ABSTRACT
Expanding the two-state approach to multi-state approach in reliability analysis, we take into account the importance of safety and operating process effectiveness of technical systems. The assumption that the systems are composed of multi-state components with reliability states degrading in time (Kolowrocki 2001, Kolowrocki 2004) gives the possibility for more precise analysis and diagnosis of their reliability and operational processes’ effectiveness. This assumption allows us to distinguish a system reliability critical state to exceed which is either dangerous for the environment or does not assure the necessary level of its operational process effectiveness. Then, an important system safety characteristic is the time to the moment of exceeding the system reliability critical state and its distribution, which is called the system risk function. This distribution is strictly related to the system multi-state reliability function that is a basic characteristic of the multi-state system. The main results determining the multi-state reliability functions and the risk functions of typical series, parallel, seriesparallel, parallel-series, series-“m out of n” and “m out of n”- series systems with ageing components are given in (Kolowrocki 2001, Kolowrocki 2004, Xue and Yang 1995). The paper is devoted to transmitting these results on the multi-state ageing series-consecutive “m out of k: F” systems (Barlow et al. 1975, Guze 2007a,b,c, Guze 2008, Hwang 1982, Kossow and Preuss1995, Malinowski & Preuss 1995, Malinowski 2005, Shanthikumar 1987).
