Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

Abstract

In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.

Semi-Markov approach for reliability modelling of light utility vehicles

“…One of the most important 3-state semi-Markov models is the generalized object reliability model developed by Grabski [13], validated with assumed parameter values, without specified references to technical data. In the course of the research, the authors developed original 3-state models applicable to specific objects and systems, e.g., four types of repairable systems [8], single-use systems [9], special vehicles [5], lithium-ion batteries [55] and repairable systems [3]. Mengistu et al [28] identified a five-state phase space of the semi-Markov model for volunteer cloud systems and Wu et al [56] for power stations.…”

“…Technical objects (general) [13] Four types of repairable systems [8] Single-use system [9] Special vehicles [5] Lithium-ion batteries [55] Repairable systems [3] 5-state model Volunteer cloud systems [28] Power station [56] 4-and 6-state models Repairable systems under alternative environments [50] 7-state model Modular multilevel converter system [57] 9-state model Two machines operating in parallel [4]…”

“…The objective of this publication is to develop an operation process model for light utility vehicles that enables analysing their reliability through determining basic reliability characteristics, such as the reliability function, failure probability density function, failure intensity, expected time to failure and readiness indices. A novel contribution to the current state of the source literature is the expansion of existing stochastic modelling methods in terms of their applications within the field of engineering and technical sciences [3,5,13]. In addition, the presented research complements the subject matter niche, because none of the previously published papers applied to the reliability of military light utility vehicles based on the semi-Markov model.…”

On a Mixed Transient–Asymptotic Result for the Sequential Interval Reliability for Semi-Markov Chains

“…In this paper, we study a specific reliability indicator of discrete-time semi-Markov systems called sequential interval reliability (SIR) which has been recently introduced in [1].…”

Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields

“…(ii3) Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems, by Barbu, V.S., D'Amico, G. Gkelsinis, T. [19]. This is another paper of the special issue concerned with reliability indicators; however, this one is dedicated to semi-Markov systems.…”