Reliability for k-out-of-n:F balanced systems with m sectors

Rapid technological developments have resulted in the development of new reliability systems, such as unmanned aerial vehicles with balanced engine systems, whose reliability analysis cannot be covered by currently existing techniques. Thus, research on this topic is very important and significant. In this article, a k-out-of-n:F balanced system with m sectors is introduced based on some real background and then four related system reliability models are developed. Several methods, such as the order statistics technique, Markov process imbedding technique, recursive method, and convolution method, are used on the various models for different situations. The elegant Markov process imbedding technique is extensively considered in order to obtain the smallest number of system states. The labeling of system states is presented and the state labeling formula is given for exponential distributions and the presented models, which is very convenient for usage. To the best of our knowledge, this is the first report in the literature on such a balanced system, and the corresponding research results are new contributions. In addition to system reliability formulas, the moments of the system lifetime are given. Finally, some numerical examples are presented to illustrate the results obtained in this article.