred in production process and the loss borne by customers because of the shift of means and the drift of variation. The economic bounds where the process is shut down if the search indicates the presence of an assignable cause are also being considered. A program written in Matlab 7.0 is used to determine the optimum parameters including the sample size n, the sample interval h and the width of the control limits k. Finally, an example is given to illustrate the proposed economic design and sensitivity analysis is carried out.     

Bounds on the Maximum Number of Factors in Designs with Two Distinct Groups of Factors

This article focuses on designs involving two distinct groups of factors. In particular, we assume that between-group interactions are more important than within-group interactions. Under this assumption, a new word-length pattern is proposed to characterize the aliasing severity of a design, and the concepts of resolution and aberration are defined accordingly. Furthermore, we have obtained various bounds on the maximum number of factors that a design with given resolution can accommodate.     

A Multivariate Synthetic Control Chart for Monitoring the Process Mean Vector of Skewed Populations Using Weighted Standard Deviations

This article proposes a multivariate synthetic control chart for skewed populations based on the weighted standard deviation method. The proposed chart incorporates the weighted standard deviation method into the standard multivariate synthetic control chart. The standard multivariate synthetic chart consists of the Hotelling's T ² chart and the conforming run length chart. The weighted standard deviation method adjusts the variance–covariance matrix of the quality characteristics and approximates the probability density function using several multivariate normal distributions. The proposed chart reduces to the standard multivariate synthetic chart when the underlying distribution is symmetric. In general, the simulation results show that the proposed chart performs better than the existing multivariate charts for skewed populations and the standard T ² chart, in terms of false alarm rates as well as moderate and large mean shift detection rates based on the various degrees of skewnesses.     

On the distribution of quadratic forms and applications in the analysis of repeated measurements

In this paper a unified approach is given to the distribution of scalar quadratic forms for dependent variables. Necessary and sufficient conditions are found for the sums of squares of the various hierarchical layers in ANOVA to be distributed as multiples of chi-square variables. Results concerning the usual univariate F-tests in ANOVA of repeated measurements are derived as a special case.     

Cross-over Designs in the Presence of Higher Order Carry-overs

In cross-over experiments, where different treatments are applied successively to the same experimental unit over a number of time periods, it is often expected that a treatment has a carry-over effect in one or more periods following its period of application. The effect of interaction between the treatments in the successive periods may also affect the response. However, it seems that all systematic studies of the optimality properties of cross-over designs have been done under models where carry-over effects are assumed to persist for only one subsequent period. This paper proposes a model which allows for the possible presence of carry-over effects up to k subsequent periods, together with all the interactions between treatments applied at k + 1 successive periods. This model allows the practitioner to choose k for any experiment according to the requirements of that particular experiment. Under this model, the cross-over designs are studied and the class of optimal designs is obtained. A method of constructing these optimal designs is also given.     

The Design and Performance of the Multivariate Synthetic-T 2 Control Chart

One of the objectives of research in statistical process control is to obtain control charts that show few false alarms but, at the same time, are able to detect quickly the shifts in the distribution of the quality variables employed to monitor a productive process. In this article, the synthetic-T ² control chart is developed, which consists of the simultaneous use of a CRL chart and a Hotelling's T ² control chart. The ARL is calculated employing Markov chains for steady and zero-state scenarios. A procedure of optimization has been developed to obtain the optimum parameters of the synthetic-T ², for zero and steady cases, given the values of in-control ARL and magnitude of shift which needs to be detected rapidly. A comparison between (standard T ², MEWMA, T ² with variable sample size, and T ² with double sampling) charts reveals that the synthetic-T ² chart always performs better than the standard T ² chart. The comparison with the remaining charts demonstrate in which cases the performance of this new chart makes it interesting to employ in real applications.     

On some optimal fractional 2m factorial designs of resolution V

This paper presents the trace of the covariance matrix of the estimates of effects based on a fractional 2^m factorial (2^m-FF) design T of resolution V for the following two cases: One is the case where T is constructed by adding some restricted assemblies to an orthogonal array. The other is one where T is constructed by removing some restricted assemblies from an orthogonal array of index unity. In the class of 2^m-FF designs of resolution V considered here, optimal designs with respect to the trace criterion, i.e. A-optimal, are presented for m = 4, 5, and 6 and for a range of practical values of N (the total number of assemblies). Some of them are better than the corresponding A-optimal designs in the class of balanced fractional 2^m factorial designs of resolution V obtained by Srivastava and Chopra (1971b) in such a sense that the trace of the covariance matrix of the estimates is small.     

企业的合约经济理论探索和统计检验

对企业本质的认识是微观经济学中的一个重要问题,其对中国的国企改革有着重要意义。本文中,我们对企业的合约本质进行了经济理论探索和统计检验,并突出关注企业的激励合约问题。     

Comparison of normal probability plots and dot plots in judging the significance of effects in two level factorial designs

In this article, we present a study carried out to compare the effectiveness of the normal probability plot (NPP) and a simple dot plot in assessing the significance of the effects in experimental designs with factors at two levels (2 ^k?p designs). Several groups of students who had just completed a course that covered factorial designs were asked to identify the significant effects in a total of 32 situations, 16 of which were represented using NPPs and the other 16 using dot plots. Although the 32 scenarios were said to be different, there were really only 16 different situations, each of which was represented using the two methods to be compared. A simple graphical analysis shows no evidence that there is a difference between the two procedures. However, in designs with 16 runs there are some cases where NPP seems to give slightly better results.     

