Reliability analysis of a K-out-of-N system with random effort

D'Amico Guglielmo, Department of Economics, University G. d'Annunzio of Chieti-Pescara
Raj Raina, Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India
Selvamuthu Dharmaraja, Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India

The study of k-out-of-n systems' reliability is significant both theoretically and practically. These models find applications in various real-world scenarios, such as telecommunication, transmission, transportation, manufacturing, and services. Analyzing the probabilistic aspects of real-world k- out-of-n systems help in developing optimal strategies to maintain high system-level reliability. Numerous studies focus on the reliability analysis of such systems; see [1, 2]. In our research, we have developed a mathematical model for a k-out-of-n system, where the system functions until k out of its n components fail. We have introduced a random rate of effort function, r_{J(t)}(t;X(t)), which means that the repair process depends on the number of faulty components and the time elapsed in the repair phase and on the accumulated effort function. This model is designed for unmanned rotor-craft high-altitude platforms and is validated using an experimental prototype. We have devised an algorithm to calculate the reliability function for this system, providing closed-form representations for special cases where k = 2 and n = 3. Special numerical cases are investigated marking the initial step toward understanding how the repair time distributions of components aect the reliability characteristics of k-out-of-n systems. These analytical findings are verified using simulations.

Area: CS29 - Advances in Stochastic Control and System Modeling (Bernardo D'Auria)

Keywords: Reliability characteristics, reliability function, repairable k-out-of-n system, general distribution.

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