The consecutive-k system was first studied around 1980, and it soon became a very popular subject. The reasons were many-folded, includ ing: 1. The system is simple and natural. So most people can understand it and many can do some analysis. Yet it can grow in many directions and there is no lack of new topics. 2. The system is simple enough to become a prototype for demonstrat ing various ideas related to reliability. For example, the interesting concept of component importance works best with the consecutive-k system. 3. The system is supported by many applications. Twenty years have gone and hundreds of papers have been published on the subject. This seems to be a good time for retrospect and to sort the scattered material into a book. Besides providing our own per spective, the book will also serve as an easy reference to the numerous ramifications of the subject. It is hoped that a summary of work in the current period will become the seed of future break-through.
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The consecutive-k system was first studied around 1980, and it soon became a very popular subject. The reasons were many-folded, includ ing: 1. The system is simple and natural. So most people can understand it and many can do some analysis. Yet it can grow in many directions and there is no lack of new topics. 2. The system is simple enough to become a prototype for demonstrat ing various ideas related to reliability. For example, the interesting concept of component importance works best with the consecutive-k system. 3. The system is supported by many applications. Twenty years have gone and hundreds of papers have been published on the subject. This seems to be a good time for retrospect and to sort the scattered material into a book. Besides providing our own per spective, the book will also serve as an easy reference to the numerous ramifications of the subject. It is hoped that a summary of work in the current period will become the seed of future break-through.
Since its start in 1980 the study of the consecutive-k system has resulted in the accumulation of hundreds of research papers. Its popularity is due to its close ties with many mathematical topics such that the system has become a prototype of how mathematical analysis can help in the study of system reliability. This is the first book to put together all the material on the subject. However, it is not just a collection of results. The authors have built a framework to fit the results into and then sort them and compare them, so that the reader has a good idea what is currently the best methodology. The authors also cover important extensions such as window systems, network systems, graph systems, and 2-dimensional systems. The consecutive-k system is known for its wide applicability and the authors have included a chapter on applications.
Audience: All systems engineering researchers, not just those specializing in the consecutive-k system. The book could also be used for a graduate course to demonstrate how mathematics is actually applied to systems engineering.
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