Minimax Second-Order Disigns over Hypercubes for the Difference Between Estimated Response at two Points on a Straight Line Through the Origin

1998 ◽  
Vol 48 (1-2) ◽  
pp. 101-108 ◽  
Author(s):  
S. Huda
Keyword(s):  
Design Criterion ◽  
Second Order ◽  
Optimal Designs ◽  
Straight Line ◽  
Order Polynomial ◽  
Polynomial Models ◽  
The Difference ◽  
Experimental Region

Minimization of the variance of the difference between estimated responses at two points on a straight line through the origin maximized over all pairs of such points in the experimental region is taken as the design criterion. Optimal designs are obtained for second-order polynomial models over hypercubes. The performance of best designs within some commonly used classes of designs is also investigated.

Ultimate Compression Strength and Probabilistic Analysis of Stiffened Plates

1997 ◽  
Vol 119 (4) ◽  
pp. 270-275 ◽  
Author(s):  
Y. Pu ◽  
P. K. Das ◽  
D. Faulkner
Keyword(s):  
Model Uncertainty ◽  
Numerical Data ◽  
Original Method ◽  
Second Order ◽  
Stiffened Plates ◽  
Straight Line ◽  
Reliability Method ◽  
First Order Second Moment ◽  
The Difference ◽  
Second Moment Method

In the paper, a formulation for predicting the ultimate strength of a stiffened plate is proposed by incorporating Guedes Soares’s formula, which gives the best prediction for unstiffened plates according to the calibration carried out recently by the authors, into Faulkner’s method (Faulkner et al., 1973). The proposed algorithm is then calibrated by using a considerable amount of experimental and numerical data. It is observed that: (a) The proposed method shows better prediction than Faulkner’s original method if only the experimental data (63 samples) are included in the calibration, the bias and COV of the model uncertainty of the proposed method are 0.992 and 0.099, respectively, while they are 1.039 and 0.143 for Faulkner’s original method, and the skewness of the proposed method is small (only −0.105 slope, which is defined as the slope of the regressed straight line on the plot of model uncertainty against predicted value). (b) On the whole, including experimental and numerical data, the results of the proposed method demonstrate more or less the same accuracy as that of the original Faulkner method with better bias and skewness, but slightly larger scatters than the original Faulkner method. In addition, the reliability analyses of stiffened plates are carried out by using advanced first-order second-moment method (AFOSM), the second-order reliability method (SORM), and Monte Carlo simulation to investigate the accuracy of the first and second-order methods. It is found that the difference between the two methods is so small that the values obtained from AFOSM are acceptable in practice, considering the nominal nature of the reliability index.

Optimal designs for clinical trials with second-order polynomial treatment effects

2007 ◽  
Vol 16 (6) ◽  
pp. 523-537 ◽  
Author(s):  
Bjorn Winkens ◽  
Hubert J. A. Schouten ◽  
Gerard J. P. van Breukelen ◽  
Martijn P. F. Berger
Keyword(s):  
Clinical Trials ◽  
Treatment Effects ◽  
Second Order ◽  
Optimal Designs ◽  
Order Polynomial

Automatic Tread Gaging Machine

1979 ◽  
Vol 7 (1) ◽  
pp. 31-39
Author(s):  
G. S. Ludwig ◽  
F. C. Brenner
Keyword(s):  
Experimental Tests ◽  
Automatic Machine ◽  
Wear Rates ◽  
Handling Device ◽  
Straight Line ◽  
Component Systems ◽  
Before And After ◽  
Good Repeatability ◽  
The Difference ◽  
Straight Lines

Abstract An automatic tread gaging machine has been developed. It consists of three component systems: (1) a laser gaging head, (2) a tire handling device, and (3) a computer that controls the movement of the tire handling machine, processes the data, and computes the least-squares straight line from which a wear rate may be estimated. Experimental tests show that the machine has good repeatability. In comparisons with measurements obtained by a hand gage, the automatic machine gives smaller average groove depths. The difference before and after a period of wear for both methods of measurement are the same. Wear rates estimated from the slopes of straight lines fitted to both sets of data are not significantly different.

scholarly journals XXIII.—On the Disruptive Discharge of Electricity: An Experimental Thesis for the Degree of Doctor of Science, Department A

1878 ◽  
Vol 28 (2) ◽  
pp. 633-671 ◽  
Author(s):  
Alexander Macfarlane
Keyword(s):  
Copper Wire ◽  
Late Summer ◽  
The Other ◽  
Straight Line ◽  
Summer Session ◽  
The Difference ◽  
A Chain ◽  
The One ◽  
Metallic Parts ◽  
The University

The experiments to which I shall refer were carried out in the physical laboratory of the University during the late summer session. I was ably assisted in conducting the experiments by three students of the laboratory,—Messrs H. A. Salvesen, G. M. Connor, and D. E. Stewart. The method which was used of measuring the difference of potential required to produce a disruptive discharge of electricity under given conditions, is that described in a paper communicated to the Royal Society of Edinburgh in 1876 in the names of Mr J. A. Paton, M. A., and myself, and was suggested to me by Professor Tait as a means of attacking the experimental problems mentioned below.The above sketch which I took of the apparatus in situ may facilitate tha description of the method. The receiver of an air-pump, having a rod capable of being moved air-tight up and down through the neck, was attached to one of the conductors of a Holtz machine in such a manner that the conductor of the machine and the rod formed one conducting system. Projecting from the bottom of the receiver was a short metallic rod, forming one conductor with the metallic parts of the air-pump, and by means of a chain with the uninsulated conductor of the Holtz machine. Brass balls and discs of various sizes were made to order, capable of being screwed on to the ends of the rods. On the table, and at a distance of about six feet from the receiver, was a stand supporting two insulated brass balls, the one fixed, the other having one degree of freedom, viz., of moving in a straight line in the plane of the table. The fixed insulated ball A was made one conductor with the insulated conductor of the Holtz and the rod of the receiver, by means of a copper wire insulated with gutta percha, having one end stuck firmly into a hole in the collar of the receiver, and having the other fitted in between the glass stem and the hollow in the ball, by which it fitted on to the stem tightly. A thin wire similarly fitted in between the ball B and its insulating stem connected the ball with the insulated half ring of a divided ring reflecting electrometer.

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