Optimal mission abort policy with multiple abort criteria for a balanced system with multi-state components

Highlights

• A mission abort policy with multiple criteria is designed for a balanced system.

• Mission success probability and system survivability are derived by MPI technique.

• Two optimization models are constructed to determine the optimal abort thresholds.

• Numerical examples based on a UAV performing a surveillance mission are developed.

Abstract

In some engineering fields, systems are required to complete a mission over a period. However, for some safety-critical systems, the survival of systems often has higher priority than the successful achievement of the mission. In these cases, a mission needs to be aborted when a certain criterion is met, and a rescue procedure would be carried out to avoid system failure. Nowadays, reliability problems on balanced systems have attracted more and more attention because they often perform critical missions in industrial fields such as military weapons and new energy storage. In reported studies, no mission abort policy has been considered for balanced systems with multi-state components. To fill this gap, a novel mission abort policy is designed with multiple abort criteria to adapt to the characteristics of such systems. Two competing abort criteria are considered, including the maximum component state distance and the number of damaged components which are defined as components working in states no better than a predetermined state. Two optimization models are constructed to determine the optimum mission abort thresholds. Finally, numerical examples based on UAVs performing a surveillance mission are presented to illustrate the proposed mission abort policy.

Introduction

In many industrial cases, systems are required to conduct a specific mission over a period (Bedford and Cooke, 1997, Wu and Hillston, 2015, Yang et al., 2016). To evaluate the achievement of the target mission, an important indicator is the mission success probability, which is defined as the probability that a mission can be completed (Levitin and Finkelstein, 2018, Zhao et al., 2021). However, in some situations, the survival of some safety-critical systems such as UAVs, military weapons, and aircrafts, has higher priority than the successful achievement of the mission because of the fatal consequence caused by system failure, including casualties and huge economic losses (Levitin et al., 2018a, Levitin et al., 2018b, Qiu et al., 2017, Zhao et al., 2020). In these cases, the mission can be aborted, and a rescue procedure could be carried out to avoid system failure when a certain condition is met. Another indicator, system survivability, is often used to assess the probability that a system can survive through the mission (Levitin and Finkelstein, 2018, Wu et al., 2020, Zhao et al., 2021, Zhao et al., 2021). When solving a practical mission abort problem and designing the optimal mission abort policy, there are mainly two key issues to be determined and formulated. One is the system characteristic, such as structure and failure rules, and the other is the abort criterion based on which the mission should be aborted and thereby the mission success probability and the system survivability can be well traded off. Based on these two points, two main contributions are provided in this paper as presented below.

First, the balanced system is considered as a new type of system to perform a mission, leading to new reliability problems due to its complicated structure. In recent years, reliability analysis of balanced systems has attracted more and more scholars’ attention because of their crucial roles in many fields such as the new energy storage, military weapons, aeronautics, and astronautics (Hua and Elsayed, 2016b, Wang et al., 2020, Wang et al., 2021). Reported studies on balanced systems mainly focus on the operation features of the system itself, including system structure, definition of balance, failure rule, and maintenance policy. Few research studies have considered the situation where a balanced system is assigned to perform a mission. The structure of balanced system is very common in engineering systems, such as the UAV and the battery pack of new energy vehicle, which are often used to performing missions. However, the unbalance or failure of such systems may cause serious economic losses, or even casualties. Thus, to avoid unexpected consequences, the mission abort policy for balanced systems is urgently needed to be developed. Apart from this, the complicated structures of balanced systems bring a great challenge for evaluating the corresponding reliability indices. In existing research, balanced systems can be generally classified into three categories: k-out-of-n pairs:G balanced systems (Hua and Elsayed, 2016a, Hua and Elsayed, 2016b), balanced systems with m sectors (Cui et al., 2018), and balanced systems with multi-state components (Cui et al., 2019). In this paper, we focus on the balanced systems with multi-state components, in which system balance is defined based on the component state difference (Cui et al., 2019). Systems with multi-state components have wide applications in engineering areas, such as manufacturing systems, computing systems and monitoring systems (Levitin et al., 2018a, Levitin et al., 2018b, Liu et al., 2019, Xiao et al., 2020). Performance-balanced systems operating in a shock environment was first developed by Wang, Zhao, Wang et al. (2020). A general multi-state balanced system (Zhao, Wang et al., 2020) and a multi-state balanced system with multiple failure criteria (Wu, Cui et al., 2020) have also been investigated based on different realistic industrial applications.

Second, new abort criteria are proposed based on the features of balanced systems with multi-state components. In existing studies on mission abort policy, a mission is usually aborted when a certain criterion is met. The abort criterion and the relevant indicators are often determined based on the mission features, the system characteristics, or the operating environment. A typical indicator for multi-component systems is the number of failed components. A mission abort policy for a k-out-of-n:G system was first proposed by Myers (2009), and the number of failed components was used as an indicator to abort a mission. Furthermore, Levitin et al., 2018a, Levitin et al., 2018b extended it into a more realistic case by considering the impact of failure propagations in a mission abort policy for a 1-out-of-N:G warm standby system. In this paper, multiple abort indicators are considered according to the characteristics of balanced system with multi-state components. One is the number of damaged components in the whole system. A damaged component is defined in this paper as a component working in states no better than a predetermined state, considering that too many components operating in relatively low states may decrease the efficiency in accomplishing the mission. The other is the balance degree of the system, which is defined as the maximum state distance among all components in this paper, as too large state difference may lead to imbalance of the system, thereby causing system breakdown and mission failure.

