Birnbaum Importance Research Articles

Remaining useful life prediction of weighted k-out-of-n systems based on dynamic random weights of importance

With the increasing complexity of various industrial systems, the reliability assessment and remaining useful life prediction of weighted k-out-of-n systems considering stochastic correlation have become a concern in the field of reliability. The components’ varying locations and operating environments result in fluctuating reliability and different impacts on normal system operation. In this study, the Birnbaum importance of components is modeled for a weighted k-out-of-n continuous degradation system consisting of different types of components with stochastic correlation. Furthermore, a reliability model and a remaining useful life prediction model based on kernel diffeomorphism estimation with dynamic random weights of Birnbaum importance are developed for weighted k-out-of-n systems. First, the component state reliability model is established by a nonparametric method of adaptive kernel diffeomorphism estimation. Second, the multivariate copula function is used to characterize the stochastic correlation of different types of component degradation. In addition, the Birnbaum importance model with stochastic correlation of components was developed using Akaike Information Criterion for copula function preference. A remaining useful life prediction model for the weighted k-out-of-n continuous degradation system is established considering the dynamic random weights of Birnbaum importance measures. Finally, the validity and accuracy of the proposed weighted k-out-of-n system remaining useful life model are verified using a cluster of plant protection unmanned aerial vehicles.

Multitype Optimal Component Allocation of Multicomponent Systems Considering Fuzzy State

A real system may go through several states ranging from full performance to complete failure, carrying out infinite partial performances during service time. This paper portrays such a non-binary state of systems via the fuzzy membership function. Then, the relation between the system reliability under the binary state and that under the fuzzy state is deduced, on which a multi-type component allocation problem (MCAP) is investigated to search for the optimal permutation of different types of components to maximize the fuzzy system reliability. After that, we inherit the exploration ability of genetic algorithm (GA) and the exploitation ability of Birnbaum importance (BI) to propose a fuzzy-BI-based two-stage approach combined with GA (FBITS-GA) in order to deal with the MCAP under fuzzy state assumption efficiently and accurately. The k-out-of-n systems in both low and high dimensions are presented to illustrate the effectiveness of the proposed algorithm and demonstrate the similarity and difference between the MCAP under binary state and that under fuzzy state. The experimental results showcase that the proposed approach outperforms the existing state-of-the-art approaches for MCAP.

Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis

Drones, or UAVs, are developed very intensively. There are many effective applications of drones for problems of monitoring, searching, detection, communication, delivery, and transportation of cargo in various sectors of the economy. The reliability of drones in the resolution of these problems should play a principal role. Therefore, studies encompassing reliability analysis of drones and swarms (fleets) of drones are important. As shown in this paper, the analysis of drone reliability and its components is considered in studies often. Reliability analysis of drone swarms is investigated less often, despite the fact that many applications cannot be performed by a single drone and require the involvement of several drones. In this paper, a systematic review of the reliability analysis of drone swarms is proposed. Based on this review, a new method for the analysis and quantification of the topological aspects of drone swarms is considered. In particular, this method allows for the computing of swarm availability and importance measures. Importance measures in reliability analysis are used for system maintenance and to indicate the components (drones) whose fault has the most impact on the system failure. Structural and Birnbaum importance measures are introduced for drone swarms’ components. These indices are defined for the following topologies: a homogenous irredundant drone fleet, a homogenous hot stable redundant drone fleet, a heterogeneous irredundant drone fleet, and a heterogeneous hot stable redundant drone fleet.

Reliability modeling of modular k-out-of-n systems with functional dependency: A case study of radar transmitter systems

The k-out-of-n systems are among the most important redundancy structures in engineering practices, and their reliability assessment has been extensively studied in the past decades. However, components in a k-out-of-n structure are often subject to functional dependency (FDEP), in which component states are affected by other components’ states in the system. In this article, we study a new system structure, namely modular k-out-of-n system with FDEP. In such a system, the failure of some specific components will disable some components in the k-out-of-n structure. Bayesian network (BN) models are used to construct the structure function of modular k-out-of-n systems. The parameters encoded in the graphical structure of the modular k-out-of-n system are automatically generated by a customized algorithm. Furthermore, a dynamic BN (DBN) is developed to update the reliability of modular k-out-of-n system dynamically when observation data are collected from either component or system level. The Birnbaum importance measure of the different types of components in the modular k-out-of-n system is also evaluated by the DBN model via inserting evidence of the components’ states overtime. A real-world case of a radar transmitter system in the space launch site is studied to demonstrate the effectiveness of the proposed method.

