Showing papers on "Fractional factorial design published in 1984"
TL;DR: In this paper, the Fries and Hunter algorithm was used for a wider range of n and m and for designs with factors at p levels where p ≥ 2 is prime, and a matrix is given for generating 3 n-m designs with m, n ≤ 6, which have, or nearly have, minimum aberration.
Abstract: Fries and Hunter (1980) presented a practical algorithm for selecting standard 2 n–m fractional factorial designs based on a criterion they called “minimum aberration.” In this article some simple results are presented that enable the Fries–Hunter algorithm to be used for a wider range of n and m and for designs with factors at p levels where p ≥ 2 is prime. Examples of minimum aberration 2 n–m designs with resolution R ≥ 4 are given for m, n – m < 9. A matrix is given for generating 3 n–m designs with m, n – m ≤ 6, which have, or nearly have, minimum aberration.
101 citations
TL;DR: In this article, summation formulas for the Welch-James procedure are presented for the 2 x 2 design, and matrix formulas that permit routine application of the procedure to crossed factorial designs are presented.
Abstract: The Welch-James procedure may be used to test hypotheses on means, when independent samples from populations with heterogeneous variances are available. Until recently the complexity of the available presentations of this procedure limited the application of this procedure. To resolve this state of affairs, summation formulas for the Welch-James procedure are presented for the 2 x 2 design. In addition, matrix formulas that permit routine application of the procedure to crossed factorial designs are presented.
33 citations
TL;DR: In this paper, four general classes of partially balanced designs for 2n factorials, corresponding to four different forms of a general null hypothesis H on factorial effects, are presented, and the typical design in each class, the simplified form of the non-centrality parameter λ2 of the asymptotic chi-square distribution of the likelihood ratio statistic for testing the corresponding form of H0 is derived under defined local alternatives.
Abstract: Four general classes of partially balanced designs for 2n factorials, corresponding to four different forms of a general null hypothesis H on factorial effects, are presented. For the typical design in each class, the simplified form of the non-centrality parameter λ2 of the asymptotic chi-square distribution of the likelihood ratio statistic for testing the corresponding form of H0 is derived under defined local alternatives. Optimal designs d1 maximizing λ2 in the i-th class and minimizing the trace, determinant and largest eigenvalue of a defined covariance matrix, i =1,…,4, are determined.
10 citations
Journal Article•
TL;DR: The stability of chlorpromazine hydrochloride in some hypothetical tablet formulations was evaluated through a fractional factorial design of the type N = 2(6-3) and the best multi-component excipient mixture was evaluated on the basis of the information deduced from thefactorial design.
Abstract: The stability of chlorpromazine hydrochloride in some hypothetical tablet formulations was evaluated through a fractional factorial design of the type N = 2(6-3). The factors studied were the type of filler (X1), lubricant (X2), binder (X3), disintegrant (X4), the absence or presence of light ( X5 ) and/or humidity ( X6 ). Statistical analysis of the stability data allowed the derivation of a regression equation which determined the magnitude and direction of change of each factor level to optimize drug stability. The significance of the factors could be arranged in the following order: X5 greater than X2 greater than X3 greater than X6 greater than X1. The effects of X4 and the two-factor interaction X2X3 were found to be insignificant. The best multi-component excipient mixture was evaluated on the basis of the information deduced from the factorial design.
4 citations
TL;DR: A fractional factorial design of experiments was formulated for the reaction of formaldehyde with cotton cellulose in the presence of hydroxymethanesulfonic acid in the conventional pad-dry-cure process as discussed by the authors.
Abstract: A fractional factorial design of experiments was formulated for the reaction of formaldehyde with cotton cellulose in the presence of hydroxymethanesulfonic acid in the conventional pad-dry-cure process. None of the 30 experimental treatments of cotton offered an attractive balance of durable press performance properties. Ap plication of multiple linear regression analysis to the experimental data resulted in equations relating the experimental variables to eight textile physical properties. These equations were used to calculate predicted values for each textile property that met or exceeded a minimum acceptable specification (MAS). The MAS was satisfied or exceeded (except for Accelerotor abrasion resistance) within small regions of profile plots for finishing reactions only at 140°C and in these cases, with decreasing area of regions for cures of 1, 3, 5, and 7 minutes. Experiments failed to confirm the validity of the regions of MAS. Correlation coefficients for the cellulose-formaldehyde- hydroxymeth...
