Abstract: In practical applications, due to the uncertainty of the working environment of the Phased Mission System (PMS) and the limited amount of measured fault data it is a challenge to obtain accurate and sufficient information about the failure of components, which causes difficulties with evaluating the reliability of the PMS under the actual operating environment. To address these difficulties, existing studies commonly rely on experts to qualitatively assess the reliability parameters of components, leveraging their extensive professional knowledge and research experience. However, experts have limited knowledge and experience and may have an unclear understanding of the degradation laws of systems or components to provide uncertain assessments for the performance of components. Furthermore, the PMS, which consists of multiple consecutive and non-overlapping phases, may experience different mission environments at each phase, causing changes in the reliability parameters of components. Existing research mainly focuses on single-stage mission systems, where the failure probability of components is directly obtained via the subjective assessment of experts, which cannot be applied to PMSs and cannot solve the reliability assessment problem of the complex and variable PMS.
To address the problem of insufficient and imprecise information in the reliability assessment of the PMS, this paper proposes a reliability assessment method for the PMS based on the Triangular Intuitionistic Fuzzy Number (TIFN) and the Binary Decision Diagram (BDD) model. Firstly, the exponential operation of TIFN is defined, its related conclusions are presented, and the properties it satisfies are proved. Secondly, to consider the lifetime distribution of components, we require multiple experts to evaluate the Mean Time to Failure (MTTF) of components instead of directly evaluating the failure probability of components, and employ TIFN to describe the evaluation information of the experts. By comparing pieces of the assessment information of multiple experts pairwise to calculate the similarity degree of the assessment information between various experts, we construct a method to determine the membership and non-membership degrees of TIFN by denoting the coincidence of the degree of the assessment information of an individual with that of the other individuals as the membership degree of TIFN, and the non-coincidence degree as the non-membership degree of TIFN. On this basis, an intuitionistic fuzzy failure evaluation model is proposed to determine the intuitionistic fuzzy failure rate of the component. Then, the fuzzy failure function of components is defined according to the proposed exponential operation of TIFN and the exponential distribution function. Further, a reliability evaluation model of PMS is established based on the BDD model. Finally, an example of reliability assessment of a geosynchronous orbit satellite control system is presented to illustrate the implementation process and effectiveness of the proposed reliability evaluation model for PMS. Furthermore, we compare and analyze the traditional PMS-BDD method, the fuzzy fault tree method, and the intuitionistic fuzzy fault tree method with the proposed model. From the comparison results, it is obvious that the traditional PMS-BDD method is a special case where the proposed method only considers the most probable reliability parameters of components and cannot handle uncertainty information. The fuzzy reliability values of the fuzzy fault tree and intuitionistic fuzzy fault tree are higher than the one calculated by the proposed method, which is explained by the fact that they regard the cross-stage component as multiple different components and the three phases of the PMS as three independent phases and they are based on the bottom event probability to derive the top event probability of the fault tree.
The comparison analysis results illustrate that the proposed method is a more general fuzzy reliability assessment method, which can better handle the uncertain and fuzzy information of components in the PMS than the traditional PMS-BDD method. Meanwhile, the proposed method can better process the correlation of the cross-stage components and more accurately calculate the reliability of the PMS than the fuzzy fault tree method and the intuitionistic fuzzy fault tree method.

Key words: phased mission system, reliability evaluation, triangular intuitionistic fuzzy number, BDD

摘要： 针对多阶段任务系统(Phased Mission System,PMS)可靠性评估中对系统或部件退化规律认识不清、主观知识不完备、环境变化等原因造成部件的信息不足或不精确问题,基于三角直觉模糊数(Triangular Intuitionistic Fuzzy Number,TIFN)和二元决策图(Binary Decision Diagram,BDD)模型, 提出了一种PMS可靠性评估方法。首先, 定义了TIFN的指数运算法则,证明了其满足的性质;其次,通过多位专家对部件平均故障时间(Mean Time to Failure, MTTF)进行评估,利用TIFN量化专家意见,建立了直觉模糊失效率评估模型,构建了一种计算TIFN的隶属度和非隶属度的方法,根据TIFN的运算法则和指数分布函数定义了部件的模糊失效函数; 最后,运用示例说明了该方法的有效性,并与传统PMS-BDD方法、模糊故障树方法和直觉模糊故障树方法进行了对比分析。

关键词: 多阶段任务系统(PMS), 可靠性评估, 三角直觉模糊数(TIFN), 二元决策图(BDD)