Models of Failure (Ingenieurwissenschaftliche Bibliothek Engineering Science Library)

The increase in the requirements on the reliability of units makes it necessary to analyze the relationship between mathematicalmeth ods of calculating reliability and the physical nature of fail ures. The difficulty of such an analysis is obvious. On the one hand, in making a representation of the physical picture of a phe nomenon, one can make an error in the direction of excessive sim plification. On the other hand, in the mathematical treatment of the physical scheme, it may be necessary to use extremely complex and fine analytical methods, and their simplified exposition bor ders on vulgarization. Without the aid of a large number of specialists working in the field of analysis and calculation of systems reliability, an ex posi tion of models of failures and their mathematical treatment would be unobtainable. The authors take this opportunity to express their gratitude to Academicians N. G. B r u y vic e h and Y u. V. Lin n i k conversations with whom clarified a number of problems treated, to active member of the Academy of Sciences of the UkrSSR B. V. I. Classifications of Causes of Failures.- II. Instantaneous Damage.- The exponential distribution.- The threshold of sensitivity.- Superposition of exponential distributions.- III. Cumulative Damages.- Models of wear.- The gamma distribution of the lifetime.- Normal distribution of lifetime.- The gamma distribution with bias parameter.- The functional gamma distribution.- The logarithmic normal distribution.- Linear sample functions of wear.- Analysis of sample functions of wear.- IV. Processes of Damage with Relaxation.- V. Superposition of Causes of Failures. Chain Systems.- The simultaneous action of several causes of failure.- The Weibull-Gnedenko distribution.- The Weibull-Gnedenko functional distribution.- VI. The Failure Rate.- The failure rate and the residual lifetime.- Monotonically increasing failure rate.- Nonmonotonic failure rate.- Conclusion.