Gordon M. Clark

System Reliability in the Presence of Common-Cause Failures

This paper presents a method for calculating the reliability of a system depicted by a reliability block diagram, with identically distributed components, in the presence of common-cause failures. To represent common-cause failures, we use the Marshall & Olkin formulation of the multivariate exponential distribution. That is, the components are subject to failure by Poisson failure processes that govern simultaneous failure of a speciflc subset of the components. The method for calculating system relability requires that a procedure exist for determining system reliability from component reliabilities under the statistically-independent-component assumption. The paper includes several examples to illustrate the method and compares the reliability of a system with common-cause failures to a system with statistically-independent components. The examples clearly show that common-cause failure processes as modeled in this paper materially affect system reliability. However, inclusion of common-cause failure processes in the system analysis introduces the problem of estimating the rates of simultaneous failure for multiple components in addition to their individual failure rates.

Use of Polya distributions in approximate solutions to nonstationary M/M/s queues

which implement his algorithm in detail. Our approach departs from Nutts in its basis in discrete-event simulation. As in sequential simulation there are cases where discrete-event approaches are preferable to time driven simulations and there are cases where the reverse is true. The running time of the distributed algorithm depends upon the model being simulated. It is known empirically [15] that the distributed scheme approaches ideal performance when there are no multiple loops in the network. Extensive experimentation with various models is necessary in order to predict the performance of the proposed algorithm.

Estimating Parameters of the Power Law Process With Two Measures of Failure Time

We introduce a method of combining two time indices, such as mileage and age, into a single index that resembles the Cobb-Douglas production function. Then we present the power law process with this synthesized time index as a model for the reliability ..

A Bonferroni selection procedure when using commom random numbers with unknown variances

This paper presents a Bonferroni procedure for selecting the alternative with the largest mean when the variances are unknown and unequal and correlation is induced among the observations for each alternative by common random numbers. Simulation results show that the Bonferroni procedure is more efficient than Dudewicz and Dalals procedure when the percentage of variance reduction is high.

Statistical Engineering — Forming the Foundations

Editors: Christine M. Anderson-Cook, Lu Lu, Panelists: Gordon Clark, Stephanie P. DeHart, Roger Hoerl, Bradley Jones, R. Jock MacKay, Douglas Montgomery, Peter A. Parker, James Simpson, Ronald Snee, Stefan H. Steiner, Jennifer Van Mullekom, G. Geoff Vining, Alyson G. Wilson Los Alamos National Laboratory, Los Alamos, New Mexico Ohio State University, Columbus, Ohio DuPont, Roanoke, Virginia GE Global Research, Schenectady, New York SAS, Cary, North Carolina University of Waterloo, Waterloo, Ontario, Canada Arizona State University, Tempe, Arizona NASA, Langley, Virginia Eglin Air Force Base, Valparaiso, Florida Snee Associates, Newark, Delaware DuPont, Richmond, Virginia Virginia Tech, Blacksburg, Virginia Institute for Defense Analyses, Washington, DC INTRODUCTION

Introduction to manufacturing applications

This tutorial introduces manufacturing applications of simulation through three illustrative example applications. These examples illustrate the additional understanding of system behavior gained by the use of simulation models. Individuals using simulation should use a structured process in applying simulation. The second example illustrates this structured process. The examples also illustrate the use of both stochastic and deterministic variables in modeling manufacturing systems.

Statistical Engineering—Roles for Statisticians and the Path Forward

Experts from diverse areas of industry, government, and academia are asked about the changing roles for statisticians in the SE workplace and discuss some of the opportunities and challenges for the future.

Order release planning in a job shop using a bi-directional simulation algorithm

Order release is an important job shop scheduling function that plans and controls the release of jobs to the shop floor. Deterministic simulation has been proposed to determine order release times with either a forward or a reversed approach. We develop a bi-directional algorithm that always starts and ends with a forward simulation run, and the algorithm includes a number of additional reversed and forward runs in between the first and last runs. A reversed simulation run determines potential job release times, and these potential times become actual release times when they are all non-negative. When one or more potential release times are negative, the algorithm modifies them to specify job release times for the succeeding forward simulation run. The last forward simulation run determines the job completion times. Experimental results show that the bi-directional simulation algorithm produces a significantly improved mean flow time, and the algorithm can improve mean tardiness in some cases.

Estimating operation times from machine center arrival and departure events

We develop a methodology for using bar code scanner timing information from an automated shop floor data collection system to estimate operation times within a flexible manufacturing system environment. The purpose of the methodology is to estimate mean operation times for multiple product types when the scanning only occurs when products arrive to and depart from a machine center. This methodology partially reconstructs the shop floor operations from captured bar code scanner timing information and then through the use of regression techniques estimates the mean operation times for each of the product types. This paper develops and evaluates the methodology within an operational context. The accuracy and precision of the estimators is evaluated via discrete event simulation under various experimental conditions to identify key factors which effect the performance of the estimators. We identified guidelines for achieving estimator accuracy and we applied the estimator to an actual industrial situation.

A Computational Algorithm for Reliability Bounds in Probabilistic Design

Kapur formulated quadratic programming problems for determining bounds on the design reliability, given some bounds on the probabilities of the stress and strength random variables. We modify Kapurs formulation to improve its accuracy, and present a solution to the resulting quadratic programming problems that can be evaluated manually.