Mathematical methods of statistical quality control

BOOKREVIEW* K. SARKHADI and I. VINCZE. Mathematical methods of statistical qualio control. 415~. Akademiai Kiado, Budapest, 1974. Statistical control of the quality of production is one of the most important fields of application of the theory of probability and mathematical statistics. There are a number of books (including some in Russian), devoted to this field of applied mathematics, but many of them are at too low a mathematical level, and hence they do not satisfy the demands of modem complex production. In the book reviewed, written by two prominent Hungarian specialists, the methods of mathematical quality control are based on the serious foundation of the theory of probability and mathematical statistics. Therefore a large part of the book is devoted to the principles of these disciplines, without forgetting the main purpose of the book. Of course it will not serve as a textbook on the theory of probability and mathematical statistics, since it expounds the principles of these sciences in outline, without detailed proofs of the theorems, without a large number of training examples and problems, which are characteristic of every textbook. Accordingly the book is intended for a wide range of applied mathematicians, engineers, students of higher educational establishments and others interested in the applications of the theory of probability and mathematical statistics. For all these categories of readers it will constitute an excellent reference book. The book consists of three parts and an appendix. The first part is introductory. Here the fundamental concepts and definitions used in the following parts are explained. The second part occupies more than half the book. Here the fundamental theorems of probability are explained. In particular the fundamental types of probability distribution, the principles of the sampling method, theories of order statistics etc. are explained in great detail. Also explained are the fundamental methods of mathematical statistics: the theory of estimation, the statistical testing of hypotheses, the principles of correlation and regression analysis, the theory of statistical decisions, the principles of stochastic processes etc. The third part is devoted to methods of statistical quality control. Here, after presenting the fundamental ideas, detailed explanations are given of the methods of continuous control and acceptance control, based on the main types of control charts and on various standards. The last paragraph of this part is devoted to the principles of reliability theory. The book is supplemented by 14 basic statistical tables. Among them there are tables of random numbers, the normal probability density and function, the Poisson distribution, the binomial distribution, the percentage points of the F-distribution, Student’s distribution, the x2-distribution. the Kolmogorov-Smimov distribution etc. There is an extensive bibliography, separated into books, papers, tables and standards, and also the necessary indexes. The printing of the book is excellent. The translation of this fundamental work into Russian is extremely desirable. M. K. Kerimov Translated by J. Berry. *Zk vj%hisL Mot mat. Fir., 17, 1, 281, 1977.

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