Template:Methodology fleet rsa

Methodology
Figures Repairable and Fleet illustrate that the difference between repairable system data analysis and fleet analysis is the way that the dataset is treated. In fleet analysis, the time-to-failure data from each system is stacked to a cumulative timeline. For example, consider the two systems in Table 13.2.

The data set is first converted to an accumulated timeline, as follows:
 * •	System 1 is considered first. The accumulated timeline is therefore 3 and 7 hours.
 * •	System 1's End Time is 10 hours. System 2's first failure is at 4 hours. This failure time is added to System 1's End Time to give an accumulated failure time of 14 hours.
 * •	The second failure for System 2 occurred 5 hours after the first failure. This time interval is added to the accumulated timeline to give 19 hours.
 * •	The third failure for System 2 occurred 4 hours after the second failure. The accumulated failure time is 19 + 4 = 23 hours.
 * •	System 2's end time is 15 hours, or 2 hours after the last failure. The total accumulated operating time for the fleet is 25 hours (23 + 2 = 25).

In general, the accumulated operating time $${{Y}_{j}}$$  is calculated by:


 * $${{Y}_{j}}={{X}_{i,q}}+\underset{q=1}{\overset{K-1}{\mathop \sum }}\,{{T}_{q}},\text{ }m=1,2,...,N$$


 * where:


 * •	 $${{X}_{i,q}}$$ is the  $${{i}^{th}}$$  failure of the  $${{q}^{th}}$$  system
 * •	 $${{T}_{q}}$$ is the end time of the  $${{q}^{th}}$$  system
 * •	 $$K$$ is the total number of systems
 * •	 $$N$$ is the total number of failures from all systems ( $$N=\underset{j=1}{\overset{K}{\mathop{\sum }}}\,{{N}_{q}}$$ )

As this example demonstrates, the accumulated timeline is determined based on the order of the systems. So if you consider the data in Table 13.2 by taking System 2 first, the accumulated timeline would be: 4, 9, 13, 18, 22, with an end time of 25. Therefore, the order in which the systems are considered is somewhat important. However, in the next step of the analysis the data from the accumulated timeline will be grouped into time intervals, effectively eliminating the importance of the order of the systems. Keep in mind that this will NOT always be true. This is true only when the order of the systems was random to begin with. If there is some logic/pattern in the order of the systems, then it will remain even if the cumulative timeline is converted to grouped data. For example, consider a system that wears out with age. This means that more failures will be observed as this system ages and these failures will occur more frequently. Within a fleet of such systems, there will be new and old systems in operation. If the dataset collected is considered from the newest to the oldest system, then even if the data points are grouped, the pattern of fewer failures at the beginning and more failures at later time intervals will still be present. If the objective of the analysis is to determine the difference between newer and older systems, then that order for the data will be acceptable. However, if the objective of the analysis is to determine the reliability of the fleet, then the systems should be randomly ordered.