Multivariate copula based dynamic reliability modeling with application to weighted-k-out-of-n systems of dependent components

Reliability assessment models for dependent competing failure processes considering correlations between random shocks and degradations

“…Proposed a type of bivariate degradation model based on inverse Gaussian processes and copula function. When the system is assumed to have n dependent components with individually different weights, a multivariate copula for dynamic reliability modeling of weighted‐ k ‐out‐of‐ n systems was applied in Eryilmaz . And Eryilmaz studied a three‐state degraded system that have random and statistically dependent degradation rates, in which dependence is modeled by copula .…”

“…When the system is assumed to have n dependent components with individually different weights, a multivariate copula for dynamic reliability modeling of weighted-k-out-of-n systems was applied in Eryilmaz. 27 And Eryilmaz 28 studied a three-state degraded system that have random and statistically dependent degradation rates, in which dependence is modeled by copula. 29 Presented the mixed copula models for time-independent reliability analysis of several typical systems, considering the nonlinear correlation between failure modes by using the chosen optimal copula functions.…”

Stochastic comparisons of total capacity of weighted-k-out-of-n systems

“…, 1). As described in Samaniego and Shaked (2008), there are many real systems that can 9 be modelled by weighted-k-out-of-n systems, therefore investigating stochastic properties of various characteristics, such 10 as survival function, mean residual life function and hazard rate function of S T w (t) and T T w and their behaviour with respect 11 to t as well as (w 1 , . .…”

“…for t < s. Eryilmaz (2015b) used (1.1) to analyse the residual capacity of the system while it is working at time s and used 9 (1.2) to evaluate the capacity loss between time points t and s. The main purpose of this paper is to study the effect of the 10 component weights and component lifetimes on the total and residual capacity of the weighted-k-out-of-n system. 11 Next, we recall some definitions of stochastic orderings that are used later in this paper.…”

Time domain series system definition and gear set reliability modeling

“…The majority of classical system reliability models were developed with the assumption of independent component failures. However, the so called common cause failure or common mode failure effect are normally ignorable for system reliability modeling [5][6][7] .…”