Reliability assessment of system under a generalized cumulative shock model

Abstract

Reliability assessment of system suffering from random shocks is attracting a great deal of attention in recent years. Excluding internal factors such as aging and wear-out, external shocks which lead to sudden changes in the system operation environment are also important causes of system failure. Therefore, efficiently modeling the reliability of such system is an important applied problem. A variety of shock models are developed to model the inter-arrival time between shocks and magnitude of shocks. In a cumulative shock model, the system fails when the cumulative magnitude of damage caused by shocks exceed a threshold. Nevertheless, in the existing literatures, only the magnitude is taken into consideration, while the source of shocks is usually neglected. Using the same distribution to model the magnitude of shocks from different sources is too critical in real practice. To this end, considering a system subject to random shocks from various sources with different probabilities, we develop a generalized cumulative shock model in this article. We use phase-type distribution to model the variables, which is highly versatile to be used for modeling quantitative features of random phenomenon. We will discuss the reliability characteristics of such system in some detail and give some clear expressions under the one-dimensional case. Numerical example for illustration is also provided along with a summary.

A Reliability Modeling Method Based on Phase-Type Distribution Aiming at Shock Model

“…In this paper, the inter-arrival times follow PH distribution. M. Gong et al [14] considered a system subject to random shocks from various sources with different probabilities, and used PH distribution to model the variables for discussing the reliability characteristics of the system. In [15], two random threshold shock models for a repairable deteriorating system were established using PH distribution and an ordering policy and a replacement policy ware then investigated to minimizing the long-run average cost rate.…”

Reliability assessment of a system with multi‐shock sources subject to dependent competing failure processes under phase‐type distribution

“…The phase‐type distribution has been performed to be useful for modeling times of two successive shocks. Mathematical models of the survival function and some other reliability specifications have been proposed based on phase‐type distributions 31–34 . Eryilmaz and Kan 35 created a new shock model, where the distribution function of shock magnitudes changed when the magnitudes of shock exceeded the corresponding threshold.…”

“…Mathematical models of the survival function and some other reliability specifications have been proposed based on phase-type distributions. [31][32][33][34] Eryilmaz and Kan 35 created a new shock model, where the distribution function of shock magnitudes changed when the magnitudes of shock exceeded the corresponding threshold. And lifetime function of the system has been given considering the interval time between shocks subject to the continuous phase-type distribution.…”

Two novel critical shock models based on Markov renewal processes

“…Several attempts have been made to characterize the fatigue damage, which can be classified into two types: cumulative shock models and run shock models. 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.…”