Multivalued decision diagram-based common cause failure analysis in phased-mission systems

https://doi.org/10.1016/j.cie.2020.106622Get rights and content

Highlights

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    Common cause failures are modeled and analyzed for non-repairable phased-mission systems.

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    Combinatorial methods based on multiple-valued decision diagrams are proposed.

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    An explicit method and two implicit methods are compared.

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    All three methods are applicable to arbitrary distribution types for component time-to-failure.

Abstract

Due to a shock or shared root cause, multiple system components may fail at the same time contributing significantly to the entire system failure. Such dependent component failures are referred to as common cause failures (CCFs). A rich body of research has been conducted for addressing effects of CCFs in reliability analysis of diverse types of systems. This paper first adapts multiple-valued decision diagrams (MDDs) for analyzing reliability of a non-repairable phased-mission system (PMS) subject to CCFs caused by external shocks. An explicit method and two implicit methods based on MDDs are proposed and compared. While the three MDD-based methods differ in terms of space and computation complexities, examples show that all these methods offer low computational complexity while addressing dynamics and dependencies caused by CCFs and phased operations.

Introduction

A phased-mission system (PMS) is often required to accomplish multiple different tasks under different stress levels or operational conditions, leading to dynamic system structure functions and component failure distributions during different phases (Li et al., 2018, Zhao et al., 2019). In addition, there exist statistical dependencies across different phases for each component (Xing & Amari, 2015). PMSs abound in real-world applications, including but not limited to wireless sensor networks (Wang, Xing, Zonouz, Vokkarane, & Sun, 2017), the Mars orbiter mission system (Xing, 2007), body sensor networks (Wang, Xing, Levitin, & Huang, 2018), the space tracking, telemetry and command system (Yang & Wu, 2014), and aircraft fleets (Yang et al., 2018).

A rich body of research has been conducted in reliability modeling and analysis of PMSs (Wu, Peng, & Xing, 2019). The techniques suggested in literature consists of two main categories: simulations (Yang & Wu, 2014) and analytical models (Mo et al., 2014, Wang et al., 2020, Wu and Wu, 2015). Simulations are flexible in modeling dynamic and dependent behaviors; but can only offer approximate reliability results (Wu et al., 2019). In contrast, analytical modeling methods can provide accurate reliability results. Moreover, once an analytical model is constructed, it can be reused for reliability evaluation using different component failure parameter values. This advantage lends the analytical modeling methods to applications that involve numerous iterations of reliability evaluation like design optimizations. Examples of analytical methods include combinatorial models (Mo et al., 2014, Wang et al., 2020), state space-based methods (Wu & Wu, 2015), and hybrid methods (Zhao et al., 2019). The multivalued decision diagram (MDD)-based methods (Mo et al., 2014) are among the combinatorial models, and have shown to be computationally more efficient than other analytical models for PMS analysis. However, the MDD-based method for reliability analysis of PMSs cannot be applied to PMSs with common cause failures (CCFs), “a subset of dependent failures in which two or more component fault states exist at the same time, or within a short interval, because of a shared cause” (NUREG/CR-4780, 1988&1989). Such a shared cause is also known as a common cause (CC) (Yu, Yang, Lin, & Zhao, 2017). Note that in (Mo & Xing, 2013) an MDD-based method was proposed for reliability analysis of systems subject to CCFs; the method however is only applicable to single-phased systems, not suitable for PMSs. To the best of our knowledge, there is no work on adapting MDDs to reliability analysis of PMSs with CCFs.

This paper makes contributions by extending the efficient MDD-based method for accurate reliability analysis of non-repairable PMSs undergoing CCFs, advancing the state-of-the-art methods for modeling complex systems subject to both the phased-mission requirements and CCFs.

The rest of this paper is arranged as follows. Section 2 presents representative relevant works on addressing CCFs in system reliability analysis. Section 3 presents the system and CCF models as well as an illustrative example of PMSs. Section 4 gives a brief review on the MDD-based PMS analysis method. Section 5 presents an explicit MDD-based method for CCF analysis, illustrated by a detailed analysis of the example PMS. An improved version using a hybrid BDD-MDD model is also proposed. Section 6 presents two implicit methods for CCF analysis, illustrated by a detailed analysis of the same example PMS. Section 7 compares the performance of the three proposed methods. Section 8 concludes the paper and gives directions of our future work.

Section snippets

Related CCF works

Numerous studies have been conducted to consider effects of CCFs in the reliability analysis of single-phase systems (Dai et al., 2004, Qin and Li, 2019) and PMSs (Levitin et al., 2013, Wang et al., 2015, Xing, 2007, Xing and Levitin, 2013). Among the existing methods, binary decision diagram (BDD)-based methods have been proved to be both efficient and effective and they can be applied to systems with any structure and any type of time-to-failure distribution (Wang et al., 2015). The BDD-based

System model

This section describes the modeling of PMS, CCF model considered, assumptions of the proposed methods, and an illustrative example system to make the type of PMS considered tangible.

Preliminary method

In Xing and Dai (2009), MDDs were first formulated for analyzing generic multi-state systems. In Mo et al. (2014), MDDs were applied to analyze PMSs with demonstrated high computational efficiency as compared to other PMS analysis methods.

The MDD-based method for the reliability analysis of PMS (without considering CCFs) can be described as the following three-step procedure.

  • Step 1) Component-level MDD modeling

For each component in a PMS with M phases, a (M+1)-valued variable x is defined and

Proposed MDD-based explicit approach

The idea of the explicit method is to incorporate the effects of CCFs by modeling each external CC as a basic event in the system PMFT model and including an OR gate for each component affected by the CC; this OR gate connects the component’s individual failure event and the basic event representing the occurrence of the CC. After the above process, an expanded reliability/fault tree model that explicitly considers the effects of CCFs is generated, which is then analyzed using the PMS MDD

Proposed MDD-based implicit approaches

In contrast to the explicit MDD-based method in Section 5 that explicitly incorporates impacts of CCFs through expanding the system fault tree model, the implicit methods work by decoupling the impacts of CCFs from the solution combinatorics based on the total probability law, generating a set of reduced reliability problems. Each reduced problem can then be modeled and analyzed ignoring CCFs using the PMS MDD method. Results of the reduced problems are integrated with probability coefficients

Comparisons and discussions

The three proposed MDD-based methods and the BDD-based implicit method in (Wang et al., 2015) are compared in Table 5. The comparisons in the first five rows are self-explained based on explanations of the methods in 5 Proposed MDD-based explicit approach, 6 Proposed MDD-based implicit approaches. Next we provide more details for comparisons in the last three rows.

s-relationship among CCs: for the explicit method, the occurrence of each CC is modeled as an independent node in the expanded PMFT.

Conclusions and future work

In this paper, we make contributions by proposing three new MDD-based methods for reliability analysis of non-repairable PMSs subject to CCFs. The proposed explicit method expands the system reliability model to consider effects of CCFs while the proposed implicit methods decouple effects of CCFs from the solution combinatorics based on the total probability law. As demonstrated by the example analyses, all three methods are applicable to any arbitrary types of time-to-failure distributions for

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was partially supported by the National Natural Science Foundation of China, China under Grant No. 61702219, the Scientific Research Program Funds of Guangzhou, China under Grant No. 201804010305, the Guangdong Basic and Applied Basic Research Foundation, China under Grant No. 2019A1515011369, the Science and Technology Planning Project of Guangdong Province, China under Grant No. 2019A050510024, the Fundamental Research Funds for the Central Universities, and the Special Funds for

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