A new cumulative shock model with damage and inter-arrival time dependency

• Published in: Reliability engineering & system safety 2019-12, Vol.192, p.106047, Article 106047
• Main Authors: Ranjkesh, Somayeh Hamed, Hamadani, Ali Zeinal, Mahmoodi, Safieh
• Format: Article
• Language: English
• Subjects: Cumulative damage; Degradation; Dependency; Economic models; Parameter estimation; Phase-type distribution; Reliability; Reliability analysis; Reliability engineering; Shock process; System reliability; Time dependence
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2018.01.006

•System performance and reliability a system subjected to random shocks or external loads occurring randomly at different times with random intensities or damage sizes is studied in this paper.•In this paper, a new cumulative shock model is developed based on possible dependencies between inter-arrival time and magnitude of random shocks to evaluate in a reasonable and realistic manner the time-dependent shock-based reliability of systems.•If shocks occur at close intervals, the system lacks the time necessary for self-recovery, thereby, larger damages might be inflicted to the system. In other words, shocks occurring at short intervals are more fatal and cause larger damages to the system.•The effect of each shock causes a random damage with a general distribution.•The present paper employs the versatile properties of the PH distribution to fit the data for the time between shocks and shock sizes, this leads to the easier and more tractable computation of convolutions (evaluating the distribution of the sum of times until the arrival of multiple consecutive shocks and their cumulative damage). In this paper, a system is considered that fails when the cumulative damage due to shocks exceeds the handling capacity of the system. It is also supposed that if the time between two consecutive shocks is not large enough, the system lacks the time necessary for recovering to receive subsequent shocks; hence, larger damages might be inflicted upon the system. In other words, shocks occurring at short intervals are more fatal and cause larger damages to the system. Based on these assumptions, a new model is developed for evaluating system reliability that takes into account the likely dependencies between inter-arrival times and random shock magnitudes. The proposed model is then validated through a method based on phase-type distributions that enables the model to be efficiently and easily evaluated. Approximation of its reliability function and estimation of model parameters are also investigated. Finally, an illustrative example is provided to demonstrate the efficiency of the proposed model.