Abstract
In reliability theory, an important role is played by Bernoulli trials. In reliability theory, the negative binomial distribution has to be considered. Along with Bernoulli's formulas, another scheme plays an important role in reliability theory; it is known as “sampling without replacement”. Poisson distributions play a special role in reliability theory because under broad conditions, they describe the phenomena of catastrophic failures in complex systems. The most complete characterization of a random variable is given by its distribution function, which shows the values that the given random variable assumes and with what probabilities. In probability theory and its applications, including reliability theory, a considerable role is played by certain constants that are obtained from distribution functions in accordance with definite rules. In reliability theory, positive random variables are considered. For such variables, it is convenient to use the Laplace transform and not the Fourier transform, which is studied in probability theory courses.
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