Reliability of non-repairable phased-mission systems with propagated failures

Highlights

• Reliability of non-repairable phased-mission systems with propagated failures is analyzed.

• The proposed method considers time-varying, phase-dependent failure rates and associated cumulative damage effects for the system elements.

• The proposed method is recursive and can be fully automated.

Abstract

In this paper, we propose a recursive and exact method for reliability evaluation of phased-mission systems with failures originating from some system elements that can propagate causing the common cause failures of groups of elements. The system consists of multiple, consecutive, non-overlapping phases of operation, and non-identical binary non-repairable elements that can fail individually or due to propagated failures originating from other elements. The overall system can have binary states corresponding to the mission success and failure or multiple states characterized by different levels of system performance. Based on conditional probabilities as well as the branch and bound principle, the proposed method takes into account dynamic changes in system structure and demand across different phases. It also considers time-varying, phase-dependent failure rates and associated cumulative damage effects for the system elements. The main advantage of this method is that it does not require composition of decision diagrams and can be fully automated. Both an analytical example and a numerical example are analyzed to illustrate the proposed method.

Introduction

In many practical applications such as aerospace, nuclear power, airborne weapon systems, and distributed computing systems, the system mission involves multiple, consecutive and non-overlapping phases of operation [1], [2], [3], [4], [5]. During each phase, the system has to accomplish a specified task and may be subject to different stresses and environmental conditions as well as different reliability requirements [1]. Thus, system configuration, success criteria, and component failure behavior may change from phase to phase. For a particular example, a Mars orbiter mission system involves launch, cruise, Mars orbit insertion, commissioning, and orbit phases that must be accomplished in sequence [2]. Those systems are referred to as phased-mission systems (PMSs).

The dynamics in system configuration and component behavior typically requires a distinct model for each phase of the PMS, which poses unique challenges to existing reliability analysis methods. Further complicating the analysis of PMS is statistical dependence across different phases for a given component. For example, the state of a component at the beginning of a phase should be identical to its state at the end of the previous phase in a non-repairable PMS [6]. Various approaches have been developed for the reliability analysis of PMS. They can be divided into two classes: analytical modeling and simulations [7], [8]. The analytical modeling approaches can be further classified into three categories: combinatorial methods (e.g., binary decision diagrams) [6], [9], [10], [11], state-space oriented approaches based on Markov chains or/and Petri nets [12], [13], [14], [15], and a phase modular approach that combines the former two methods as appropriate [16], [17]. A state-of-the-art review of reliability modeling and analysis techniques for PMS is provided in Ref. [18]. However, even with advances in computing technology, only small-scale PMS problems can be solved accurately due to high computational complexity of the existing methods.

Recently Ref. [19] proposed an efficient and exact method for the reliability evaluation of non-repairable PMS with the arbitrary system structure and non-identical binary-state elements. In this paper we extend the method in Ref. [19] to the case of PMS with propagated failures assuming that failures originating from some system elements can propagate causing the common cause failures (CCF) of groups of elements.

Note that besides the internal cause considered in this work (in particular, propagated failures originating from some elements within the system), CCF can also be caused by external factors (e.g., sudden changes in environment, power-supply disturbances, and design mistakes). Many studies have shown that both types of CCF tend to increase the joint system failure probabilities and thus contribute significantly to the overall system unreliability [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31]. Therefore, it is significant to consider the effect of CCF for the accurate reliability analysis of systems with CCF. However, the existing works have various limitations, such as being concerned with a specific system structure [32], [33], [34]; being applicable to systems with exponential time-to-failure distributions [24], [25], [35]; being subject to combinatorial explosion as the system redundancy increases [36], [37]; having a single common cause that affects all the system components [33], [38]. In addition, most of the existing works on CCF are dedicated to single-phase systems; few of them consider CCF for PMS [2], [39], [40] and they focus on external causes. Particularly, implicit methods were developed in Refs. [2], [39], which consider CCF in the process of binary decision diagram based analysis rather than in the modeling stage; the explicit method was applied in Ref. [40], which models CCF as shared basic events in the system fault tree model, and then applies the minimal cut sets based inclusion–exclusion method with deletion for analysis. As compared to the implicit method, the explicit method may involve adding a large number of CCF basic events into the system model, which is tedious to handle especially for high level redundancy [27].

In this paper we propose a recursive method for the reliability analysis of PMS subject to CCF caused by internal causes, i.e., propagated failures. In particular, we consider the case when the system contains several disjoint groups of elements, referred to as common cause groups (CCGs), and the failure of any element in a CCG can cause with some probability the failure of the entire group. The conditional probability of the failure propagation given the element fails can be specific for any element and phase.

The remainder of the paper is organized as follows. Section 2 describes the binary and multi-state systems and defines the system mission success probability based on an acceptability function in each phase. Section 3 presents the assumptions. Section 4 summarizes the method for evaluating the conditional reliability of an element and a CCG at a particular phase given that it is working at the beginning of the phase. Section 5 describes the proposed recursive PMS reliability evaluation algorithm. Section 6 illustrates the proposed algorithm using both an analytical example and a realistic size numerical example. Section 7 presents conclusion and future work.