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 ${{T}_{j}}\,\!$	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
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 ${\widehat {\lambda }}\,\!$ 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.