Abstract
We analyze the influence of repair on a two-component warm-standby system with switching and back-switching failures. The repair of the primary component follows a minimal process, i.e., it experiences full aging during the repair. The backup component operates only while the primary component is being repaired, but it can also fail in standby, in which case there will be no repair for the backup component (as there is no indication of the failure). Four types of system failures are investigated: both components fail to operate in a different order or one of two types of switching failures occur. The reliability behavior of the system is investigated under three different aging assumptions for the backup component during warm-standby: full aging, no aging, and partial aging. Four failure and repair distributions determine the reliability behavior of the system. We analyzed two cases—in the First Case, we utilized constant failure rate distributions. In the Second Case, we applied the more realistic time-dependent failure rates. We used three methods to identify the reliability characteristics of the system: analytical, numerical, and simulational. The analytical approach is limited and only viable for constant failure rate distributions i.e., the First Case. The numerical method integrates simultaneous Algebraic Differential Equations. It produces a solution in the First Case under any type of aging, and in the Second Case but only under the assumption of full aging in warm-standby. On the other hand, the developed simulation algorithms produce solutions for any set of distributions (i.e., the First Case and the Second Case) under any of the three aging assumptions for the backup component in standby. The simulation solution is quantitively verified by comparison with the other two methods, and qualitatively verified by comparing the solutions under the three aging assumptions. It is numerically proven that the full aging and no aging solutions could serve as bounds of the partial aging case even when the precise mechanism of partial aging is unknown.
Highlights
We will focus on a two-component system with a standby arrangement where the backup components may fail either while in standby, or during operation after some imperfect switching mechanism has put those online
Example 3 will illustrate the behavior of the 2SBRSBF system with Second Case distributions where the failures of the backup component in operation have a Decreasing Failure Rate (DFR)
Another expected result is that the state probability functions for partial aging are between the state probability functions for no aging and full aging
Summary
Our goal is to analyze how this affects the system reliability under different aging assumptions in standby In such a system, the primary component begins operation, and when it fails, the system will try to activate the backup component, but a switching failure is possible. There are no simultaneous ODEs that describe the behavior of 2SBRSBF with time-dependent distributions (i.e., Second Case) under no aging or partial aging assumptions in standby. To facilitate the simulational solution, we will introduce a novel method to generate failure times of the backup component in standby under the assumptions of full aging, no aging, or partial aging Using this method, we will modify and generalize the algorithm from [17] to simulate the behavior of 2SBRSBF and to calculate its most important reliability characteristics.
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