Reliability evaluation of consecutive-k-out-of-n: F systems with two performance sharing groups

From previous studies on performance sharing systems, the system structure is considered to be either series, or series-parallel, or k-out-of-n structure. To enrich the research and extend application on performance sharing systems, the consecutive-k-out-of-n: F system with two performance sharing groups is investigated in this paper. Such systems consist of n units and two common buses, and each unit has a random performance to satisfy its random demand. Units connected by the same common bus make up one performance sharing group. If a unit has surplus performance, the surplus performance can be transmitted to the units which are experiencing performance deficiency and belonging to the same performance sharing group via the common bus. If the demand of one unit is not satisfied, the unit has to be shut down. The system fails due to at least k consecutive shut-down units. The universal generating function technique is used to analyze the system reliability. Analytical and numerical examples of the heating system are presented to demonstrate the new model under study.