Two-point Design Research Articles

Improved probabilistic design method to quantify the fracture properties of roller compacted concrete

In this paper, the material parameters pertaining to fracture properties of Roller Compacted Concrete (RCC) were evaluated using the boundary element method (BEM). The fictitious crack growth length Δafic is determined by the relative size (T-a0)/di, while the individualized values of material parameters (KIC&ft) of RCC for different water-to-cement ratios were obtained. In this study, the three-parameter Weibull fracture statistical model was proposed for the first time to analyze the discreteness of these individualized values of material parameters (KIC&ft) of RCC. The statistical analysis minimum value of material parameters (KIC&ft) of each group is obtained. The failure curves of each group of RCC were predicted from the three-parameter Weibull fracture statistical model, and the simple calculation model for material parameters (KIC&ft) was validated. Further, a two-point design method was proposed for RCC material parameters (KIC&ft) with varying strengths and water-to-cement ratios.

A web-based tool to design and analyze single- and double-stage acceptance sampling plans

Acceptance sampling plans are used to determine whether production lots can be accepted or rejected. Existing tools only provide a limited functionality for the two-point design and the risk analysis of such plans. In this article, a web-based tool is presented to study single- and double-stage sampling plans. In contrast to existing solutions, the tool is an interactive applet that is freely available. Analytic properties are derived to support the development of search strategies for the design of double-stage sampling plans that are more efficient and accurate in comparison with existing routines. Several case studies are presented.

Does sequential augmenting of simple linear heteroscedastic regression reduce variances of ordinary least-squares estimators?

If uncorrelated random variables have a common expected value and decreasing variances, then the variance of a sample mean is decreasing with the number of observations. Unfortunately, this natural and desirable variance reduction property (VRP) by augmenting data is not automatically inherited by ordinary least-squares (OLS) estimators of parameters. We derive a new decomposition for updating the covariance matrices of the OLS which implies conditions for the OLS to have the VRP. In particular, in the case of a straight-line regression, we show that the OLS estimators of intercept and slope have the VRP if the values of the explanatory variable are increasing. This also holds true for alternating two-point experimental designs.

Adjoint Aerodynamic Design Optimization for Blades in Multistage Turbomachines—Part II: Validation and Application

This is the second part of a two-part paper. First, the design-optimization system based on the adjoint gradient solution approach as described in Part I is introduced. Several test cases are studied for further validation and demonstration of the methodology and implementation. The base-line adjoint method as applied to realistic 3D configurations is demonstrated in the redesign of the NASA rotor 67 at a near-choke condition, leading to a 1.77% efficiency gain. The proposed adjoint mixing plane is applied to the redesign of a transonic compressor stage (DLR compressor stage) and an IGV-rotor-stator configuration of a Siemens industrial compressor at a single-operating point, both producing measurably positive efficiency gains. An examination on the choice of the operating mass flow condition as the basis for the performance optimization, however, highlights the limitation of the single-point approach for practical applications. For the three-row compressor configuration, a near peak-efficiency point based redesign leads to a measurable reduction in the choke mass flow, while a near-choke point based redesign leads to a significant performance drop in other flow conditions. Subsequently, a parallel multipoint approach is implemented. The results show that a two-point design optimization can produce a consistently better performance over a whole range of mass flow conditions compared with the original design. In the final case, the effectiveness of the present method and system is demonstrated by a redesign applied to a seven-row industrial compressor at the design point, leading to a remarkable 2.4% efficiency gain.

Genetic algorithm-based design of transonic aerofoils using Euler equations

The paper describes the adaptation of genetic algorithms (GA) to the design of inviscid transonic aerofoils. GA is effective in optimization strategies for designing transonic aerofoils where the non-linear aerodynamic phenomenon of shock wave results in flow discontinuity. The Euler equations are discretized through the flux-vector splitting method with Poisson's equation-based grid generation. Advanced strategies in the GA such as directed crossover and multi-stage searches are employed in the context of function-based global optimization. The objective is to determine the best combination of weighted parameters of a analytic function for the aerofoil surface, by maximizing the L/ D ratio. The paper first covers the optimization of transonic aerofoils to enhance the baseline design of NACA0012. A two-point design problem is also conducted to accommodate both transonic and subsonic regimes represented by the Mach number and angle of attack. The optimized aerofoils have shown improved aerodynamic performance for both flight regimes.

