Robert N. Braswell

Statistical tolerance analysis using FRPDF and numerical convolution

Computer-aided statistical tolerancing methods have helped to improve the quality of products while reducing their manufacturing costs. The Monte-Carlo simulation is the most popular statistical tolerancing technique currently in use. However, simulation has a severe drawback in terms of speed. Other tolerancing methods such as moment methods have limited capabilities in tackling many manufacturing problems. The objective of this paper is to demonstrate the feasibility of a new methodology for statistical tolerance analysis. The proposed method makes use of a new probability distribution function to model non-normal manufacturing data and a numerical method to perform statistical tolerance stack-up analysis. Comparative studies show that this new method has better accuracy than existing moment based techniques and is faster than simulation. It appears that it can be used in future computer-aided tolerancing systems.

Distribution-Free Approximations for Chance Constraints

This paper concerns developing methods for approximating a chance-constrained set when any information concerning the random variables must be derived from actual samples. Such a situation has not been presented in the literature. When existing chance-constrained programming techniques are used, it is not possible to relate the accuracy of sample-based assumptions to actual constraint satisfaction. The methods presented here employ the concept of a distribution-free tolerance region to construct various sets whose elements have the common property of satisfying the chance constraint with a preassigned level of confidence. The sample size required to meet the desired confidence is readily available in tabular or graphical form.

An evaluation of vector Fortran 200 generated by Cyber 205 and ETA-10 pre-compilation tools

Vectorizing precompilers such as KAP/205 and VAST-2 complement the efficient use of Fortran on the CDC Cyber 205. With the advent of the ETA-10 and its EOS/VSOS environment, the performance of these Fortran 200 preprocessors has come under closer scrutiny. The extent or quantity of vectorization that can be achieved has been examined elsewhere with reference to a test set of Fortran DO loops. The quality of the translated code is also considered. KAP/205 and VAST-2 are contrasted in this respect to reveal differences in the vectorized Fortran.<<ETX>>

Laplace Transforms for the Two-Unit Cold-Standby Redundant System

A conditional transform approach is applied to the two-unit standby redundant system with instantaneous switchover, and with failure and repair times that follow general well-behaved distributions for each unit. Transforms of distributions are obtained for T, the time to system failure, the number of repairs completed during T, the time spent on repair during T, and the idle time of the repairman during T. Applicable numerical methods are also discussed.

I. Development of basic models

Based on the concept that task progress is the growth of developments in a structured work and activity process, mathematical models ore developed to define, identify, and follow work progress and resourco utilization patterns. These models ore developed from the Pearl-Roed Logistic function and describe operating characteristics in the micro resource allocation and control problem. The model3 are the Task Operating Characteristic (TOC) curve and the Resource Operating Characteristic (ROC) curve. A second paper extends the theoretical results and gives examples (Braswell 1971).

A generalized procedure for the constrained optimization problem

Abstract The necessary and the sufficient conditions for the solution of the equality constrained optimization problem with N variables and (N−1) constraints are first derived and generalized to N variables and m constraints. Directional derivatives are used in the approach. The necessary and sufficient conditions for the problem with N−1 constraints are shown to be equivalent to the unconstrained one-variable problem, when the ordinary derivatives are replaced by the corresponding directional derivatives of the objective function in the direction tangent to the intersection of the constraints. The general equality constrained optimization problem of N variables and m constraints is then analysed using the directional derivative approach. Feasible direction vectors are defined and obtained in terms of first partial derivatives of the constraints. Necessary and sufficient conditions in terms of directional derivatives are derived and their equivalent with results in the literature. Sufficient conditions hi...

Non-Parametric Sensitivity Analysis in Linear Programming

Abstract A linear programming problem subject to uncertainty in the requirements vector is solved deterministically, then sensitivity analysis is performed to determine the effect of the random variation on this solution. Since there could be an appreciable cost of modifying a solution once implemented, the probability of the random components perturbing a solution is considered. Unlike existing methods of linear programming under uncertainty, this article assumes no knowledge of the distributions of the random variables. Rather, the notion of non-parametric tolerance limits is employed to establish a criterion for changing basic solutions.

A directional derivative computer algorithm for non-linear optimization†

This paper describes the computer solution to a non-linear optimization problem by the use of directional derivatives. Newtons method is used to find stationary points and when these points satisfy conditions of sufficiency, they are determined optima.

Necessary and sufficient conditions for the inequality constrained optimization problem using directional derivatives

The directional derivatives approach is used in the solution, of the classical optimization problem with inequality constraints. Necessary and second-order sufficient conditions are obtained. A procodure to generate all the stationary points is developed, and the further evaluation of those points up to sufficient conditions is presented. The general non-linear programming problem is discussed and an example illustrating the technique is presented.