3 citations
TL;DR: In this article, factorial analyses were used in conjunction with a heat-transfer model to identify variables important for heat transfer through pelage, and nine of eleven variables tested had statistically significant effects.
Abstract: FRACTIONAL factorial analyses were used in conjunction with a heat-transfer model to identify variables important for heat transfer through pelage. Nine of eleven variables tested had statistically significant effects.
3 citations
TL;DR: In this paper, the robustness of balanced fractional 2m factorial (2mBFF) designs of resolution VII derived from simple arrays (S-arrays) was studied.
Abstract: By use of the algebraic structure, we study the robustness of balanced fractional 2m factorial (2mBFF) designs of resolution VII derived from simple arrays (S-arrays) in the sense that, when any single observation is missing, all unknown effects are still estimable in the model assumed. In addition, we present robust designs for Shirakura’s A-optimal designs.
2 citations
TL;DR: In this article, the authors considered the problem of constructing E-optimal balanced resolution III designs for the 2 m × 3 n series and obtained the inverse of the information matrix for general resolution III balanced 2 m×3 n designs.
2 citations
TL;DR: An algorithm for constructing nests of 2 factor design with orthogonal factorial structute is described in this paper, which utilizes a combinatorial structure which is found to be inherent in most designs with orthographic factorial structure.
Abstract: An algorithm for constructing nests of 2 factor design with orthogonal factorial structute is described in this paper. The algorithm utilizes a combinatorial structure which is found to be inherent in most designs with orthogonal factorial structure. Some useful modifications of the algorithm are also considered. Several examples illustrating the performance of the algorithm are given.
2 citations
TL;DR: In this paper, a lower bound for the number of experimental runs required in search designs for two-level factorial models is given, and the lower bound is also shown for the case of two-dimensional models.
1 citations
01 Sep 1984
TL;DR: In this article, the authors discuss the situation where factors may influence not only the location but also the dispersion of the data, and the aliasing of location and dispersion effects is explored and methods for identifying an appropriate location - dispersion model are considered.
Abstract: : Unreplicated fractional factorial designs are frequently employed as screening designs when it is believed that a condition of effect sparisity will ensure that only a few of the possible effects are likely to be large. After considering the concept of effect sparisity as a justification for the use of unreplicated fractional designs, we discuss the situation where factors may influence not only the location but also the dispersion of the data. The aliasing of location and dispersion effects is explored and methods for identifying an appropriate location - dispersion model are considered.
TL;DR: The sharpened Stirling's formula approximates well the factorial of a large number N as mentioned in this paper, and the relative error of this approximation decreases with the magnitude of N. The upper limit of the method is about N = 108.
Abstract: The sharpened Stirling's formula approximates well the factorial of a large number N. The relative error of this approximation decreases with the magnitude of N and is about 10?7 for the factorial of 101. The upper limit of the method is about N = 108. The program listing and execution protocol of the routine for a HP41C programmable calculator are presented.
01 Jan 1984
TL;DR: This paper is an exposition of the various forms of these designs and their analysis of the fractional factorials.
Abstract: Multivariate methods of data collection and analysis extend to experimental designs, most particularly to the fractional factorials. This paper is an exposition of the various forms of these designs and their analysis.
01 Jan 1984
TL;DR: In this paper, the problem of connectedness, robustness against incomplete data and semi-separability of the irregular fractional factorial designs is considered. But the authors focus on linear on log-linear models.
Abstract: This paper is devoted to the fractional factorial designs analysed by meas of linear on log-linear models. The problems of connectedness, robustness against incomplete data and semi-separability of the irregular fnactions are considered. Some computational solutions are described which use erron-free procedures with fixed point and residue arithemtics.