THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

The Analysis of Time Series: An Introduction, 4th edn. By C. Chatfield. ISBN 0 412 31820 2. Chapman and Hall, London, 1989. 242 pp. £13.50.

The Analysis of Time Series: An Introduction

Simulation modelling involves the development of models that imitate realworld operations, and statistical analysis of their performance with a view to improving efficiency and effectiveness This nontechnical textbook is focused towards the needs of business, engineering and computer science students

Simulation: The Practice of Model Development and Use

WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

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Reversibility and Stochastic Networks

Representing uncertainty in a simulation study is referred to as input modeling, and is often characterized as selecting probability distributions to represent the input processes. This is a simple task when the input processes can be represented as sequences of independent random variables with identical distributions. However, dependent and multivariate input processes occur naturally in many service, communications, and manufacturing systems. This chapter focuses on the development of multivariate input models which incorporate the interactions and interdependencies among the inputs for the stochastic simulation of such systems.

Chapter 5 Multivariate Input Processes

We study a subset selection procedure -- one of the well-known statistical methods of ranking and selection for stochastic simulations -- in the presence of input parameter uncertainty; i.e., the parameters of the input distributions are unknown and there is only a limited amount of input data available for input parameter estimation. The goal is to present a new decision rule which identifies subsets of stochastic system designs including the best (i.e., the design with the largest or smallest expected performance measure) with a probability that exceeds some user-specified value. At WSC 2013, we studied this problem by restricting focus to the method of asymptotic normality approximation to represent input parameter uncertainty. Motivated by the limitations of the asymptotic normality approximation for simulations of complex systems with large numbers of input parameters, we revisit this problem with the simulation replication algorithm as an alternative method to capture input parameter uncertainty.

Subset selection for simulations accounting for input uncertainty

Motivated by innovative rental business models, we study a rental system with random loss of inventory due to use. We utilize a discrete-time model in which the inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Demand, rental durations, and rental unit lifetimes are stochastic; sample path coupling allows us to derive structural results that hold under limited distributional assumptions. Considering different “recirculation” rules (i.e., which unit to select to meet a demand), we prove the concavity of the expected profit function and identify the optimal recirculation rule under two different models of a rental unit’s state: the number of times rented out or its condition. We develop two upper bounds on the number of lost rental units and two heuristics for the inventory decision. Numerical study shows the following: (1) accounting for rental unit loss can increase the expected profit by 7% for a single season; (2) the optimal inventory l...

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Managing Rentals with Usage-Based Loss

Time-series input processes occur naturally in the stochastic simulation of many service, communications, and manufacturing systems, and there are a variety of time-series input models available to match a given collection of properties, typically a marginal distribution and an autocorrelation structure specified via the use of one or more time lags. The focus of this paper is the situation in which the collection of properties are not “given,” but data are available from which a time-series input model is to be estimated. The input model we consider is the very flexible autoregressive-to-anything (ARTA) model of Cario and Nelson [Cario, M. C., B. L. Nelson. 1996. Autoregressive to anything: Time-series input processes for simulation. Oper. Res. Lett.19 51--58]. Recently, we developed a statistically valid algorithm (ARTAFIT) for fitting this model to stationary univariate time-series data using marginal distributions from the Johnson translation system. In this paper, we perform a comprehensive numerical study to assess the performance of our algorithm relative to the two most commonly used approaches: (a) fitting the marginal distribution but ignoring the autocorrelation structure, and (b) fitting separately the marginal distribution as in (a) and the autocorrelation structure using the sample autocorrelation function. We find that ARTAFIT, which fits the marginal distribution and the autocorrelation structure jointly, outperforms both (a) and (b), and we demonstrate the importance of taking dependencies into account while developing input models for stochastic simulation.

http://users.iems.northwestern.edu/~nelsonb/Publications/BillerNelsonEvaluate.pdf

Evaluation of the ARTAFIT Method for Fitting Time-Series Input Processes for Simulation

An important step in designing stochastic simulation is modeling the uncertainty in the input environment of the system being studied. Obtaining a reasonable representation of this uncertainty can be challenging in the presence of dependencies in the input process. This tutorial attempts to provide a coherent narrative of the central principles that underlie methods that aim to model and sample a wide variety of dependent input processes.

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Bahar Biller

Papers

Chapter 5 Multivariate Input Processes

Subset selection for simulations accounting for input uncertainty

Managing Rentals with Usage-Based Loss

Evaluation of the ARTAFIT Method for Fitting Time-Series Input Processes for Simulation

Dependence modeling for stochastic simulation