Reliability measures of dynamic circular sliding window system

In this modern era of dynamic reliability analysis, this paper introduces the dynamic circular multi-state sliding window system (DCMSWS), an innovative mathematical model that extends the concept of a circular sliding window system into dynamic scenarios. DCMSWS is considered to have failed when the combined performance of r consecutive multistate elements (MEs) falls below a predefined threshold, W. Each component type has a number of distinct individual components with variable states that change over time, making the state probabilities of those components time-dependent. By employing an algorithm grounded in Lz-transform, dynamic reliability measures comprising reliability, availability, mean expected performance, and expected profit are derived for the water supply system. This study represents a pioneering effort in dynamic circular multi-state sliding window systems and their evaluation using the Lz transform, intimately connected with queuing theory.