Samuel P. Marin

Surface chemistry models of carbon monoxide oxidation on supported platinum catalysts

Rates of CO oxidation on noble metal catalysts are often represented by a Langmuir-Hinshelwood rate expression that assumes the competitive equilibrium adsorption of CO and O2 on the active metal surface. Surface chemistry studies reported in the literature have shown, however, that this assumption cannot be justified under all conditions. As a result, the usual Langmuir-Hinshelwood rate expression is unable to explain the data of several reported studies of CO oxidation on Pt catalysts. In this report we develop two reaction models which include separate adsorption, desorption, and surface reaction steps, and which do not assume adsorption equilibrium. The ability of each model to fit CO oxidation rate data taken with an alumina-supported Pt catalyst is compared with that of the usual Langmuir-Hinshelwood rate expression. Unlike the usual rate expression, the surface chemistry models successfully simulate the abrupt transition in steady-state rate that occurs between the CO inhibition regime and the first-order regime. The parameter values used to fit the supported Pt data are similar to those determined with Pt crystals. However, they indicate that CO may be adsorbed less strongly on the supported Pt and that most of the surface Pt atoms in the supported catalyst were deactivated by an oxidizing pretreatment.

Modeling of Manufacturing Complexity in Mixed-Model Assembly Lines

Mixed-model assembly lines have been recognized as a major enabler to handle product variety. However, the assembly process becomes very complex when the number of product variants is high, which, in turn, may impact the system performance in terms of quality and productivity. This paper considers the variety induced manufacturing complexity in manual mixed-model assembly lines where operators have to make choices for various assembly activities. A complexity measure called “operator choice complexity” (OCC) is proposed to quantify human performance in making choices. The OCC takes an analytical form as an information-theoretic entropy measure of the average randomness in a choice process. Meanwhile, empirical evidences are provided to support the proposed complexity measure. Based on the OCC, models are developed to evaluate the complexity at each station and for the entire assembly line. Consequently, complexity can be minimized by making system design and operation decisions, such as error-proof strategies and assembly sequence planning.

Balancing and optimizing a portfolio of R&D projects

A mathematical formulation of an optimization model designed to select projects for inclusion in an R&D portfolio, subject to a wide variety of constraints (e.g., capital, headcount, strategic intent, etc.), is presented. The model is similar to others that have previously appeared in the literature and is in the form of a mixed integer programming (MIP) problem known as the multidimensional knapsack problem. Exact solution of such problems is generally difficult, but can be accomplished in reasonable time using specialized algorithms. The main contribution of this paper is an examination of two important issues related to formulation of project selection models such as the one presented here. If partial funding and implementation of projects is allowed, the resulting formulation is a linear programming (LP) problem which can be solved quite easily. Several plausible assumptions about how partial funding impacts project value are presented. In general, our examples suggest that the problem might best be formulated as a nonlinear programming (NLP) problem, but that there is a need for further research to determine an appropriate expression for the value of a partially funded project. In light of that gap in the current body of knowledge and for practical reasons, the LP relaxation of this model is preferred. The LP relaxation can be implemented in a spreadsheet (even for relatively large problems) and gives reasonable results when applied to a test problem based on GMs R&D project selection process. There has been much discussion in the literature on the topic of assigning a quantitative measure of value to each project. Although many alternatives are suggested, no one way is universally accepted as the preferred way. There does seem to be general agreement that all of the proposed methods are subject to considerable uncertainty. A systematic way to examine the sensitivity of project selection decisions to variations in the measure of value is developed. It is shown that the solution for the illustrative problem is reasonably robust to rather large variations in the measure of value. We cannot, however, conclude that this would be the case in general.

Compliant Assembly Variation Analysis Using Component Geometric Covariance

Dimensional variation is one of the most critical issues in the design of assembled products. This is especially true for the assembly of compliant parts since clamping and joining during assembly may introduce additional variation due to part deformation and springback. This paper discusses the effect of geometric covariance in the calculation of assembly variation of compliant parts. A new method is proposed for predicting compliant assembly variation using the component geometric covariance. It combines the use of principal component analysis (PCA) and finite element analysis in estimating the effect of part/component variation on assembly variation. PCA is used to extract deformation patterns from production data, decomposing the component covariance into the individual contributions of these deformation patterns. Finite element analysis is used to determine the effect of each deformation pattern over the assembly variation. The proposed methodology can significantly reduce the computational effort required in variation analysis of compliant assemblies. A case study is presented to illustrate the methodology.

Adsorption effects during temperature-programmed desorption of carbon monoxide from supported platinum

Experimental data are presented for the temperature-programmed desorption (TPD) of CO from porous PtAl2O3 into a vacuum. Most of the preadsorbed CO desorbs in a peak between 380 and 550 K. Other workers have measured desorption at substantially higher temperatures during TPD of CO into a carrier gas rather than a vacuum. A comparison of the experimental conditions suggests that the competition of CO adsorption with CO desorption may contribute to the differences between the TPD results. To investigate the effects of CO adsorption, we develop a mathematical model and use it to compute desorption spectra for the TPD of CO from Pt dispersed over a porous support into (a) an inert carrier gas and (b) a vacuum. Over the realistic parameter range considered, our model predicts that adsorption effects, caused by high concentrations of gaseous CO in the system, are always an important feature, broadening the desorption peaks and shifting them to higher temperatures. Indeed, we find that adsorption competes with desorption to the extent that adsorption equilibrium is always approached closely within the porous supported Pt samples. For desorption into a carrier gas, the adsorption effects result from limitations to the flow of CO from the sample cell, whereas for desorption into a vacuum, the adsorption effects result from limitations to the diffusion of CO from the porous sample. Our results suggest that significant adsorption effects will also be present during the TPD of CO from other Group VIII precious metals dispersed over porous supports.