Impliciete leiderschapstheorieën en de perceptie van transformationeel leiderschap: een replicatie van Duits onderzoek

Implicit leadership theories and the perception of transformational leadership: a replication of German research Implicit leadership theories and the perception of transformational leadership: a replication of German research Birgit Schyns & Karin Sanders, Gedrag & Organisatie, volume 17, April 2004, nr. 2, pp. 143-154. Results of a German study show that implicit leadership theories do influence the evaluation of leaders. In this article the German study is replicated in a Dutch situation. In an experimental setting, the effects of two implicit leadership theories, Romance of Leadership and transformational leadership, on the evaluation of a described leader were tested. The experiment was conducted as a two-point design: At time point one 81 Dutch students were questioned about their implicit leadership theories and at time point two the students evaluated descriptions of either a transformational or a transactional leader. As hypothesized (hypothesis 1) transformational leadership as an implicit leadership theory (ILT) has an effect on perceptions of the described leader. Hypothesis 2 could not be confirmed: Romance of leadership has no significant influence on perceptions of the described leader.

A note on optimal designs for a two-part model

D- and D A -optimal designs are investigated for a model where the response is a mixture of zero and a lognormal random variable, and can be modelled using a logit model combined with a linear regression on the logarithm of the lognormal part. The D A -optimal design for estimating the logit model parameters is shown to coincide with the D-optimal design for the usual logit model. The D A -optimal design for estimating the linear model parameters is derived analytically. Among two-point designs, an analytic solution is given for the design that maximizes the D-optimality.

Multi-point optimal design for diffuser cascades of centrifugal compressors

The ‘multi-point design’ approach for single airfoils in aeronautical engineering is introduced into the optimal design for diffuser cascades of centrifugal compressors. Genetic algorithms are used to solve the multi-point problem. The proposed approach is applied to a ‘two-point design’ of a real diffuser cascade. The numerical results show that a group of optimal blade profiles can be obtained, from which the designer can select performance compromises for the two given design condition points.

Critical Assessment of the C-Optimality Design Criteria for Estimating the Median Effective Dose in Quantal Dose-Response Curves

In this paper the properties of C-optimal designs constructed for estimating the median effective dose within the framework of two-parametric linear logistic models are critically assessed. It is well known that this design criterion which is based on the first-order variance approximation of the exact variance of the maximum likelihood estimate of the ED50 leads to a one-point design where the maximum likelihood theory breaks down. The single dose used in this design is identical with the true but unknown value of the ED50. It will be shown, that at this one-point design the asymptotic variance does not exist. A two-point design in the neighbourhood of the one-point design which is symmetrical about the ED50 and associated with a small dose-distance would be nearly optimal, but extremely nonrobust if the best guess of the ED50 differs from the true value. In this situation the asymptotic variance of the two-point design converging towards the one-point design tends to infinity. Moreover, taking in consideration, that for searching an optimal design the exact variance is of primary interest and the asymptotic variance serves only as an approximation of the exact variance, we calculate the exact variance of the estimator from balanced, symmetric 2-point designs in the neighbourhood of the limiting 1-point design for various dose distances and initial best guesses of the ED50. We compare the true variance of the estimate of the ED50 with the asymptotic variance and show that the approximations generally do not represent suitable substitutes for the exact variance even in case of unrealistically large sample sizes. Kalish (1990) proposed a criterion based on the second-order asymptotic variance of the maximum likelihood estimate of the ED50 to overcome the degenerated 1-point design as the solution of the optimization procedure. In fact, we are able to show that this variance approximation does not perform substantially better than the first–order variance. From these considerations it follows, that the C-optimality criterion is not useful in this estimation problem. Other criteria like the F-optimality should be used.

Critical Assessment of the C-Optimality Design Criteria for Estimating the Median Effective Dose in Quantal Dose-Response Curves

