The optimal schedule to produce a given number of acceptable parts with a specified confidence level

This paper deals with the problem of finding the optimal schedule for producing, with a probability α, a finite number H, of parts which have a diameter within specified tolerance limits. It is assumed that the diameter is a normally distributed variable that exhibits a linear trend in the process mean. The solution involves determining the optimal run size(s), as well as the specific number of runs of each size, required to produce at least H parts, with probability α, at minimum cost. A solution algorithm is provided and computational experience reported.     

Analysis of robot positioning error

Positioning errors of robots used for material handling and assembly can be sufficiently large to cause problems. These errors are due to imperfect repeatability of the robots, and their effects can be ameliorated or exacerbated by tolerances on the workpieces and on the jigs and fixtures. In this paper, a model for characterizing the positioning errors of robots is developed. A statistical analysis of positioning error data is performed to make inferences about the stochastic nature of the robotic system. The basic issue is whether the positioning errors of the robot are state dependent or state invariant.     

Identification of large scale distributed parameter systems—some simplifications in the multidimensional Poisson moment functional (MDPMF) approach

This paper is concerned with two practically important aspects of identification of large scale distributed parameter systems by the multidimensional Poisson moment functional (MDPMF) method (Saha and Prasada Rao 1980). The existing methods of (i) development and diagrammatic representations of the relations among the MDPMFs of partial derivative terms and those of the original multivariable function, and (ii) elimination of the effects of boundary functions and their partial derivatives from the identification equations, become extremely unwieldy as the order and dimensions of the model increase. This paper suggests alternative techniques in these two situations, leading to a simplification of the algorithm and an enormous reduction of the related analytical and computational burden. In the former situation, the suggested alternative uses the concept of separated variables. In the latter, the boundary function effects are estimated and then inserted into the algorithm to simplify it.     

Determination of optimal part delivery dates in a stochastic assembly line

We consider the problem of determining the optimal part delivery dates of a low volume, small lot assembly line which manufactures large and costly products. Parts are assembled at each stage to a subassembly. The arrival time of an assembly part from a vendor is assumed to be a normally distributed random variable. A dynamic programming algorithm is developed to minimize work-in-process inventory of parts and subassemblies. It is implemented on the single job problem. Its further extensions to the multi-job case and to incorporate the cost of setting delivery dates are also discussed.     

DIRECTED DIVERGENCE AND CYCLIC SYMMETRY

Abstract

The authors have axiomatically characterized Directed Divergence assuming cyclic symmetry which is weaker than the symmetry.     

Numerical simulation for determination of limit strains of a cold rolled and solution treated Nimonic C-263 alloy sheet

Nimonic alloys are Ni-base superalloys used for several high temperature applications, notable among them are the components in space vehicles, rocket engines, submarines, nuclear reactors, chemical processing vessels and heat exchange tubing as they exhibit excellent mechanical strength and creep resistance at high temperatures. Hence, evaluation of their formability characteristics is of utmost importance to make them into several useful components. Limit strains or forming limit curve is one of the parameters that indicates the formability, especially the drawability of sheet metal for deep drawing applications. In this paper, the limit strains of Nimonic C-263 alloy is investigated and presented using an explicit finite element code LSDYNA 3D. The material properties and the material model are evaluated by conducting tensile tests. The limit strains obtained from the simulation are verified by the analytical equations developed using vertex theory. The results tally within ±10% error.     

Crystallization Kinetics of Lithia-Silica Glasses: Effect of Composition and Nucleating Agent

The kinetics of crystallization of a 25Li₂O · 75SiO₂ (wt%) glass doped with Pt, Cu, Au, TiO₂, and P₂O₅ were studied using nonisothermal techniques. The activation energy, E , and the frequency factor, v , for the overall crystallization process depended directly on the critical cooling rate for the glass formation, R_c , of these glasses. The crystallization kinetics of several other glasses in the lithia-silica system were also studied as a function of composition, critical cooling rate, and liquidus temperature, T_m. E and v for these glasses were more dependent on the liquidus temperature than on R_c .     

Crystallization of Calcia-Gallia-Silica Glasses

The critical cooling rate, R _c, for glass formation and the kinetics of crystallization of the compositions 18.4CaO-(81.6 - X )Ga₂O₃- X SiO₂ (in wt%), with X =3, 6, 9, and 13.8, were studied by using a thermal image furnace. Crystallization was studied nonisothermally and the data were analyzed by using the Avrami equation. The R _c and activation energy for crystallization both decrease with increasing silica content. The results obtained by the present technique agree with those obtained from DTA measurements.     

Glass Formation and Properties in the System Calcia-Gallia-Germania

The critical cooling rate for glass formation, R^c, was measured for four compositions in the system calcia-gallia-germania. The activation energy, E, and frequency factor, u, for the crystallization process were determined by reheating the glasses at varied constant heating rates and measuring the temperature of crystallization. Both E and v increased, with increasing germania content of the glass, whereas R^c decreased. The density, refractive index, and Abbe number were also measured; all decreased with increasing GeO² content. These results are compared with those for calcia-gallia-silica glasses of comparable compositions.