By Enrico Zio

The need of craftsmanship for tackling the advanced and multidisciplinary questions of safety and danger has slowly permeated into all engineering purposes in order that threat research and administration has won a suitable position, either as a device in help of plant layout and as an crucial ability for emergency making plans in unintended events. This includes the purchase of applicable reliability modeling and chance research instruments to counterpoint the fundamental and particular engineering wisdom for the technological quarter of software. geared toward offering an natural view of the topic, this ebook presents an advent to the valuable innovations and matters regarding the protection of recent business actions. It additionally illustrates the classical strategies for reliability research and hazard overview utilized in present perform.

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Additional resources for An Introduction to the Basics of Reliability and Risk Analysis (Series on Quality, Reliability and Engineering Statistics) (Series on Quality, Reliability and Engineering Statistics)

Example text

7: Shaded area represents Event E = A u B (iii) F=A n B nC v 4 I I : ! 30 I I I I I I I I I I I I 20 I I : Fig. 4 Mutually Exclusive D and E are not mutually exclusive. (Because D nE f 0, in fact D n E = D, ). A and C are not mutually exclusive. ( B e c a u s e A n C g AnC=D). 3 27 Logic of uncertainty: definition of probability As previously explained, for a statement to be an event, it can only have two possible states, either true or false, and at a certain point in time the exact state will become known as a result of the actual perfonning of the associated experiment.

For example, we can describe any event associated with the outcomes of an experiment of rolling a dice by a real variable X in %. 72) corresponds to the union of the outcomes (1 2 3 4); the event {XS 0} is the null set since the outcomes of the roll of the dice are not associated to any negative value of X ; for x=oo the event (XI a}is the full sample space R . u u u 4 Basic of Probability Theory for Applications to Reliability and Risk Analysis 40 By establishing a univocal mapping between the outcomes of a random experiment and the values of a random variable, one can handle the uncehain events in terms of their mathematical abstractions, sparing the need of an actual word description for each particular physical phenomenon.

E. it defines probability resorting to a concept of frequency. 1, independently of the definition. All the theorems of probability follow from these three axioms. g. R = (0,l). Indeed, continuous intervals cannot be constructed by adding elementary points in a countable manner and correspondingly, probabilities of continuous intervals cannot be assigned by the addition law of probability. In other words, if we were to assign to each E E (0,l) a probability p ( E ), then the sum of all p ( E ) ’s would go to infinity, unless p ( E ) = 0 for ‘almost all’ E E (0,l).

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