Multiperformance Measure Multistate Systems: General Definitions and Concepts

As an extension of binary system model, multistate systems (MSSs) are more flexible for modeling reliabilities of real-life engineering systems. In the conventional MSS theory, it is usually assumed that the performance of the system and components can be characterized by one measure. However, the assumption is difficult to be satisfied for some complex engineering systems that have different forms of performances at the same time. For example, the integrated energy system can supply various forms of energy simultaneously, including electrical power, natural gas, and heat. Therefore, the conventional MSS is difficult to model the system with multiple performances. In this article, a general multiperformance measure MSS model is proposed. The fundamental assumptions and key definitions are provided for such systems. The ordering methods to compare performance measure vectors are introduced. The concepts of separability, monotonicity, relevancy, coherency, and equivalency of the component and the system are developed to characterize the system properties. Examples are given to illustrate these definitions.