Reliability assessment of system under a generalized run shock model

Abstract

In this paper we are concerned with modelling the reliability of a system subject to external shocks. In a run shock model, the system fails when a sequence of shocks above a threshold arrive in succession. Nevertheless, using a single threshold to measure the severity of a shock is too critical in real practice. To this end, we develop a generalized run shock model with two thresholds. We employ a phase-type distribution to model the damage size and the inter-arrival time of shocks, which is highly versatile and may be used to model many quantitative features of random phenomenon. Furthermore, we use the Markovian property to construct a multi-state system which degrades with the arrival of shocks. We also provide a numerical example to illustrate our results.

A New Shock Model With a Change in Shock Size Distribution

“…Theorem 2: Let the interarrival times between successive shocks follow Erlang distribution with pdf (8). Then S 2 ∼ ME 2k (γ, A, a) with γ = (b 1 , .…”

“…See, e.g., [13] and [16] for other types of mixed shock models. Gong et al [8] studied a run-based shock model with two critical levels c 1 and c 2 . According to the model, the system fails if at least k 1 consecutive shocks with magnitude above c 1 or k 2 consecutive shocks with magnitude above c 2 occur.…”

Reliability Evaluation of Smart Meters Under Degradation-Shock Loads Based on Phase-Type Distributions

“…To reduce the calculation in the degradation-shock model, t is taken as one year; that is, in the subsequent analysis of this paper, X t represents the damage when the smart meter is subjected to temperature and humidity stresses for one year. Then, in combination with (21), the result of X t can be calculated, i.e., X i . X i ∼ N (0.0469, 0.2808) Next, we convert the damage amount X t into the form of the PH distribution using the method described in Section II.…”

“…Segovia and Labeau [20] concluded that when the shock amplitude does not reach the shock threshold, the values of the initial vector of the PH distribution change, increasing the probability that the system will enter a dangerous state at the next moment. Gong et al [21] developed a generalized run shock model with two thresholds. Zhao et al [22] proposed a multistate shock model in which three types of shocks were considered.…”

Two novel critical shock models based on Markov renewal processes

“…In a cumulative shock model, a system failure occurs when the cumulative damage caused by shocks exceeds a given level (e.g., Gong et al, 2020; Kijima & Nakagawa, 1991; Ranjkesh et al, 2019). In a run shock model, the system fails only when the magnitudes of a specified number of consecutive shocks are greater than a preset threshold, which was first proposed by Mallor and Omey (2001), and further studied by Gong et al (2018), Ozkut and Eryilmaz (2019), and so on.…”