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Quality control and reliability. (English) Zbl 0673.62089

Handbook of Statistics, 7. Amsterdam etc.: North-Holland. xiv, 473 p. $ 120.00; Dfl. 290.00 (1988).
[The articles of this volume will not be indexed individually.]
This volume being No.7 in the series “Handbook of Statistics” contains 24 articles, 18 of them concerning reliability theory and applications while the remaining 6 articles deal with statistical quality control. All articles are written by outstanding researchers or practitioners. They give an excellent survey of recent developments in the two fields mentioned above though the first paper by W. E. Deming seems to be misplaced in a handbook of statistics: He gives a 14-point recommendation for the US-management in order to withstand the challenge from abroad in industrial production.
F. B. Bastani and C. V. Ramamoorthy give some models used in software reliability such as reliability growth models, error and non- error counting models and sampling models. R. A. Johnson discusses some stress-strength models in reliability, leading to the estimation of the probability that one random variable (strength) exceeds another one (stress). He reviews some non-parametric as well as parametric and Bayesian procedures for solving this problem. M. Mazumdar discusses some reliability indexes and some methods to compute them approximately; he also gives some numerical results.
T. A. Mazzuchi and N. D. Singpurwalla describe some models for the software failure process and appropriate estimation methods. N. R. Chaganti and K. Joag-Dev provide some concepts of stochastic dependence with respect to the classification of life distributions including special Markov processes while B. W. Woodruff and A. H. Moore give a short review on goodness-of-fit tests useful in reliability. H. W. Block and T. H. Savits discuss in their article several multivariate nonparametric distributions such as MIFRA (multivariate increasing failure rate average), multivariate NBUE (new better than used in expectation) a.s.o.
Mainly subset selection procedures for various families of distributions used in reliability theory are outlined by S. S. Gupta and S. Panchapakesan, followed by some considerations about the impact of reliability methods on mathematics and statistics by P. J. Boland and F. Proschan. They discuss total positivity as well as associated random variables, renewal theory and the majorization concept.
M. C. Bhattacharjee investigates reliability analogies and arguments useful in economics and social sciences, e.g. Arrow’s impossibility theorem, more general voting games and the comparability of wealth distributions. F. Guess and F. Proschan give a short review on theory and applications of the concept of the mean residual life function. R. E. Barlow and once more F. Proschan discuss estimation methods and credible interval selection for incomplete data, especially for the exponential and the Weibull distribution. Also estimation methods play the main part in the article of G. M. Mimmack and F. Proschan. The authors compare a so-called piecewise geometric estimator with other estimators developed for the estimation of the probability distribution of the lifelength of items by truncated data. L. F. Pau discusses some concepts of technical diagonostics with emphasis on correspondence analysis. W. J. Padgett outlines different types of nonparametric density estimates for incomplete (censored) data.
F. B. Alt and N. D. Smith deal with multivariate control problems concerning the monitoring of two or more correlated quality characteristics simultaneously, especially they discuss control charts (Shwehart charts) both for the mean and the dispersion. B. Hoadley describes two methods in quality control: The Universal Sampling Plan (USP) and the Quality Measurement Plan (QMP).
P. R. Krishnaiah together with B. Q. Miao give a review on methods for estimating the number and positions of change points (e.g. jumps in the mean) of given data. The same problem is studied in the article of M. Czörgö and L. Horwáth, who deal with non- sequential nonparametric procedures for detecting at most one change point. They also give asymptotic results.
In their article, E. El-Neweihi, F. Proschan and J. Sethuraman investigate the reliability of systems with components with more than two levels (e.g. “functioning” and “failed”) of performance. Order statistics is the main object of H. L. Harter, who gives a review on methods (and tables) for order statistics of the Weibull, Log-Weibull and gamma-distribution together with some methods for estimating parameters and intervals by using order statistics.
A. P. Basu discusses several extensions of the one-dimensional exponential distribution to the multivariate case, especially the bivariate one. Finally S. Iyengar and G. Patwardhan give a review on recent results and developments concerning the inverse Gaussian distribution as a supplement to the reviews of Folks and Chhikara.
Summing up the impressions while reading this book it is clear that it is not a “handbook” in the usual sense: It covers much more recent developments and results in reliability and quality control than that it gives a review on these topics.
Reviewer: B.Rauhut

MSC:

62N05 Reliability and life testing
62P30 Applications of statistics in engineering and industry; control charts
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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