Reliability and importance analysis of uncertain system with common cause failures based on survival signature

Highlights

• Possible CCF scenarios are modeled and quantified by decomposed partial α factors.

• Uncertainties for CCF events are reduced by hierarchical Bayesian inference method.

• Reliability of redundant uncertain system with CCFs is modeled by survival signature.

• Importance of components and CCF events are defined and ranked.

• The proposed method is effectively used to analyze the reliability of a satellite subsystem.

Abstract

Redundant design has become the commonly used technique for ensuring the reliability of complex systems, which calls for great concern to common cause failure problems in such systems. Incomplete data in combination with vague judgments from experts introduce imprecision and epistemic uncertainties in the performance characterization of components. These issues need to be taken into account for assessing the system reliability. In this paper, a comprehensive reliability assessment method is presented by adopting the concept of survival signature to estimate the reliability of complex systems with multiple types of components. Particular attention is devoted to common cause failures (CCFs), which are modeled and quantified by decomposed partial α-decomposition method. Uncertainties caused by incomplete data for CCF events are reduced by hierarchical Bayesian inference. The component importance measure is enhanced to assess the importance of various possible CCF scenarios and to identify their potential impact on system reliability. The presented method is used to analyze the reliability of a dual-axis pointing mechanism for communication satellite, which is a commonly used satellite antenna control mechanism. The engineering application demonstrates the effectiveness of the method.

Introduction

Redundant design has become one of the critical measures to ensure the high reliability and long lifetime requirement of large complex systems, such as nuclear systems [1], [2], [3], aerospace systems [4, 5], etc., especially for nonrepairable systems [6]. Common cause failure (CCF), which is failure or degradation of multiple components that triggered by shared causes [7], has become the dominating type of dependent failure in modern complex system. CCFs can lead to a decrease of system reliability, which is critical in view of the original intention of improving system reliability by redundant design. Dependent failure and CCF have attracted a large number of concerns in past decades. In the early stage, the CCFs modeling was introduced for probability safety assessment (PSA) of systems in nuclear industry, explicit and implicit methods have proposed for modeling of CCF [8]. Many parametric models such as the basic parameter model, β-factor model, α-factor model, etc. have been developed for quantification of CCF parameters. Hokstad and Rausand [9] presented a review and trends of CCF modeling in 2008, especially focused on the development of the β-factor model and its extension.

After the aforementioned CCF quantification parameter models have been proposed, comprehensive work on CCF modelling and evaluate the effect of CCFs is devoted to system reliability. O'Connor summarized the CCF quantification models and proposed an extended α-factor model and a general dependency model based on a Bayesian network (BN) for system risk and reliability assessment [10, 11]. Some extension works have been implemented to integrate the effect of CCF with other impact factors, such as uncertainties, on system reliability. Mi et al. [12, 13] proposed an evidential network (EN)-based method and a Belief universal generation function (UGF)-based method for reliability analysis of complex multi-state systems (MSSs) with CCF and epistemic uncertainty. Le Duy and Vasseur [1] put forward a new practical method of modelling multi-unit CCFs in a nuclear PSA context. To further investigate the influence of coupling causes on CCFs and system reliability, Zheng et al. [14] proposed a α-factor decomposition method to combine the coupling common cause information in traditional models. Troffaes et al. [15] presented a robust Bayesian approach to modelling epistemic uncertainty in α-factors. Zubair and Amjad [16] used an α-factor model and Bayes theory to calculate and update the system unavailability with consideration of CCFs. Recently, George-Williams, et al. [17] has investigated the sensitivities of multiple component failure modes to system survivability, and the critical common cause component group (CCCG) can be identified. However, this sensitivity work performed till CCCGs level, and did not drill down to the vaiours CCF events and common cause layers. Therefore, all those works investigated the relationship between CCFs with system reliability without distinguishing various scenario of CCFs which are caused by several coupling common causes. It is necessary to find a proper method to model the system reliability with different CCF modes and quantify the importance of various CCF scenarios to system reliability.

