from: Mc Graw Hill - 1999 - Perry - Chemical engineers handbook (VII Edition)

In monitoring a moving threadline, one criterion of quality would be the frequency of broken filaments. These can be identified as they occur through the threadline by a broken filament detector mounted adjacent to the threadline. In this context, the random occurences of broken filaments can be modeled by the Poisson distribution. This is called a Poisson process and corresponds to a probalistic description of the frequency of defects or, in general, what are called arrivals at points on a continous line or in time.

1. the number of cars (arrivals) that pas a point on a high -speed highway between 10:00 and 11:00 a.m. on Wednesdays.

2. the number of customers arriving at a bank between 10:00 and 10:10 a.m.

3. the number of telephone calls received through a switchboard between 9:00 and 10:00 a.m.

4. the number of insurance claims that are filed each week.

5. The number of spinning machines that break down during 1 day at a large plant

• x Total number of arrivals in total length L or a total period T

• a Average rate of arrivals for a unit length or unit time

• \[ \lambda = aL \] expected or average number of arrivals for the total length L or total time T

\[P(x) = \frac{\lambda^x}{x!}\cdot e^\lambda ; x=0,1,2,...\]

Insert Period (or Length) in the range of 0-10. Choose the Average Rate. Slide the total Number of Arrivals to center the distribution.

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