## Proceedings of the International School of Physics "Enrico Fermi", Volume 94 |

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Page 60

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

transition rate matrices of concern require the use of numerical

these the eigenvalue - eigenvector schema is the major candidate to exploit the ...

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

transition rate matrices of concern require the use of numerical

**methods**. Amongthese the eigenvalue - eigenvector schema is the major candidate to exploit the ...

Page 62

9 ) Un = * ( 1 — aha , \ " ( 1 + aha , ) % It can be easily seen that the

stable provided that ( 3 . 10 ) Olyadi . Furthermore , the local error ( 3 . 11 ) T = 1

andi – exp ( – 2n ] = ( 1 2hX ) ( 1 – ahaz + 22h2 « ) – 1 + 2ha , – ( 1 – 2n + 2 * 1 ...

9 ) Un = * ( 1 — aha , \ " ( 1 + aha , ) % It can be easily seen that the

**method**is a -stable provided that ( 3 . 10 ) Olyadi . Furthermore , the local error ( 3 . 11 ) T = 1

andi – exp ( – 2n ] = ( 1 2hX ) ( 1 – ahaz + 22h2 « ) – 1 + 2ha , – ( 1 – 2n + 2 * 1 ...

Page 65

i ) Keeping under control stiffness by means of an implicit

Triangulating the linear algebraic system the implicit

and ii ) are common to all noteworthy

equations ...

i ) Keeping under control stiffness by means of an implicit

**method**. ii )Triangulating the linear algebraic system the implicit

**method**leads to . Actions i )and ii ) are common to all noteworthy

**methods**for numerically handling Markovequations ...

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### Contents

STATISTICAL THEORY OF RELIABLITY | 8 |

Definitions and characterizations | 12 |

J KEILSON Stochastic models in reliability theory | 23 |

Copyright | |

37 other sections not shown

### Common terms and phrases

analysis application approach associated assume assumption BARLOW Bayesian calculation called complex components consider constant continuous correctness Course defined density depends derived described detected determine discussed distribution edited epochs equations equivalence ergodic errors estimate example exists expected exponential fact fail failure rate fault function given Hence important increasing independent input integration interest interval known likelihood limit Markov matrix mean measure method modules normal Note observed obtain occur operational parameters performance phase positive possible posterior predictive prior probability problem procedure prove random variables renewal repair requirements rule sample selected sequence simple software reliability space specification statistical stochastic structure Suppose task theorem theory tion transition tree University values York