Abstract
Minimal Cut Vectors (MCVs) and Minimal Path Vectors (MPVs) are one of the key concepts of reliability analysis. They allow us to estimate system availability or to analyze influence of individual system components on the entire system. However, the main problem of their use, especially in reliability analysis of complex systems, lies in their identification. Several algorithms have been proposed to solve this task. Some of the most universal ones are based on logical differential calculus. These algorithms use integrated direct partial logic derivatives to find situations that can correspond to the MCVs (MPVs) and a special type of logic conjunction to select only those situations that really agree with the MCVs (MPVs). In this paper, we summarize the ideas behind these algorithms in more formal way and present results of some experiments performed to study their time complexity.
Highlights
Reliability has been considered as an important characteristic of many systems [1 - 6]
In the case of Multi-State Systems (MSSs), the Minimal Cut Vectors (MCVs) for a given system state describe circumstances under which a minor improvement of any non-perfectly working component causes that the system achieves at least the considered state, while the Minimal Path Vectors (MPVs) for system state j agree with situations in which a minor degradation of any working component results in decrease in system state below value j
MCVs and MPVs are very useful in reliability analysis
Summary
Reliability has been considered as an important characteristic of many systems [1 - 6]. One of the current issues of reliability engineering is the analysis of complex systems [7] These systems are characterized by the fact that they consist of many elements (components) with very different behavior. A healthcare system consists of very variable components that can be identified as hardware, software, organizational, and human, while a gas network is composed of many different hardware components, such as pipelines with various capacities, compressor stations, and supply and demand centers This variability implies that such systems can operate at several performance levels. In case of MSSs, this task can be generalized as identification of minimal scenarios whose occurrence causes that the system performance decreases below a given level or minimal scenarios ensuring that the system achieves its mission Special instances of these scenarios are Minimal Cut Vectors (MCVs) and Minimal Path Vectors (MPVs). Time complexity of these algorithms has not been studied in [12, 22 and 23] and, we decided to perform some experiments whose results are presented in this paper
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