In this paper the properties of C-optimal designs constructed for estimating the median effective dose within the framework of two-parametric linear logistic models are critically assessed. It is well known that this design criterion which is based on the first-order variance approximation of the exact variance of the maximum likelihood estimate of the ED50 leads to a one-point design where the maximum likelihood theory breaks down. The single dose used in this design is identical with the true but unknown value of the ED50. It will be shown, that at this one-point design the asymptotic variance does not exist. A two-point design in the neighbourhood of the one-point design which is symmetrical about the ED50 and associated with a small dose-distance would be nearly optimal, but extremely nonrobust if the best guess of the ED50 differs from the true value. In this situation the asymptotic variance of the two-point design converging towards the one-point design tends to infinity. Moreover, taking in consideration, that for searching an optimal design the exact variance is of primary interest and the asymptotic variance serves only as an approximation of the exact variance, we calculate the exact variance of the estimator from balanced, symmetric 2-point designs in the neighbourhood of the limiting 1-point design for various dose distances and initial best guesses of the ED50. We compare the true variance of the estimate of the ED50 with the asymptotic variance and show that the approximations generally do not represent suitable substitutes for the exact variance even in case of unrealistically large sample sizes. Kalish (1990) proposed a criterion based on the second-order asymptotic variance of the maximum likelihood estimate of the ED50 to overcome the degenerated 1-point design as the solution of the optimization procedure. In fact, we are able to show that this variance approximation does not perform substantially better than the first–order variance. From these considerations it follows, that the C-optimality criterion is not useful in this estimation problem. Other criteria like the F-optimality should be used.

Airfoil design and optimization methods: recent progress at NLR

We consider the problem of aerodynamic airfoil shape optimization where the shape of an airfoil is to be determined such that a priori specified design criteria will be met to the best possible extent. The design criteria are formulated by defining an objective or cost function, the minimum of which represents the solution to the design problem. A survey is given of developments at NLR applying the adjoint operator approach, utilizing a compressible inviscid flow model based on the Euler equations and a compressible viscous flow model based on the Reynolds-averaged Navier-Stokes equations. Computational results are presented for a two-point drag-reduction design problem

Optimal two-point designs for the michaelis-menten model with heteroscedastic errors

We construct D-optimal designs for the Michaelis-Menten model when the variance of the response depends on the independent variable. However, this dependence is only partially known. A Bayesian approacn is used to find an optimal design by incorporating the prior lnformation about the variance structure. We demonstrate the method for a class of error variance structures and present efficiencies of these optimal designs under prior mis-specifications. In particular, we show that an erroneous assumption on the variance structure for the Michaelis-Menten model can have serious consequences.

Bayesian D-optimal designs for exponential regression models

We consider the Bayesian D-optimal design problem for exponential growth models with one, two or three parameters. For the one-parameter model conditions on the shape of the density of the prior distribution and on the range of its support are given guaranteeing that a one-point design is also Bayesian D-optimal within the class of all designs. In the case of two parameters the best two-point designs are determined and for special prior distributions it is proved that these designs are Bayesian D-optimal. Finally, the exponential growth model with three parameters is investigated. The best three-point designs are characterized by a nonlinear equation. The global optimality of these designs cannot be proved analytically and it is demonstrated that these designs are also Bayesian D-optimal within the class of all designs if gamma-distributions are used as prior distributions.

Linear and quadratic growth curve models with intraclass covariance structure and related optimal designs

s 255 [2] Jure6kov~ J, Sen PK (1993) Asymptotic equivalence of regression rank scores estimators and R-estimators in linear models. Ibid 279-292 [3] Jure6kovh J, Sen PK (1995) Robust statistical procedures: Asymptotics and interrelations. J Wiley New York in press [4] Sen PK (1993) Perspectives in multivariate nonparametrics: Conditional functionals and ANOCOVA models. Sankhya Ser A 55:516 532 Linear and Quadratic Growth Curve Models with lntraclass Covariance Structure and Related Optimal Designs BIKAS K. SINHA Indian Statistical Institute, 203 BT Road, Baraivagar, Calcutta-700035, India MARKUS ABT Institute for Mathematics, University of Augsburg, 86135 Augsburg Germany ERKKI LISK1 University of Tampere, Finland The t rad i t iona l growth curve model s t ipulates that for every exper imenta l unit in the "universe", there is a response var iable Y varying with time t and we take it to be l inear in the t ime point t so that we start with Y(t) = ~ + flt + e(t) . O) We assume, based on physical constraints , that the time poin ts accessible for ac tual measurements of Y are given by k , ( k 1 ) , ( k 2 ) . . . . . 2 , 1 , 0 , 1,2 . . . . . k 2 , k l , k . (2) The intraclass e r ror s t ructure is relevant when an exper imenta l unit is measured at two or more consecutive t ime points. We will assume that for the observat ions taken at t ime poin ts i th rough j , the covar iance s t ructure is given by = a2[(1 -p)Iij + p l l j l l j ] (3) i j 256 Abstracts where lij = identity matrix of order (j i + 1) and l~j = (1 . . . . . 1) of order ( j i + 1) x 1. Let n~ be the number of experimental units measured through the time points i to j . Cost constraint stipulates that ~ ~ no( j i + 1) = N. For convenience we discuss only the approximate theory according to which the number nit will be replaced by the proportion ~j := n U N so that the constraint is: ~ ~ (,j(j i + 1) = 1. The information matrix l~(0)will be given by ( i j ( j i q-1)(aij bij ) (ar be) I~(0) = ~ = . (4) , , l t 2 where aij = 1 + Pij , blj = #l,lj , ao , dii = P2,~j + Px,~jP~j (5) P i j = s l j ( j i + 1) , sij= -p / [1 + ( j i ) p ] (6) J and/~'r.lj := ~ t r / ( J i+ 1) denotes the r-th order raw moment of the time t = i points i through j; r = 1, 2. The role of symmetry which is so evident in the framework of independent and identically distributed observations, also continues to hold with the intraclass correlation structure in the linear growt model. The following results have been established. Theorem 1: In a linear growth model with intraclass correlation structure, the optimal design for maximum precision of the estimate of the slope parameter is, in an approximate sense, given by ~-k-k = ~kk = 0.5 whenever p _ (2k 1)/3k . (8) Theorem 2: In a linear growth model with intraclass correlation structure, a robust optimal design for prediction of linear growth at all points k to k is essentially the two-point design: ~-k-k = ~kk = 0.5 unless p is very high when only a small portion has to be shared with ~-kk" As in the linear growth model, the role of symmetry is crucial in the study of the quadratic growth curve model as well. In ABT et al. (1993, 1994) the basic structures of optimal designs were identified.

