A note on the signature and dynamic signature of coherent systems

Document Type : Original Article

Authors

Ahmad Mirjalili ¹

Mohammad Khanjari Sadegh ²

¹ Department of Statistics, Maybod Branch, Islamic Azad University, Maybod, Iran

² Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran

10.22067/smps.2025.92495.1043

Abstract

This paper investigates new properties and applications of the system signature and its dynamic counterpart, which serve as effective tools for analyzing stochastic ordering and aging properties in both coherent and used systems. For coherent systems with exchangeable components, the system signature offers a more powerful comparative framework than the traditional structure function. In the context of used systems with different exchangeable components, we propose an alternative to the dynamic signature that is simpler to implement and often preferable to the standard dynamic signature. This alternative also proves useful in scenarios where the traditional dynamic signature is inapplicable. Additionally, by examining all 28 coherent systems of order ‎$‎n \leq 4‎$‎, we establish a unique property of series systems: under both identical and non-identical independent component lifetimes, series systems are the only ones that are decreasing failure rate (DFR) closed. The results extend several existing findings related to system signatures and their dynamic versions. Illustrative examples are provided to demonstrate the practical relevance of the theoretical results.

Keywords

Coherent systems‎

‎Dynamic signature

DFR‎

‎IFR

‎Signature

‎Stochastic ordering

‎Used systems

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