Search

Orthogonal‐array composite designs (OACDs) and orthogonal‐uniform composite designs (OUCDs) are orthogonal composite designs that combine two‐level full or fractional factorial and three‐level orthogonal‐array/uniform designs for estimation of the linear, bilinear, and quadratic effects in a second‐order response surface model. In this study, the effects of missing one observation in the various design portions (factorial (f) axial (a) and center (c)), on the precision of parameter estimates, prediction variance and design efficiency of OACDs and OUCDs for 5 ≤ k ≤ 9 factors at different values of α (the distance of a non‐zero co‐ordinate in an additional design point from the center) are evaluated. The results showed that missing a factorial and an axial point have adverse effect on the precision of parameter estimates of OACDs and OUCDs, while missing a center point has little effect. Missing an axial point caused the highest effect on the prediction variance and design efficiencies. The FDS plots showed OACDs to be better designs for k ≤ 7 and OUCDs for k = 8 and 9 factors. [ABSTRACT FROM AUTHOR]

In this work, four orthogonal composite designs (orthogonal-array composite designs (OACDs), orthogonal-array composite minimax-loss (OACM) designs, orthogonal uniform composite designs (OUCDs) and orthogonal uniform composite minimax-loss (OUCM) designs) for second-order models were evaluated in the presence of errors for 3 ≤ k ≤ 7 factors with 1 ≤ nc ≤ 3 center points. The design efficiency (in terms of D- and G-efficiency values) and fraction of design space (FDS) plots were used to evaluate the performance of these designs in the presence of errors. The results showed that in terms of D-efficiency values, OACDs and OUCDs performed poorly for k = 6 and 7 factors in the presence of errors while OACM designs were the best-performing designs. The OUCM designs outperformed all the other designs for G-efficiency values with OACM designs as the next best performing designs. The FDS plots showed that OACM and OUCM designs maintained high G-efficiency values in the presence of errors. [ABSTRACT FROM AUTHOR]

In this paper, the stability of the prediction variance of orthogonal composite designs (orthogonal array composite, orthogonal array composite minimax loss, orthogonal uniform composite and orthogonal uniform composite minimax loss designs) was evaluated and compared for 3 ≤ k ≤ 6 using the fraction of design space plot in the hypersphere and hypercube regions. These designs were shown to have stable and consistent scaled prediction variance (SPV) throughout the design region. The orthogonal array composite minimax loss designs performed better with the least SPV than the other orthogonal composite designs for most factors in the hypersphere region. Also, the orthogonal array composite designs performed better in the hypercube region compared to other competing designs. [ABSTRACT FROM AUTHOR]

AbstractOutliers are outrageous values that occur in an experiment and can almost be inevitable. The presence of outliers in an experiment can affect the results of a response surface design due to disruption in the design’s structure. In this paper, a new class of orthogonal uniform composite designs (OUCD4) for fitting third-order response surface model are constructed using the minimax outlying effect criterion that minimizes the maximum outlying effect. These constructed designs referred to as orthogonal uniform composite minimax outlying (OUCO4) designs are robust to a single outlier. The OUCO4 designs are shown to be more efficient in terms of relative efficiency compared to the OUCD4. [ABSTRACT FROM AUTHOR]

Missing observations are practical problems that occur frequently even in a well-planned experiment and can significantly impact the statistical accuracy of the experiment. This work introduces a new class of third-order designs called augmented orthogonal uniform composite minimax loss (AOUCM) designs, which are more robust to a single missing design point as a variation of the existing third-order augmented orthogonal uniform composite designs (AOUCDs). The AOUCM designs are constructed using the minimax loss criterion. The constructed AOUCM designs are evaluated and compared with AOUCDs based on the relative D- and G-efficiency criteria, generalized scaled deviation, and the fraction of design space plot. The AOUCM designs are shown to be robust and more efficient in estimating the parameters of the third-order model. Moreover, although the AOUCDs and AOUCM designs are stable and uniformly distributed throughout the design space, the AOUCM designs have the least scaled prediction variance. [ABSTRACT FROM AUTHOR]

Outliers are inconsistent values that commonly occur in every experimental setting and damage the designs' properties to be explored. Based on the orthogonal uniform composite designs (OUCDs) proposed by Zhang et al., this article introduces a new class of second-order designs called orthogonal array composite minimax outlying designs by using the minimax outlying criterion that minimizes the maximum outlying effect of all design points. The proposed designs' efficiencies and generalized scaled standard deviations are compared with central composite design, small composite designs, orthogonal array composite designs, orthogonal array composite minimax loss designs, and OUCDs. The proposed designs are more robust to outlier than the existing OUCDs. These new designs are more optimal in terms of D-, E-, G- and T- efficiencies in most cases than the existing composite designs. [ABSTRACT FROM AUTHOR]

In this paper, the prediction variance capabilities of two new second-order designs orthogonal uniform composite designs and orthogonal array composite designs are examined using the variance dispersion graph and the fraction of design space plot in the spherical region. Also, the D- and G-optimality criteria are evaluated for these two response surface designs. The orthogonal array composite designs were shown to have a better prediction variance in terms of the fraction of design space plot and the variance dispersion graphs over the orthogonal uniform composite designs. [ABSTRACT FROM AUTHOR]

This work examined the sensitivity of randomization test and F‐test in completely randomized design, randomized complete block design and Latin square design in order to ascertain which is more robust in terms of power (sensitivity) of the test and type I error rate in cases with normal error, skewed error (Chi‐square and Exponential distributions), by varying the sample sizes. Using Monte Carlo simulation, response observations were generated for normal error, skewed error at various sample sizes for each of the experimental designs. The results showed that for the normal error, the power and type I error rate of the F‐test were slightly smaller and greater respectively in each of the designs than that of the randomization test. Furthermore, for the skewed error, the randomization test was more sensitive than the F‐test, and also, the type I error was smaller in each of the designs. [ABSTRACT FROM AUTHOR]

Missing data can hardly be prevented in most experiments due to setbacks that occur during the data entry process, and may grossly affect the estimation of the regression coefficients. The effects of missing data may be extremely significant if the design is almost saturated, saturated or fully saturated. It is of practical significance to identify designs that are least affected by missing data. In this paper, new orthogonal uniform minimax loss (OUCM) designs are constructed. These designs are more robust to one missing design point than the original orthogonal uniform composite designs (OUCDs) of Zhang, Liu, and Zhou (2020). The proposed designs are compared with central composite design (CCDs), small composite designs (SCDs), orthogonal array composite designs (OACDs), orthogonal array composite minimax loss designs (OACMs), and orthogonal uniform composite designs (OUCDs) based on the D-efficiency, A-efficiency and T-efficiency for estimating the parameters of the second-order model and under the generalized scaled standard deviations. These designs perform better in term of losses and also have higher D-efficiency, A-efficiency and T-efficiency. [ABSTRACT FROM AUTHOR]

Missing data are inevitable problem in almost every research such as experimental and observational researches. In this paper, we proposed a non-iterative least square formulae for estimating missing data in rectangular lattice designs (simple and triple) without repetitions of the basic design using the intra-block information when one or more observations are missing. A numerical example was used to show the applicability of the proposed formulae in terms of estimated values, standard errors and p-value. Results showed that the estimated values were significantly approximate to the complete data which indicate the effectiveness of the proposed formulae for estimating missing data in rectangular lattice designs without repetitions. [ABSTRACT FROM AUTHOR]