Bayesian D-optimal designs for the exponential growth model

Bayesian optimal designs for nonlinear regression models are of some interest and importance in the statistical literature. Numerical methods for their construction are well-established, but very few analytical studies have been reported. In this paper, we consider an exponential growth model used extensively in the modelling of simple organisms, and examine the explicit form of the Bayesian D-optimal designs. In particular, we show that D θ-optimal designs for this model are balanced two-point designs for all values of the parameters. We further derive explicit expressions for Bayesian D-optimal designs which are based on exactly two points of support, and provide necessary and sufficient conditions for such designs to exist. We illustrate our results by means of two examples.

Two-point transonic airfoil design using optimization for improved off-design performance

A two-point, aerodynamic design method is presented that improves the aerodynamic performance of transonic airfoils over a range of the flight envelope. It couples an Euler flow solver and a numerical optimization tool. The major limitation of single-point design is the poor off-design performance. Two-point design is used to extend the optimized performance range over more of the desired flight envelope. The method is applied to several transonic flow design points, and the results are compared to single-point design results. The secondary design points are chosen by varying the Mach number and the angle of attack. The two-point designs perform better than the single-point design over the design-point range.

D-optium design for logistic model

In this paper, a general technique is proposed to determine optimum proportion of the logistic regression model for all even and odd number points. It is shown that a design with an even number of points requires symmetry for its optimality and is a replication of two-point design. Further, the optimum proportions for a D-optimal design involving an odd number of observations asymptotically approaches to the optimum proportion for the two-point design.

Optimal design of experiments for the estimation of precise hyperbolic kinetic and binding parameters

Optimal designs were evaluated for the estimation of precise parameters in kinetic and binding experiments in which the concentration dependence of the response (reaction velocity or bound ligand concentration) is characterized by a hyperbola. The designs were evaluated by maximizing the determinant of the appropriate information matrix. It is demonstrated that highest precision is obtained by replicating basic two-point designs. However, the calculated optimal designs should serve only as guidelines and not rules for experimentation. In the presence of constant variance, half of the observations should be obtained at the highest practically attainable concentration. In kinetic studies, the remaining measurements should yield half of the maximally attainable velocity. In binding experiments, the second half of observations for either bound (b) or free (f) ligand concentrations should be made at a total concentration of c = P + K ( K is the dissociation constant, and P the binding capacity). With constant coefficient of variation (constant relative error), kinetic experiments should be performed, at equal frequency, at the highest and lowest attainable concentration. Half of the binding experiments should be made at their lowest precision: at the highest possible concentration when b is measured, and at the smallest feasible concentration when f is obtained. The other half of the readings should be taken at c = P − K (if P > K) for the measurement of b, and at c = P + K for observations of f. Deviations from the calculated optimal designs result in diminished efficiency (increased variance) of the estimated parameters. The reduction can be substantial with some frequently used experimental designs, especially when the number of observations is not very small. Therefore, the first few readings could consider the validation of the model, but additional measurements should follow the guidelines presented here.