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A number of recent publications have dealt with problems of analyzing the performance of multi-component systems and evaluating their reliability. For example, a comprehensive theory of two-terminal networks was presented in [I] by Moore and Shannon who, among other results, have developed methods for obtaining highly reliable systems using components of low reliability; some of their procedures are credited to earlier work by von Neumann [2]. Several of the concepts and results of the present paper are generalizations of the corresponding concepts and results of the Moore-Shannon paper. A discussion of complex systems interpreted as Boolean functions may be found in the paper [3] by Mine. The present study deals with general classes of systems which contain two-terminal networks and most other kinds of systems considered previously as special cases, and investigates their combinatorial properties and their reliability. These classes consist, with several variants, of systems such that the more components...

SummaryA new two parameter family of life length distributions is presented which is derived from a model for fatigue. This derivation follows from considerations of renewal theory for the number of cycles needed to force a fatigue crack extension to exceed a critical value. Some closure properties of this family are given and some comparisons made with other families such as the lognormal which have been previously used in fatigue studies.

Miner’s rule for the cumulative damage due to fatigue, a deterministic formula which is well known in engineering practice, was examined earlier from a probabilistic point of view with Birnbaum in [2]. Here the assumptions of that model are weakened. Previously the basic assumptions were that crack growth was stochastic in nature with incremental extensions having a distribution with increasing failure rate, and that the spectrum of load fluctuations was fixed and then repeated under program. We now assume, instead of the distributions of incremental crack extension having increasing failure rate, only that for a given load fluctuation, the expected residual damage increment either in crack initiation or extension, given the damage exceeds a preassigned amount, is less than the damage increment which was expected for that load fluctuation before it was imposed. We also weaken the assumptions concerning the type of loading spectra which are admitted, considering the case of random load fluctuations which a...

Samples are often obtained under circumstances which make it less likely to draw individuals from some parts of a population than from others. In this paper a method is presented which makes it possible, under certain assumptions, to correct for the resulting bias and thus reconstruct the means, standard deviations, and correlation coefficients of the original population.

A class of statistics, large enough to comprise those used in all the known distribution-free tests of fit for continuous distribution functions, is characterized by a structure called "structure ($d$)." A number of statistics of this class may be constructed and used for tests of fit. To make a reasonable choice among all these statistics, it appears desirable to introduce in the space of continuous distribution functions a distance which would reflect the type of discrepancy the proposed test is intended to detect. By studying the power of various statistics with regard to this distance one may then be able to choose those with optimal properties.