Fleet Analysis Example

From ReliaWiki
Jump to navigation Jump to search
RGA Examples Banner.png


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.

As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at RGA examples and RGA reference examples.




This example appears in the Reliability growth 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]\displaystyle{ {{T}_{j}}\,\! }[/math] Number of failures [math]\displaystyle{ {{N}_{j}}\,\! }[/math] Failure Time [math]\displaystyle{ {{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]\displaystyle{ \widehat{\lambda }\,\! }[/math] and [math]\displaystyle{ \widehat{\beta }\,\! }[/math] for this data set are then given by:

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

The next figure shows the System Operation plot.

Rga13.7.png