Unsupervised and supervised learning for the reliability analysis of complex systems

AbstractIn this paper, a strategy to deal with high‐dimensional reliability systems with multiple correlated components is proposed. The goal is to construct a state function that enables the classification of the states of components in one of two categories, that is, failure and operative, in case of dealing with a large number of units in the system. To this end, it is proposed a new algorithm that combines a factor analysis algorithm (unsupervised learning) with local‐logistic and isotonic regression (supervised learning). The reliability function is estimated and system failures are predicted in terms of the variables in the original state space. The dimensions in the latent state space are defined by blocks of units with a certain dependence structure. The flexibility of the model allows quantifying locally the effect that a particular unit has on the system performance and a ranking of components can be obtained under the philosophy of the Birnbaum importance measure. The good performance of the proposal is assessed by means of a simulation study. Also a real data case is considered to illustrate the method.

Importance measures for performance shaping factors of human reliability analysis

AbstractThe crew of a nuclear‐powered submarine under development in Brasil plays an important role in its safety. For this reason, crew members must be trained in procedures against undesired events. However, information that would help to accurately decrease human error probability (HEP) on board nuclear‐powered submarines is not available in the literature. Therefore, a methodology is required to obtain this information. This study introduces importance measures to evaluate the contribution of performance shaping factors (PSFs) and their levels to HEP. Importance measures Fussell‐Vesely, risk reduction worth, risk achievement worth, and Birnbaum importance, commonly used in probabilistic safety assessment, are introduced to identify PSFs and PSF levels that contribute the most to HEP. The proposed approach is focused on identifying HEP's main contributors, oriented toward decision‐making. The methodology uses the PSFs established in the Standardized Plant Analysis Risk‐Human Reliability Analysis method and a Bayesian network to quantify HEP. Moreover, the results of an application case demonstrate the method's effectiveness in integrating expert opinions into representative values of HEP and in identifying critical PSFs and PSF levels that should be the object of the decision‐making process to improve human performance.

Impact of adjuvant chemotherapy on prognosis in intrahepatic cholangiocarcinoma patients underwent radical resection

Objectives: To investigate the clinical value of adjuvant chemotherapy(ACT) in patients with intrahepatic cholangiocarcinoma(ICC) who underwent radical resection and to explore the optimal population that can benefit from ACT. Methods: A retrospective cohort study method was adopted. The clinical and pathological data of 685 patients with ICC who underwent curative intent resection in 10 Chinese hepatobiliary surgery centers from January 2010 to December 2018 were collected;There were 355 males and 330 females. The age(M(IQR)) was 58(14) years (range: 22 to 83 years). Propensity score matching(PSM) was applied to balance the differences between the adjuvant and non-adjuvant chemotherapy groups. Log-rank test was used to compare the prognosis of the two groups of patients. A Bayesian network recurrence-free survival(RFS) prediction model was constructed using the median RFS time (14 months) as the target variable, and the importance of the relevant prognostic factors was ranked according to the multistate Birnbaum importance calculation. A survival prognostic prediction table was established to analyze the population benefiting from adjuvant chemotherapy. Results: Among 685 patients,214 received ACT and 471 did not receive ACT. A total of 124 pairs of patients were included after PSM, and patients in the ACT group had better overall survival (OS) and RFS than those in the non-ACT group(OS: 32.2 months vs. 18.0 months,P=0.003;RFS:18.0 months vs. 10.0 months,P=0.001). The area under the curve of the Bayesian network RFS prediction model was 0.7124. The results of the prognostic factors in order of importance were microvascular invasion (0.158 2),perineural invasion (0.158 2),N stage (0.155 8),T stage (0.120 9), hepatic envelope invasion (0.090 3),adjuvant chemotherapy (0.072 1), tumor location (0.057 5), age (0.042 3), pathological differentiation (0.034 0), sex (0.029 3), alpha-fetoprotein (0.028 9) and preoperative jaundice (0.008 5). A survival prediction table based on the variables with importance greater than 0.1 (microvascular invasion,perineural invasion,N stage,T staging) and ACT showed that all patients benefited from ACT (increase in the probability of RFS≥14 months from 2.21% to 7.68%), with a more significant increase in the probability of RFS≥14 months after ACT in early-stage patients. Conclusion: ACT after radical resection in patients with ICC significantly prolongs the OS and RFS of patients, and the benefit of ACT is greater in early patients.

Performance Degradation Based on Importance Change and Application in Dissimilar Redundancy Actuation System

The importance measure is a crucial method to identify and evaluate the system weak link. It is widely used in the optimization design and maintenance decision of aviation, aerospace, nuclear energy and other systems. The dissimilar redundancy actuation system (DRAS) is a key aircraft control subsystem which performs aircraft attitude and flight trajectory control. Its performance and reliability directly affect the aircraft flight quality and flight safety. This paper considers the influence of the Birnbaum importance measure (BIM) and integrated importance measure (IIM) on the reliability changes of key components in DRAS. The differences of physical fault characteristics of different components due to performance degradation and power mismatch, are first considered. The reliability of each component in the system is then estimated by assuming that the stochastic degradation process of the DRAS components follows an inverse Gaussian (IG) process. Finally, the weak links of the system are identified using BIM and IIM, so that the resources can be reasonably allocated to the weak links during the maintenance period. The proposed method can provide a technical support for personnel maintenance, in order to improve the system reliability with a minimal lifecycle cost.

