Fleet Analysis Example

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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 {{T}_{j}}\,\! Number of failures {{N}_{j}}\,\! Failure Time {{X}_{ij}}\,\!
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
Total52110 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 \widehat{\lambda }\,\! and \widehat{\beta }\,\! for this data set are then given by:

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

The next figure shows the System Operation plot.

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