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

Statistics for Spatial Data.

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Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

In this paper, we describe how Delphi Corporation used simulation in the concept-development phase of a new multimillion-dollar fuel injector production line. Delphi wanted to assess the financial viability of production targets and identify the critical features of the line on which it would focus its design-improvement efforts.

Using Simulation Early in the Design of a Fuel Injector Production Line

The cycle-time distribution of manufacturing systems employing dispatching rules other than FIFO can be both highly skewed and have heavy tails. Previous cycle-time quantile estimation work has suggested that the Cornish-Fisher expansion can be used in conjunction with discrete-event simulation to provide cycle-time quantile estimates for a variety of systems operating under FIFO dispatching without requiring excess data storage. However, when the cycle-time distribution exhibits heavy skewness and kurtosis, the accuracy of quantile estimates obtained using the Cornish-Fisher expansion may degrade, sometimes severely. This paper demonstrates the degradation and motivates the need for a modification to the Cornish-Fisher expansion for estimating quantiles under non-FIFO dispatching rules. A solution approach combining a data transformation, the maximum (minimum)-transformation, with the Cornish-Fisher expansion is presented. Results show that this provides significant improvements in accuracy over using the Cornish-Fisher expansion alone while still retaining the advantage of requiring minimal data storage.

Cycle-time quantile estimation in manufacturing systems employing dispatching rules

A stochastic computer simulation model is a description of a system of interrelated random variables. Realizations of the system can be used to estimate parameters of interest. Variance reduction techniques (VRTs) transform simulation models into similar models that permit more precise estimation of the parameters. The basic types of transformations are defined and a simple example is given.

Variance reduction: Basic transformations

Cycle time-throughput (CT-TH) percentile curves quantify the relationship between percentiles of cycle time and factory throughput, and they can play an important role in strategic planning for manufacturing systems. In this paper, a highly flexible distribution, the generalized gamma, is used to represent the underlying distribution of cycle time. To obtain CT-TH percentile curves, we fit metamodels for the first three CT-TH moment curves throughout the throughput range of interest, determine the parameters of the generalized gamma by matching moments, and obtain percentiles by inverting the distribution. To insure efficiency and control estimation error, simulation experiments are built up sequentially using a multistage procedure. Numerical results are presented to demonstrate the effectiveness of the approach.

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Estimation of percentiles of cycle time in manufacturing simulation

LEXIS-NEXIS frequently develops simulation models to estimate the computer system capacity required to deliver on-line information services. The load imposed by Unix Input/Output (I/O) processes is a key factor in many of these models. However, the I/O processes themselves are seldom of interest, and explicitly modeling them results in simulations executing much slower than real time. This paper presents a hybrid simulation-queueing module that can be inserted into any simulation to accurately model I/O resource consumption and queueing delays without explicitly modeling each individual I/O process. This module is in use at LEXIS-NEXIS to day (LEXIS and NEXIS are registered trademarks of Reed-Elsevier Properties, Inc., and are used under license).

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Barry L. Nelson

Papers

Using Simulation Early in the Design of a Fuel Injector Production Line

Cycle-time quantile estimation in manufacturing systems employing dispatching rules

Variance reduction: Basic transformations

Estimation of percentiles of cycle time in manufacturing simulation

A hybrid simulation-queueing module for modeling UNIX I/O in performance analysis