### Abstract

Because of their relatively simple properties, Poisson pulse models are convenient for load modelling. This paper considers the first passage analysis of a train of intermittent load applications each composed of overlapping component rectangular ('square wave') filtered Poisson pulses. The pulses have exponentially distributed inter-arrival times, exponential durations and Gausssian pulse heights. By carefully considering the start and stop of individual pulses over a given time period and applying the Wald's identity to the relevant random walks the Laplace transformation of first passage time is derived and by this, an extended version of the standard (negative exponential) form of probability of exceedence incorporating the average duration of pulses is obtained.

It is shown that in the limit as pulse duration becomes negligible, the standard first passage solution for Poisson spike processes is recovered. A comparison with Monte Carlo simulation runs for both the generalized result and the spike result is made for different threshold levels.

Original language | English |
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Title of host publication | Applications of statistics and probability, vols 1 and 2 |

Editors | RE Melchers, MG Stewart |

Place of Publication | London |

Publisher | A. A. Balkema |

Pages | 35-43 |

Number of pages | 9 |

ISBN (Print) | 9058090868 |

Publication status | Published - 2000 |

Event | 8th International Conference on Applications of Statistics and Probability (ICASP 8) - SYDNEY, Australia Duration: 12 Dec 1999 → 15 Dec 1999 |

### Conference

Conference | 8th International Conference on Applications of Statistics and Probability (ICASP 8) |
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Country | Australia |

City | SYDNEY |

Period | 12/12/99 → 15/12/99 |

### Keywords

- COMBINATION

## Cite this

*Applications of statistics and probability, vols 1 and 2*(pp. 35-43). London: A. A. Balkema.