Except for the classical reliability modeling methods, i.e. binary decision diagram (BDD) [18, 19], fault tree (FT) model [20], Bayesian networks (BNs) [21, 22] etc., survival signature has been proposed by Coolen and Coolen-Maturi [23] based on the concept of system signature [24], as an effective method for system reliability modeling especially for redundant systems with multiple types of component groups. Furthermore, they quantified the uncertainty and dependability of a system with several kinds of components, where the lifetime follows different distributions, by survival signature [25]. When CCFs are considered in system, this research included an investigation of CCFs with non-parametric predictive inference method for system reliability [26]. Moreover, an efficient simulation-based reliability analysis method was proposed by Feng et al. [27] for complex non-repairable systems following CCFs. Some other extension works are presented by Liu et al. [28, 29] to analyze stress-strength reliability (SSR) and dynamic SSR of systems with multiple types of components based on survival signature. Survival signature has the prominent advantage that can separate the structure of system from the failure time distribution of its components, and provides a better way to integrate the CCFs and imprecise into system survival function with less time consuming.

In association with system reliability analysis, component importance analysis is useful for system design, reliability improvement and system control. Depending on the purpose of the analysis, a number of different importance measures have been defined. The most commonly used importance measures address structural importance, probability importance and critical importance. Birnbaum [30] categorized importance measures into three classes, including structural importance measures, reliability measures and lifetime importance measures. Kuo and Zhu [31] gave a review of reliability importance measures. Wei et al. [32], [33], [34] published a comprehensive review on variable importance analysis, and performed considerable work on importance analysis of structural system. Feng et al. [35] integrated the modelling advantage of survival signature, presented a new component importance measures and quantified the effect of impression on the system survival function. Further, Eryilmaz et al. [36, 37] reported considerable developments on joint reliability importance for all kind of systems under several complex system characters, and proposed an extension on marginal and joint reliability importance based on survival signature. Although the research achievements on importance measures are considerable, most of the works are concentrated on the components importance measure. For the importance analysis of CCFs, Guey [38] gave a review of the state-of-the-art of CCF analysis methods, from the sensitivity study of CCF parameters, a conclusion that prevention of CCFs is more important than other analysis technical was given. To solve the problem that how to prevent CCFs, Pan and Nonaka [39] was firstly extended the importance analysis method to the field of CCF analysis, and attempted to find a better time and resources allocation strategy for system reliability analysis. Kamyab et al.[40] performed sensitivity analysis and estimated the importance measures of software CCFs, through this method, the specific contribution of software CCF in the trip failure probability can be revealed. All those works did not distinguish the various CCF types caused by different coupling common causes, there is not yet a proper method to identify the importance of CCF events associated with common causes to system reliability.

Synthesis above works, for complex system with various kinds of redundant mechanisms, such as aerospace system which always consist of components which belong to different types, CCFs are of great importance in reliability evaluation of such systems. There are mainly three problems within the above research works: (1) several coupling common causes will lead to various CCF scenarios which increase the modeling difficulty. For instance, when system reliability is modeled by fault tree or Bayesian network, the relationship between failure causes and events should be analyzed, then the basic common cause events or nodes should be added, which increases the size and complexity of models. (2) Evaluate the system reliability with consideration of CCFs, especially caused by several coupling factors, is time consuming. After the modeling of CCFs in system reliability model, the computing of minimal cut sets for fault trees and the reasoning of Bayesian networks will take much more time corresponding to complex model structures. (3) The research on importance of CCF events caused by different causes needs to further investigate, especially when influenced by other factors, such as missing data, uncertain information, etc. Therefore, it is necessary to perform reliability and importance analysis on system susceptible to CCFs with various scenarios. The importance measure of CCFs would help engineers to find the most significant factor and most efficient defence strategies against CCFs.

In this paper, we aim for advancement in this direction and propose a comprehensive system reliability and importance analysis method that quantifies information and uncertainty of CCF effects driven by the coupling mechanisms in the system. The remainder of this paper is organized as follows. Section 2 presents the problems to be addressed in this paper. Then, a comprehensive system reliability analysis approach will be proposed in Section 3. In this section, a decomposed partial α factor model is deduced, system reliability model, the importance of components and CCF events are developed based on survival signature. Reliability evaluation and importance analysis of an aerospace subsystem with consideration of dependent failure and coupling causes are discussed in Section 4. Section 5 gives a brief conclusion as well as directions for future work.