# Fleet Analysis Example

*This example appears in the Reliability Growth and Repairable System Analysis Reference*.

The following table presents data for a fleet of 27 systems. A cycle is a complete history from overhaul to overhaul. The failure history for the last completed cycle for each system is recorded. This is a random sample of data from the fleet. These systems are in the order in which they were selected. Suppose the intervals to group the current data are 10,000; 20,000; 30,000; 40,000 and the final interval is defined by the termination time. Conduct the fleet analysis.

Sample Fleet Data
| |||

System | Cycle Time [math]{{T}_{j}}\,\![/math] | Number of failures [math]{{N}_{j}}\,\![/math] | Failure Time [math]{{X}_{ij}}\,\![/math] |
---|---|---|---|

1 | 1396 | 1 | 1396 |

2 | 4497 | 1 | 4497 |

3 | 525 | 1 | 525 |

4 | 1232 | 1 | 1232 |

5 | 227 | 1 | 227 |

6 | 135 | 1 | 135 |

7 | 19 | 1 | 19 |

8 | 812 | 1 | 812 |

9 | 2024 | 1 | 2024 |

10 | 943 | 2 | 316, 943 |

11 | 60 | 1 | 60 |

12 | 4234 | 2 | 4233, 4234 |

13 | 2527 | 2 | 1877, 2527 |

14 | 2105 | 2 | 2074, 2105 |

15 | 5079 | 1 | 5079 |

16 | 577 | 2 | 546, 577 |

17 | 4085 | 2 | 453, 4085 |

18 | 1023 | 1 | 1023 |

19 | 161 | 1 | 161 |

20 | 4767 | 2 | 36, 4767 |

21 | 6228 | 3 | 3795, 4375, 6228 |

22 | 68 | 1 | 68 |

23 | 1830 | 1 | 1830 |

24 | 1241 | 1 | 1241 |

25 | 2573 | 2 | 871, 2573 |

26 | 3556 | 1 | 3556 |

27 | 186 | 1 | 186 |

Total | 52110 | 37 |

**Solution**

The sample fleet data set can be grouped into 10,000; 20,000; 30,000; 40,000 and 52,110 time intervals. The following table gives the grouped data.

Grouped Data
| |

Time | Observed Failures |
---|---|

10,000 | 8 |

20,000 | 16 |

30,000 | 22 |

40,000 | 27 |

52,110 | 37 |

Based on the above time intervals, the maximum likelihood estimates of [math]\widehat{\lambda }\,\![/math] and [math]\widehat{\beta }\,\![/math] for this data set are then given by:

- [math]\begin{matrix} \widehat{\lambda }=0.00147 \\ \widehat{\beta }=0.93328 \\ \end{matrix}\,\![/math]

The next figure shows the System Operation plot.