This problem normally requires a complex logical structure since we are trying to model many processes simultaneously.

Let's consider the following problem:

A power plant needs 2 water pumps operating at max capacity to cool its turbines with river water. Since the pumps may break down, the power plant has installed two additional pumps. These four pumps operate at 50% capacity and if one or two pumps break down, the power plant can still operate.

The calculating complexities arise because if we have failures of any pumps, the remaining pumps would have to work harder, thus increasing the remaining pumps' probability of failure. In other words, if we have all 4 pumps running together, and we only need 2 for the station to operate, then the pumps are working at half capacity but as soon as one pump fails the remaining pumps are working at 2/3 capacity, and so they have a higher failure rate or, equivalently, a lower mean time between failure.

The four pumps are of varying age and therefore of varying reliability. The following table summarises the data:

Probability of failure (fail/day) | |||
---|---|---|---|

Pump | Pumps working | ||

4 | 3 | 2 | |

A | 0.002 | 0.007 | 0.025 |

B | 0.004 | 0.013 | 0.079 |

C | 0.007 | 0.034 | 0.142 |

D | 0.002 | 0.007 | 0.025 |

Each repair of the pump takes Lognormal(20,15) days.

The questions are: a) How long will it take before a shutdown occurs? b)How many shutdowns will the station have in a year? c)What is the probability of one or more shutdowns per year?

The solution to this problem is illustrated in the model: Power Station Pumps

The links to the Power Station Pumps software specific models are provided here: