Orthogonal arrays (OAs) are widely used in industrial experiments for factor screening. Suppose that only a few of the factors in the experiments turn out to be important. An OA can be used not only for screening factors, but also for detecting interactions among a subset of active factors. In this article a set of optimality criteria is proposed to assess the performance of designs for factor screening, projection, and interaction detection, and a three-step approach is proposed to search for optimal designs. Combinatorial and algorithmic construction methods are proposed for generating new designs. Permutations of levels are used for improving the eligibility and estimation efficiency of the projected designs. The techniques are then applied to search for best three-level designs with 18 and 27 runs. Many new, efficient, and practically useful nonregular designs are found and their properties are discussed.
Quality variation in resistance spot welding is a major concern in the automotive industry. The relationship between weld quality and various process conditions, including abnormal process conditions, has not yet been systematically studied. This paper investigates this relationship using a newly developed two-stage, sliding-level experiment. In the experiment, welding current is treated as a “slid factor” whose settings are determined based on those of other process variables. Engineering knowledge is applied in statistical model selection. From the analysis, it is found that abnormal process conditions, such as axial misalignment, angular misalignment, poor fitup, edge weld, and electrode wear, significantly affect weld size and thus cause large variation in the weld quality. Although they may help increase the weld size in some cases, abnormal process conditions generally lead to a less robust process. In order to minimize the effects of the abnormal process conditions, a robust parameter design is formulated using the statistical models developed from the experimental data. The analysis suggests that high current and large electrodes should be used for reducing the weld quality variation. Developed in this study, the new experimental design and analysis procedures can also be applied to other processes, where the process variables are inter-dependent.
Factorial designs have broad applications in agricultural, engineering and scientific studies. In constructing and studying properties of factorial designs, traditional design theory treats all factors as nominal. However, this is not appropriate for experiments that involve quantitative factors. For designs with quantitative factors, level permutation of one or more factors in a design matrix could result in different geometric structures, and, thus, different design properties. In this paper indicator functions are introduced to represent factorial designs. A polynomial form of indicator functions is used to characterize the geometric structure of those designs. Geometric isomorphism is defined for classifying designs with quantitative factors. Based on indicator functions, a new aberration criteria is proposed and some minimum aberration designs are presented.
Eyelets, capstans and cylindrical surfaces are often used in thread, fiber and paper handling machinery to guide the axially moving element. In addition to providing positional control, these "guides" introduce dry friction forces that alter the vibration and stability characteristics of the system. This paper examines the lateral response of a string that slides through an elastically supported, dry friction guide. Exact expressions are derived for the linear response under free and forced conditions. Solutions for the eigenvalue spectrum exhibit unusual features including multiple divergence instabilities, regions of flutter instability, and regions of curve veering associated with mode localization. A second order perturbation solution is derived to examine the behavior of the eigenvalue spectrum in regions of flutter instability and curve veering. The analysis highlights the common features of these two phenomena and suggests ways to minimize vibration by adjusting various design variables. The analysis also demonstrates that the eigenvalue loci in regions of flutter instability and curve veering are naturally described by a local hyperbolic approximation.
Expulsion is an important phenomenon in resistance spot welding. It involves loss of metal from the liquid nugget, which often results in the reduction of weld strength. Various models have been proposed to understand expulsion mechanisms. In these models the occurrence of expulsion is often treated as a deterministic event, and depicted by a line (boundary) in conventional lobe diagrams. In this study, statistical analysis is employed to explore expulsion with consideration of the influence of random factors. Models are built based on experimental data, and one steel and two aluminum alloys are used as examples. Expulsion probabilities are presented as a function of electrode force, welding current, and time. Analytical models and their graphical form of expression (contours and surfaces) are created to present expulsion limits under various combinations of welding parameters. This study provides not only quantitative model predictions on expulsion limits for the materials studied, but also a generic statistical methodology that can be used for analyzing expulsion in various material systems. [S1087-1357(00)00602-X]
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