A multi-state shock model with mutative failure patterns. (October 2018)

• Record Type: Journal Article
• Authors: Zhao, Xian; Wang, Siqi; Wang, Xiaoyue; Cai, Kui
• Is Part Of: Reliability engineering & system safety. Volume 178(2018)
• Page Start: 1
• Page End: 11
• Publication Date: 2018-10
• Subjects: Multi-state system -- Shock model -- Mutative failure patterns -- Phase-type distribution; Reliability (Engineering) -- Periodicals; System safety -- Periodicals; Industrial safety -- Periodicals; Fiabilité -- Périodiques; Sécurité des systèmes -- Périodiques; Sécurité du travail -- Périodiques; 620.00452
• DOI: 10.1016/j.ress.2018.05.014
• Languages: English
• ISSNs: 0951-8320

Abstract

Highlights: A multi-state shock model with three types of shocks is proposed. The failure pattern mutates when the system state drops to a lower one. The finite Markov chain imbedding approach is used to obtain reliability indices. The phase-type distribution is used to depict the interarrival time of two shocks. Three different replacement policies are proposed for the new model. Abstract: In this paper, to accommodate the known fact that a multi-state system is more likely to fail when its state gets worse, a multi-state shock model is proposed, in which the system failure patterns are mutative for different states. Shocks are classified into type I, type II and type III by magnitude. A type III shock has a destructive effect on the system and causes a complete failure whenever it occurs. A type II shock triggers the system down to a lower state. The system completely fails when the additive number of type II shocks exceeds a threshold. A type I shock has different effects for different system states. The system completely fails if the cumulative number of type I shocks exceeds a threshold which decreases as the system state gets lower. Distributions of the lasting time until the end of each system state, the lifetime and the residual lifetime of the system are derived when the interarrival times between successive shocks follow a common continuous phase-type distribution. Three different replacement policies are proposed to fit the characteristic of the new model, and corresponding optimization models are constructed to gain the optimal quantities.