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Statistics --- Probabilities --- Probabilities. --- Statistics.

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The undetected propagation of a fatigue crack constitutes a significant cause of aircraft and other structural failures. To raise the structural failure load to a relatively high level, the manufacturer can divide the structure into many small elements, which significantly increases the ability of a structure to tolerate an element failure. This report presents a procedure for calculating the probability that the element has not failed, as a function of the crack propagation time and hence the crack's length. The procedure's form is so simple that computations with a desk calculator can yield reasonably accurate results. To illustrate this, the report uses data that an aircraft manufacturer developed for the structural components/elements that currently limit the service life of an existing transport aircraft.

Metals --- Probabilities. --- Fatigue. --- Fracture.

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The present reprint contains all of the articles accepted and published in the Special Issue "Probability and Stochastic Processes with Applications to Communications, Systems and Networks" from the MDPI Mathematics journal. This Special Issue is devoted to probability, statistics, stochastic processes and their different applications in system and network analysis. The Special Issue includes works related to the analysis and applications of different queuing models, which begin with general approaches in modeling queuing systems and networks; an analysis of probabilistic and statistical methods in telecommunication; an asymptotic analysis of queuing networks in the condition of a large load; general complex networks and their structures, e.g., topology and graph theory; mathematical methods and models in smart cities; exclusive statistical methods, such as statistical estimates in bio/ecology, medicine and neural networks; and studies that estimate parameters in complex technical systems, etc. We hope that the scientific results collected in this reprint will help foster future research related to probability, stochastic processes and their applications.

Stochastic processes --- Probabilities. --- Mathematical models.

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Publishes papers in all areas of probability.

Probabilities --- Probabilités --- Periodicals. --- Périodiques --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- probability theory --- mathematics --- probability --- Probabilitats.

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Stochastic processes --- Processus stochastiques --- Périodiques. --- Random processes --- Stochastic processes. --- Probabilities