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

This paper discusses simulation design and analysis for Silicon Carbide (SiC) manufacturing operations management at New York Power Electronics Manufacturing Consortium (PEMC) facility. Prior work has addressed the development of manufacturing system simulation as the decision support to solve the strategic equipment portfolio selection problem for the SiC fab design [1]. As we move into the phase of collecting data from the equipment purchased for the PEMC facility, we discuss how to redesign our manufacturing simulations and analyze their outputs to overcome the challenges that naturally arise in the presence of limited fab data. We conclude with insights on how an approach aimed to reflect learning from data can enable our discrete-event stochastic simulation to accurately estimate the performance measures for SiC manufacturing at the PEMC facility.

Semiconductor manufacturing simulation design and analysis with limited data

Input modeling is the selection of a probability distribution to capture the uncertainty in the input environment of a stochastic system. Example applications of input modeling include the representation of the randomness in the time to failure for a machining process, the time between arrivals of calls to a call center, and the demand received for a product of an inventory system. Building simulations of stochastic systems requires the development of input models that adequately represent the uncertainty in such random variables. Since there are an abundance of probability distributions that can be used for this purpose, a natural question to ask is how to identify the probability distribution that best represents the particular situation under study. For example, is the exponential distribution a reasonable choice to represent the time to failure for a machining process, or is it better to use an empirical distribution function obtained from the historical time-to-failure data? Recognizing the fact that there is no true input model waiting to be found, the goal of stochastic input modeling is to obtain an approximation that captures the key characteristics of the system inputs. The development of a good input model requires the collection of as much information as possible about the relevant randomness in the system as well as the historical data consisting of the past realizations of the random variables of interest. In the presence of a data set, the input model can be identified by fitting a probability distribution to the historical data. However, it may be difficult and/or costly to collect data for the stochastic system under study; it can also be impossible to properly collect any data at all such as when the proposed system does not exist. In the absence of historical data, any relevant information (e.g., expert opinion and the conventional bounds suggested by the underlying physical situation) can be used for input modeling. This article addresses the key issues that arise in stochastic input modeling both in the presence and in the absence of historical data. The first step in input modeling is to identify the sources of randomness in the input environment of the system under study. Many stochastic systems contain multiple sources of uncertainty, e.g., the completion time of an item on a particular machine, the potential breakdown of the machine, and the percentage of defective items produced by the machine might be among the sources of uncertainty in a manufacturing setting. Throughout, the random vector X = (X1, X2, …, X K )′ is used to represent the collection of K different inputs of a stochastic system, where X k is the random variable denoting the kth system input. The K components of this random vector might also be correlated with each other. Therefore, the stochastic properties of the random inputs X k , k = 1, 2, …, K, are captured in the joint probability

Stochastic input model selection

As companies are trying to build more resilient supply chains using digital twins created by smart manufacturing technologies, it is imperative that senior executives and technology providers understand the crucial role of process simulation and AI in quantifying the uncertainties of these complex systems. The resulting digital twins enable users to replay history, gain predictive visibility into the future, and identify corrective actions to optimize future performance. In this article, we define process digital twins and their four foundational elements. We discuss how key digital twin functions and enabling AI and simulation technologies integrate to describe, predict, and optimize supply chains for Industry 4.0 implementations.

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Implementing Digital Twins That Learn: AI and Simulation Are at the Core

Inventory management models help determine policies for managing trade-offs between customer satisfaction and service cost. Initiatives like lean manufacturing, pooling, and postponement have been proven to be effective in mitigating the trade-offs by maintaining high levels of service while reducing system inventories. However, such initiatives reduce the buffers, exacerbating supply chain issues in the event of a disruption. We evaluate stocking decisions in the presence of operational disruptions caused by random events such as natural disasters or man-made disturbances. These disruptions represent different risks from those associated with demand uncertainties as they stop production flow and typically persist longer. Thus, operational disruptions can be much more devastating though their likelihood of occurrence may be low. Using stochastic simulation, we combine the newsvendor model capturing demand uncertainty costs with catastrophe models capturing disruption/recovery costs. We apply data analytics to the simulation outputs to obtain insights to manage inventory under disruption risk.

Inventory management under disruption risk

We study a multi-item inventory system with normally distributed demands in the presence of demand parameter uncertainty - the uncertainty that stems from the estimation of the unknown demand parameters necessitated by limited amounts of historical demand data. Using an asymptotic normality approximation, we quantify the variance of the demand fulfillment probability (i.e., the probability that all item demands will be satisfied from stock) that is due to demand parameter uncertainty. We use this quantification to understand the impact of demand parameter uncertainty on the demand fulfillment probability and investigate the sensitivity of the variance of the demand fulfillment probability to selected inventory model parameters.

Bahar Biller

Papers

Semiconductor manufacturing simulation design and analysis with limited data

Stochastic input model selection

Implementing Digital Twins That Learn: AI and Simulation Are at the Core

Inventory management under disruption risk

Demand fulfillment probability under parameter uncertainty