Definitions of generalized multi-performance weighted multi-state K¯-out-of-n system and its reliability evaluations

•Basic definitions of multi-performance multi-state components are provided.•Generalized multi-performance weighted multi-state K¯-out-of-n system models are proposed.•Universal generating function approach is developed for the reliability evaluation of such systems.•Numerical examples are developed for illustrating the reliability evaluation method. The k-out-of-n system model is widely applied for the reliability evaluation of many technical systems. Multi-state system modelling is also widely used for representing real systems, whose components can have different levels of performance. For these researches, recently multi-state k-out-of-n systems have been comprehensively studied. In these studies, it is usually assumed that the system has a single task function to complete in a given environment. Moreover, the system or component performance is characterised by one measure, for example “electric power” in generation systems or “flow-rate” in transmission systems. However, this can be a simplification for some real-life engineering systems. For example, an intertwined district heating and electricity system consists of combined heat and power generating units, which can produce both electricity and heat. In this paper, definitions of multi-performance weighted multi-state components are provided and two generalized multi-performance multi-state K¯-out-of-n system models are proposed. Universal generating function approach is developed for the evaluation of such systems, with two numerical examples.