Constrained interpolation and smoothing

Numerical and theoretical questions related to constrained interpolation and smoothing are treated. The prototype problem is that of finding the smoothest convex interpolant to given univariate data. Recent results have shown that this convex programming problem with infinite constraints can be recast as a finite parametric nonlinear system whose solution is closely related to the second derivative of the desired interpolating function. This paper focuses on the analysis of numerical techniques for solving the nonlinear system and on the theoretical issues that arise when certain extensions of the problem are considered.In particular, we show that two standard iteration techniques, the Jacobi and Gauss-Seidel methods, are globally convergent when applied to this problem. In addition we use the problem structure to develop an efficient implementation of Newtons method and observe consistent quadratic convergence. We also develop a theory for the existence, uniqueness, and representation of solutions to the convex interpolation problem with nonzero lower bounds on the second derivative (strict convexity). Finally, a smoothing spline analogue to the convex interpolation problem is studied with reference to the computation of convex approximations to noisy data.

Production system design for quality robustness

In automotive assembly plants, vehicles with defects are either repaired (e.g., components are exchanged, scratches are polished, etc.) or reworked (e.g., the whole vehicle is repainted) to maintain high product quality. The performance of vehicle quality is typically characterized in terms of the first time quality and also the quality buy rate. First time quality is defined as the good job ratio of all first time processing jobs, while the quality buy rate is the good job ratio of all processed jobs, including the first time jobs and reworked jobs. In this paper, we study a repair and rework system at an automotive paint shop with random first time quality. Specifically, we show that paint quality, in terms of quality buy rate, can be described by a function of repair capacity and first time quality. Increasing the repair capacity can improve the quality buy rate and reduce unnecessary repaints. Variations in first time quality may lead to a reduction in the quality buy rate and an increase in unnecessary repaints, and consequently, a substantial waste of production capacity and materials. In addition, we observe that the average quality buy rate depends primarily on the mean and coefficient of variation of the first time quality rather than its complete distribution. Based on these results, we introduce the notion of quality robustness and show that the design of a production system should accommodate randomness in first time quality to achieve a robust quality buy rate. Finally, a case study on a repair and rework system redesign to improve paint quality is presented.

An approach to data parametrization in parametric cubic spline interpolation problems

Abstract A new approach to the problem of parametrizing data in parametric cubic spline interpolation problems is discussed. Parametrizations 0 = t 0 t 1 t N = 1 of K -dimensional data { z i } i = 0 N , z i = ( z i l ,…, z i k ) are chosen by minimizing ∑ l K ( 1 α l 2 ) ∝ 0 1 ( d 2 θ l dt 2 ) 2 dt , where φ l ( t ) is the natural cubic spline with breakpoints t 0 , t 1 , …, t N satisfying θ l ( t i = z i l , i = 0,…, N , and α l , l = 1,…, K , are positive numbers. This approach yields parametrizations which, by complementing the well-known smoothest interpolation property of natural cubic splines, leads to smoother component functions. The improvements are, in part, evidenced by reduced position overshoots and lower second derivatives. A closed form solution of the problem is derived for one-dimensional data. In higher dimensions the gradient projection method is used to obtain approximate numerical solutions. Geometric curve fitting problems and an example involving the design of a trajectory for a robot manipulator are used to illustrate the method.

Bottlenecks in Bernoulli Serial Lines With Rework

The bottleneck (BN) of a production system is a machine with the strongest effect on the systems throughput. In this paper, a method for BN identification in serial lines with rework and Bernoulli machines is developed. The method can be applied using either calculated or measured data on blockages and starvations of the machines. For the case of calculated data, a technique for evaluating performance measures of Bernoulli lines with rework is developed. Along with these quantitative contributions, the paper provides three qualitative results. First, it shows that Bernoulli lines with rework do not observe the property of reversibility. Second, it demonstrates that downstream machines may have a larger effect on the throughput than upstream ones. Third, it demonstrates that BNs may be shifting not only because of changes in machine and buffer parameters but also due to changes in quality of parts produced.

Digital Panel Assembly Methodologies and Applications for Compliant Sheet Components

This paper presents digital panel assembly (DPA) methodologies and applications for sheet component assembly in automotive body manufacturing processes. Core to DPA is the customized finite element analysis formulas we have developed, which simulates assembly processes and predicts assembly dimensions by taking into consideration the panel compliances. Two key analysis types of the DPA are presented, the deterministic analysis and variation analysis. We present a methodology to utilize the quadratic form of Taylor series expansion to approximate the assembly dimensions efficiently in variation simulation, and discuss its pros and cons versus the traditional Monte Carlo method under different modeling conditions. For either the deterministic or variation analysis, linear models (without contact, efficient but less accurate), and nonlinear models (with contact, less efficient but accurate) can be established. It is shown that the linear models are only valid when panels do not penetrate, and that the nonlinear models should generally be used for accurate assembly dimension prediction. Based on the DPA methodologies, a software tool called Elastic Assembly Variation Simulation (EAVS) is presented, followed by application case studies. The confidence intervals for variation analysis are also discussed.