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

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 use a factory simulation to 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 any percentile of interest 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.

http://users.iems.northwestern.edu/~nelsonb/Publications/YangAnkenmanNelson2.pdf

Estimating Cycle Time Percentile Curves for Manufacturing Systems via Simulation

The Winter Simulation Conference serves as the initial publication venue for many advances in ranking and selection (R&S), including the recently developed R&S procedures that exploit high-performance parallel computing. We formulate a new stylized model for representing parallel R&S procedures, and we provide an overview of existing R&S procedures under the stylized model. We also discuss why designing R&S procedures for a parallel computing platform is nontrivial and speculate on the future of parallel R&S procedures. In this chapter, “parallel computing” means multiple processors that can execute distinct simulations independently, rather than vector or array processors designed to speed up vector-matrix calculations.

Parallel Ranking and Selection

We propose an optimization-via-simulation algorithm for use when the performance measure is estimated via a stochastic, discrete-event simulation, and the decision variables may be subject to deterministic linear integer constraints. Our approach-which consists of a global guidance system, a selection-of-the-best procedure, and local improvement-is globally convergent under very mild conditions.

Optimization via simulation: a combined procedure for optimization via simulation

We develop a numerically exact method for evaluating the time-dependent mean, variance, and higher-order moments of the number of entities in aPh t / Ph t /8 queueing system. We also develop a numerically exact method for evaluating the distribution function and moments of the virtual sojourn time for any timet; in our setting, the virtual sojourn time is equivalent to the service time for virtual entities arriving to the system at that timet. We include several examples using software that we have developed and have put in downloadable form in the Online Supplement to this paper on the journal's website.

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

The Pht/Pht/8 Queueing System: Part I--The Single Node

"Input uncertainty" refers the effect of driving a simulation with input distributions that are based on real-world data. At WSC 2012, Ankenman and Nelson presented a quick-and-easy experiment to assess the overall effect of input uncertainty on simulation output. When their method reveals that input uncertainty is substantial, then the natural follow-up questions are which input distributions contribute the most to input uncertainty, and from which input processes would it be most beneficial to collect more data? To answer these questions Ankenman and Nelson proposed a sequence of additional experiments that are in no sense "quick." In this paper we provide a follow-up analysis that requires no additional simulation experiments beyond the overall assessment, and yet provides more information than Ankenman and Nelson. Numerical illustrations are provided.

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Barry L. Nelson

Papers

Estimating Cycle Time Percentile Curves for Manufacturing Systems via Simulation

Parallel Ranking and Selection

Optimization via simulation: a combined procedure for optimization via simulation

The Pht/Pht/8 Queueing System: Part I--The Single Node

A quicker assessment of input uncertainty