# 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.

System Cycle Time ${\displaystyle {{T}_{j}}\,\!}$ Number of failures ${\displaystyle {{N}_{j}}\,\!}$ Failure Time ${\displaystyle {{X}_{ij}}\,\!}$ Sample Fleet Data 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.

Time Observed Failures Grouped Data 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 ${\displaystyle {\widehat {\lambda }}\,\!}$ and ${\displaystyle {\widehat {\beta }}\,\!}$ for this data set are then given by:

${\displaystyle {\begin{matrix}{\widehat {\lambda }}=0.00147\\{\widehat {\beta }}=0.93328\\\end{matrix}}\,\!}$

The next figure shows the System Operation plot.