Based on the above-mentioned two aspects, we explore a mission abort policy with multiple abort criteria for a balanced system with multi-state components. Consider a system consisting of multiple identical and independent multi-state components. This assumption is reasonable because systems with identical and independent components are common in practice. For example, the wind driven generators located in different positions in a wind power plant can be regarded as identical and independent components. This is because they are required to perform the same function and are far away from each other so that the impact on each other can be neglected. The system is said to be balanced when the maximum component state distance is no more than a predetermined threshold. The system is failed when the number of damaged components reaches a critical value or when the system is out of balance, whichever comes first. Similarly, two mission abort criteria are constructed for this system. The mission is supposed to be aborted when the maximum component state distance is equal to or larger than a prefixed value or when the number of damaged components reaches a certain number, whichever comes first. To trade off the mission success probability and the system survivability, two optimization models are constructed. Optimization model I is to maximize the mission success probability with the constraint of system survivability not being less than a given probability. Optimization model II aims at minimizing the overall expected cost.

In order to derive the mission success probability and the system survivability, the Markov process imbedding (MPI) technique is used in this paper. Cui et al. (2019) first used the MPI technique to derive the system reliability for a balanced system. Zhao, Wu et al. (2020) used MPI technique to evaluate the reliability of k-out-of-n:F balanced systems with multiple functional sectors. Wang, Zhao, Wu et al. (2020) employed MPI technique to assess the performance of balanced systems with restricted rebalanced mechanisms. According to these studies, MPI technique proves to be an effective method when dealing with reliability problems on balanced systems, especially when the system structure is complicated and when the components are independent or Markov dependent.

The construction of such a mission abort policy is motivated by the unmanned aerial vehicle (UAV) as addressed by Levitin and Finkelstein (2018). UAVs can be modelled by a balanced system because it contains spatially distributed units (Hua and Elsayed, 2016a, Hua and Elsayed, 2016b). UAVs often carry out critical military missions such as reconnaissance, surveillance, and target acquisition (RSTA). When performing such missions, the survival of a UAV is more important than the completion of the target mission, because the exposure or capture of such military equipment by enemy could cause irretrievable consequences including intelligence leaking or technology stealing. Therefore, the mission abort policy for UAVs is a pressing issue to be solved. Consider a multi-rotor UAV performing a surveillance mission. When a certain number of rotors are in low working condition or when the performance distance among all rotors is too large, the UAV fails because some of its functions cannot be performed as required such as rotating, takeoff and landing capabilities, and so on. To avoid the complete failure of the UAV, the mission should be aborted, and a rescue procedure should be carried out. To facilitate the execution of the abort action, an optimal mission abort policy is supposed to be designed.

To summarize, the most significant contribution of this paper is to develop the mission abort policy for balanced systems with multi-state components for the first time. Compared with earlier studies, detailed contributions are presented below from the following three aspects.

From the perspective of system modeling, the mission abort policy is first developed for a balanced system with multi-state components. Reported studies on balanced systems mainly focus on the basic structure and derivation of reliability indices, but very few research has considered balanced systems performing missions. However, balanced systems have important applications in many engineering fields such as UAVs performing surveillance missions. In some cases, system survivability has higher priority than mission success, so proper mission abort policy needs to be developed. In previous studies, only Wu et al. (2021) considers a mission abort policy based on the number of failed components for a balanced system with multiple sectors. Therefore, the mission abort policy for balanced systems with multi-state components is explored for the first time in this paper.

From the perspective of reliability assessment, two mission abort thresholds are considered according to the operation characteristics of balanced systems with multi-state components. A novel threshold is first proposed in this paper, the balance degree of the system, which has been never considered in previous studies. The unbalance of systems may affect system performance, even cause serious consequences, so the mission needs to be aborted during the mission when the system balance degree is poor.

From the perspective of indices derivation approaches, the complex system structure brings huge challenges on deriving system reliability indices. Thus, MPI with high accuracy and efficiency is employed to derive the closed-form solutions of two indices, system survivability and mission success probability.

From the perspective of optimization model and solution, two optimization models are constructed to maximum the system survivability and to minimize the expected cost, respectively. An application on UAVs performing a surveillance mission is analyzed as an example. The optimum results can provide decision makers with guide on system design according to practical demands.

The remainder of this paper is organized as follows. In Section 2, the proposed model is formulated. In Section 3, the mission success probability and system survivability are derived by employing the MPI technique. In Section 4, numerical examples are provided based on the applications in UAVs to illustrate the proposed model. In Section 5, conclusion and some possible future works are discussed.