# Thread: Poisson Square Wave (PSW) and Filtered Poisson Process (FP)

1. ## Poisson Square Wave (PSW) and Filtered Poisson Process (FP)

I am currently studying a paper from Prof. Armen Kiureghian regarding stochastic load modeling (reliability engineering). I have come across Poisson Square Wave (PSW) and Filtered Poisson Process (FP) as load modeling types. does anyone know anything about them and their properties?

In that paper the author has used PSW for sustained loads and FP for transient load types. It is a mystery for me!!

thanks

2. Originally Posted by sorm
I am currently studying a paper from Prof. Armen Kiureghian regarding stochastic load modeling (reliability engineering). I have come across Poisson Square Wave (PSW) and Filtered Poisson Process (FP) as load modeling types. does anyone know anything about them and their properties?

In that paper the author has used PSW for sustained loads and FP for transient load types. It is a mystery for me!!

thanks
Well I would assume FP is just a special case of Poisson process...

A Poisson process is a way of counting independent exponential arrivals.

For definiteness:

Suppose posters arrive at this thread in independent exponential times $t_i$ with rate $\lambda$ per hour.

Set $T_i = t_1 +...+t_i =$ the time of the $i^{th}$ arrival.

Then the number of arrivals by time $t,$ is a poisson process $N(t) = \{\max\{i\}:T_i \leq t\}.$

There are many interesting properties about this counting process, but ultimatley it is used to count the number of arrivals of independent exponentials.