Problems with the Federal Economic Statistical System and Some Alternatives for Improvement

This article identifies four problems with the present federal statistical system for economics: (1) lack of comparability of data series; (2) fragmentation and poor data quality; (3) nonoptimal funding patterns; and (4) susceptibility of the system to politicization. Full centralization of the system appears to be both impractical and undesirable as a solution; however, considerable consolidation in the statistics collection process and a substantial increase in the number and professional quality of personnel devoted to planning, developing, and coordinating the federal statistical system are recommended.     

Minimum Cost Linear Trend Free 2n-(n-k) Designs of Resolution IV

This article extends the resolution of time trend free designs for sequential 2^n-p experiments from III into IV and minimizes the number of factor level changes between runs (i.e., cost) by constructing a catalog of (2^k?2 ?1) minimum cost linear trend free resolution IV 2^n?(n?k) designs (2^k?2 ≤ n ≤ 2^k?1?2) from the full 2^k factorial experiment using the interactions-main effects assignment technique. Each systematic 2^n?(n?k) design in the catalog is economic in minimum number of factor level changes and allows for the estimation of all n main effects unbiased by either the linear time trend (which may be present in the 2^n?(n?k) sequentially generated responses) or the non negligible two-factor interactions. This article provides for each 2^n?(n?k) design: (1) the defining relation or the alias structure; (2) the k independent generators for sequencing the 2^n?(n?k) runs by the generalized foldover scheme; and (3) the minimum cost represented by the total number of factor level changes between the 2^n?(n?k) runs. All k main effects of the 2^k experiment are excluded from the selection assignment process due to their nonlinear time trend resistance as well as excluding a total of (2^k?1 –k +1) interactions violating the resolution IV requirement.     

Approximation of IMSE-optimal Designs via Quadrature Rules and Spectral Decomposition

We address the problem of computing integrated mean-squared error (IMSE) optimal designs for interpolation of random fields with known mean and covariance. We assume that the mean squared error is integrated through a discrete measure and restrict the design space to its support. We show that the IMSE and its approximation by spectral truncation can be easily evaluated, which makes their global minimization affordable. Numerical experiments are carried out that illustrate the effectiveness of the approach.     

统计法制建设疑难问题及对策研究

文章指出:《统计法》已制定了20年之久,存在着许多缺陷和不足,严重地影响了我国统计法制建设的顺利进行,迫切需要进一步地修改和完善。因此,修改现行的《统计法》已成为当务之急。     

Estimation of variance components in the mixed effects models: A comparison between analysis of variance and spectral decomposition

The mixed effects models with two variance components are often used to analyze longitudinal data. For these models, we compare two approaches to estimating the variance components, the analysis of variance approach and the spectral decomposition approach. We establish a necessary and sufficient condition for the two approaches to yield identical estimates, and some sufficient conditions for the superiority of one approach over the other, under the mean squared error criterion. Applications of the methods to circular models and longitudinal data are discussed. Furthermore, simulation results indicate that better estimates of variance components do not necessarily imply higher power of the tests or shorter confidence intervals.     

Statistical issues in the assessment of health outcomes in children: a methodological review

Summary.  The lack of outcome measures that are validated for use on children limits the effectiveness and generalizability of paediatric health care interventions. Statistical epidemiology is a broad concept encompassing a wide range of useful techniques for use in child health outcome assessment and development. However, the range of techniques that are available is often confusing and prohibits their adoption. In the paper an overview of methodology is provided within the paediatric context. It is demonstrated that in many cases assessment can be performed relatively straightforwardly by using standard statistical techniques, although sometimes more sophisticated techniques are required. Examples of both physiological and questionnaire-based outcomes are given. The usefulness of these techniques is highlighted for achieving specific objectives and ultimately for achieving methodological rigour in clinical outcome studies that are performed in the paediatric population.     

Perception,Preference, and Patriotism: An Exploratory Analysis of the 1980 Winter Olympics

This article analyzes scores given by judges of figure skating at the 1980 Winter Olympics. Judges' scores are found to be highly correlated, with little evidence of scoring along political lines. However, an analysis of variance shows a small but consistent “patriotic” bias; judges tend to give higher scores to contestants from their own country. The influence of such effects on final placings is estimated.     

Economic and economic-statistical designs of the T2 control charts with SVSSI sampling scheme

Recent studies have shown that the adaptive T² chart with two different sampling interval and three sample sizes (SVSSI) shows a good performance in detecting small to large shifts in the process mean. This paper investigates the economic and economic statistical designs of the SVSSI T² charts. We use the Markov chain approach to developing the cost model proposed by Costa and Rahim (Journal of applied statistics 2001; 28: 875–885). A genetic algorithm approach is used to find the optimal solutions. Using numerical examples, we illustrate the performance of the proposed model and compare the statistical, economic, and economic statistical designs of the SVSSI T² chart with respect to the economic and statistical criteria. Furthermore, we compare the performance of the SVSSI T² chart with the other T² control schemes.