Reliability analysis of general phased mission systems with a new survival signature

Highlights

• The article addresses reliability assessment for PhasedMission Systems (PMS).

• With one type of component, we show current survival signature methods can be adapted.

• New survival signature methodology is developed for the fully general PMS setting.

• Examples demonstrate the method and show simpler examples agree with literature.

Abstract

It is often difficult for a phased mission system (PMS) to be highly reliable, because this entails achieving high reliability in every phase of operation. Consequently, reliability analysis of such systems is of critical importance. However, efficient and interpretable analysis of PMSs enabling general component lifetime distributions, arbitrary structures, and the possibility that components skip phases has been an open problem.

In this paper, we show that the survival signature can be used for reliability analysis of PMSs with similar types of component in each phase, providing an alternative to the existing limited approaches in the literature. We then develop new methodology addressing the full range of challenges above. The new method retains the attractive survival signature property of separating the system structure from the component lifetime distributions, simplifying computation, insight into, and inference for system reliability.

Introduction

A phased mission system (PMS) is one that performs several different tasks or functions in sequence. The periods in which each of these successive tasks or functions takes place are known as phases [1], [2]. Examples of PMSs can be found in many practical applications, such as electric power systems, aerospace systems, weapon systems and computer systems. A typical example of a PMS is the monitoring system in a satellite-launching mission with three phases: launch, separation, and orbiting.

A PMS is considered to be functioning if all of its phases are completed without failure, and failed if failure occurs in any phase. Therefore, the reliability of a PMS with N phases is the probability that it operates successfully in all of its phases:

$$R_S=\mathbb{P}(\text{Phase}\text{1}\text{works}\cap \text{Phase}\text{2}\text{works}\cap \cdots \cap \text{Phase}N\text{works})$$

The calculation of the reliability of a PMS is more complex than that of a single phase system, because the structure of the system varies between phases and the component failures in different phases are mutually dependent [1].

Over the past few decades, there have been extensive research efforts to analyze PMS reliability. Generally, there are two classes of models to address such scenarios: state space oriented models [3], [4], [5], [6] and combinatorial methods [2], [7], [8], [9], [10], [11], [12], [13], [14]. The main idea of state space oriented models is to construct Markov chains and/or Petri nets to represent the system behaviour, since these provide flexible and powerful options for modelling complex dependencies among system components. However, the cardinality of the state space can become exponentially large as the number of components increases. The remaining approaches exploit combinatorial methods, Boolean algebra and various forms of decision diagrams for reliability analysis of PMSs.

In particular, in recent years the Binary Decision Diagram (BDD) — a combinatorial method — has become more widely used in reliability analysis of PMSs due to its computationally efficient and compact representation of the structure function compared with other methods. Zang et al. [9] first used the BDD method to analyze the reliability of PMSs. Tang et al. [10] developed a new BDD-based algorithm for reliability analysis of PMSs with multimode failures. Mo [11] and Reed et al. [12] improved the efficiency of Tang’s method by proposing a heuristic selection strategy and reducing the BDD size, respectively. Xing et al. [13], [14] and Levitin et al. [15] proposed BDD based methods for the reliability evaluation of PMSs with common-cause failures and propagated failures. Wang et al. [16] and Lu et al. [17] studied modular methods for reliability analysis of PMSs with repairable components, by combining BDDs with state-enumeration methods.

While the BDD method has been shown to be a very efficient combinatorial method, it is still difficult to analyze large systems without considerable computational expense [1], [12]. In this paper, we propose a combinatorial analytical approach providing a new survival signature methodology for reliability analysis of PMSs. The method presented here has similar computational complexity to BDD methods (since the most efficient method currently available for computing survival signatures uses BDD methodology [18]), but for the first time brings all the advantages associated with the compact representation of a system provided by the survival signature [19] to PMSs. As such, the current work in developing the theory of survival signatures for PMSs represents a foundational contribution for many future developments. In particular, this work for example opens the door to invoking existing literature on bounding survival probabilities using the survival signature within a constrained computational budget [20] to the setting of PMSs — an exciting future research direction offering the first concrete promise of reduced computational complexity in the PMS literature.

The paper is organized as follows: section sec:PMS gives a brief background on PMSs; Section 3 first shows how the standard survival signature can be used to evaluate PMSs with similar component types in each phase, before providing a novel methodology which facilitates heterogeneity of components across the phases. Section 4 presents illustrative examples showing numerical agreement with existing literature, but where the full benefits of the interpretability of survival signatures is now available due to this work. Finally, Section 5 presents some conclusions ideas for future work.