## Proceedings of the International School of Physics "Enrico Fermi". |

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Page 60

Numerical

Even if the number of system components is small (five, six), dimensions of

transition rate matrices of concern require the use of numerical methods. Among

these ...

Numerical

**integration**of stiff equations; stiffness of Markov differential problem.Even if the number of system components is small (five, six), dimensions of

transition rate matrices of concern require the use of numerical methods. Among

these ...

Page 61

Suppose you must numerically

Xy, 3/(0) = 1/0, A >0. Denote by u„ the numerical approximation to y(nh), where h

is the

Suppose you must numerically

**integrate**the simple differential equation (3.1) y'=-Xy, 3/(0) = 1/0, A >0. Denote by u„ the numerical approximation to y(nh), where h

is the

**integration**step size. i) The simplest iteration formula for w„ is (3.2) un+1 ...Page 63

If Markov equations are to be numerically solved and CPU time is to be kept

within reasonable limits, no alternative exists to the highly stable implicit methods

which allow the

...

If Markov equations are to be numerically solved and CPU time is to be kept

within reasonable limits, no alternative exists to the highly stable implicit methods

which allow the

**integration**step size to be increased as local error constraints get...

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### Contents

System Eeliabujty | 3 |

Statistical Theory of Eeliablitt | 8 |

Definitions and characterizations | 12 |

Copyright | |

39 other sections not shown

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### Common terms and phrases

algorithm approach associated assume assumption Bayesian boundary points chain coherent system complex conjugate prior consider correctness defined denote detected discussed edited equations equivalence class ergodic errors example exponential distribution failure rate Fault Tree Analysis function gamma given human reliability IEEE Trans IFEA implementation increasing independent input domain integration interval likelihood Markov Markov chain matrix mean method modules monotone month2 N. D. Singpurwalla number of failures number of system NUMITEMS observed obtained operational output parameters phase Poisson Poisson process possible predictive prior distribution probability problem procedure Proschan R. E. Barlow random variables reliability growth models reliability theory renewal theory repair requirements sample sect sequence Software Eng software reliability software reliability models specification Stat statistical stochastic stochastic process subsection system failure system reliability techniques theorem tion tt tt values vector zero