Data Analysis for Fleet Analysis

Data Analysis

Once the accumulated timeline has been generated, it is then converted into grouped data. To accomplish this, a group interval is required. The group interval length should be chosen so that it is representative of the data. Also note that the intervals do not have to be of equal length. Once the data points have been grouped, the parameters can be obtained using maximum likelihood estimation as described in the Crow Discrete Reliability Growth Model section of this on-line reference. The data in Table 13.2 can be grouped into 5 hr intervals. This interval length is sufficiently large to insure that there are failures within each interval. The grouped data set is given in Table 13.3.

Table 13.3 - Grouped data

Failures in Interval

Interval End Time

1

5

1

10

1

15

1

20

1

25
 

The Crow-AMSAA model for Grouped Failure Times is used for the data in Table 13.3 and the parameters of the model are solved by satisfying the following maximum likelihood equations as described in the Crow Discrete Reliability Growth Model section of this on-line reference.

MATH (22)
MATH (23)

Fielded Systems Example 4

Table 13.4 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 10000, 20000, 30000, 40000 and the final interval is defined by the termination time. Conduct the fleet analysis.

Table 13.4 - 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 to Fielded Systems Example 4

For the system data in Table 13.4, the data can be grouped into 10000, 20000, 30000, 4000 and 52110 time intervals. Table 13.5 gives the grouped data.

Table 13.5 - Grouped data

Time

Observed Failures

10000

8

20000

16

30000

22

40000

27

52110

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:

MATH

Figure 13.7 shows the System Operation plot.

Figure

Figure 13.7: System Operation plot for fleet data