Demand‐Dependent Survival Signature for Reliability and Importance Analysis of Capacity‐Based Systems With Independent Component Lifetimes

ABSTRACT Reliability assessment of capacity‐based engineering systems depends on both component states and the demand imposed on the system. The same component configuration may therefore satisfy one operating demand but fail to meet a higher requirement. This study develops a demand‐dependent survival signature approach for reliability and component importance analysis of coherent systems with multiple component types and independent component lifetimes. The formulation preserves the separation between system structure and component lifetime distributions while allowing the structural representation to change with demand. Time‐dependent system reliability is derived for multiple component types, and conditional demand‐dependent survival signatures are introduced to evaluate individual component states. These conditional quantities are then used to obtain Birnbaum importance, Risk Achievement Worth, and Risk Reduction Worth under different demand levels. A numerical example illustrates the formulation and shows how increasing demand reduces the number of successful component configurations. An application considers a water treatment system consisting of nineteen components grouped into six types and operating under several production demands. The results show that demand affects both system reliability and component importance and can change component rankings. The approach supports demand‐specific identification of critical components and helps prioritize reliability improvements in capacity‐based engineering systems.