Benchmarking the failure assessment of perishable product supply chain using fault tree approach: insights from apple case study of India

PurposeThe purpose of this paper is to facilitate perishable product supply chain (PPSC) managers and practitioners to assess PPSC failure events. The paper proposed fault tree methodology for assessing failures associated with PPSC for evaluating the performance in terms of effective PPSC management adoption.Design/methodology/approachInitially, different failure events were identified from literature and semi-structured interviews from experts. Fault tree model was developed from the identified failure events. Probability of failure events was calculated using Poisson distribution based on the annual reports and interviews conducted from experts. Further, qualitative analysis – minimum cut sets (MCSs), structural importance coefficient (SIC) – and quantitative analysis – Birnbaum importance measure (BIM), criticality importance factor (CIF) and diagnosis importance factor (DIF) – were performed for ranking of failure events. In this study, fault tree development and analysis were conducted on apple supply chain to present the authenticity of this method for failure analysis.FindingsThe findings indicate that the failure events, given as failure at production and procurement (A2), that is, involvement of middleman (BE3), handling and packaging failure (BE4) and transportation failure (A3), hold the highest-ranking scores in analysis of PPSC using fault tree approach.Originality/valueThis research uses the modularization approach for evaluation of failure events of PPSC. This paper explores failures related to PPSC for efficient management initiatives in apple supply chain context. The paper also provides suggestion from managerial perspective with respect to each failure event.

On Some Structural Importance of System Components

In this note a new method of comparing component structural importance is introduced and compared to other existing ones. Especially, relationships of the new comparison method to the H-importance due to Hwang (2001,2005), the criticality ordering due to Boland et al. (1989) and Birnbaum importance are obtained. Illustrative examples are given.

Analysis of Network Reliability Characteristics and Importance of Components in a Communication Network

Network reliability is one of the most important concepts in this modern era. Reliability characteristics, component significance measures, such as the Birnbaum importance measure, critical importance measure, the risk growth factor and average risk growth factor, and network reliability stability of the communication network system have been discussed in this paper to identify the critical components in the network, and also to quantify the impact of component failures. The study also proposes an efficient algorithm to compute the reliability indices of the network. The authors explore how the universal generating function can work to solve the problems related to the network using the exponentially distributed failure rate. To illustrate the proposed algorithm, a numerical example has been taken.

Logical differential calculus for calculation of Birnbaum importance of non-coherent system

The Birnbaum importance is one of the measures often used in importance analysis. Many algorithms for the calculation of this measure have been proposed for coherent systems. Several interpretations of the Birnbaum importance for non-coherent systems also exist. These interpretations are usually based on the prime implicants of the structure function of the system. However, identification of the prime implicants is a complex problem. In this paper, we develop a method for computation of Birnbaum importance using Boolean expression (algebraic representation) and truth table (matrix representation). Both of these representations are calculated based on Logical Differential Calculus, in particular, Boolean derivatives. The Boolean expression derived based on Boolean derivatives is equal to known definitions of the Birnbaum importance. The matrix approach for the calculation of the Birnbaum importance based on Boolean derivatives is novel. This approach can be used for calculation of the Birnbaum importance for the structure function represented by truth table and does not need transformation of the structure function into Boolean expression. An important advantage of the proposed approach (in algebraic or matrix form) is a possibility to define the Birnbaum importance for the evaluation of the non-coherent system failure (restore) with respect to simultaneous changes of states of several system components.

A fault diagnostic system based on Petri nets and gray relational analysis for train–ground wireless communication systems

The system structure of train–ground wireless communication systems (TWCSs) is extremely complicated due to the use of fault tolerant technology to improve their performance. This complex structure raises several challenges in fault diagnosis for TWCSs, such as epistemic uncertainty, dynamic fault behaviors, and common cause failure (CCF). A fault diagnostic system is proposed to deal with these challenges based on Petri nets and gray relational analysis in this paper. Specifically, the fuzzy analytic hierarchy process is used to evaluate the failure data of components to handle epistemic uncertainty. Furthermore, the dynamic fault tree of TWCSs is established and converted into a generalized stochastic Petri net to calculate several reliability parameters used for fault diagnosis. Besides, a β factor model is employed to resolve the problem of CCF in TWCSs. In addition, Birnbaum importance measure (BIM), risk achievement worth (RAW) and test cost are considered comprehensively to obtain the optimal diagnostic sequence using an improved gray relational analysis. Finally, a numerical example is presented to demonstrate the efficiency of the proposed fault diagnostic system.

Reliability and importance measure analysis of networks with shared risk link groups

We consider the problem of assessing the reliability and the Birnbaum importance measure of complex networks under the shared link risk group (SRLG) failure scenario. With a view to the fact that SRLG failures can cause a global system breakdown, the reliability and the importance measure analysis is of fundamental importance to the study of critical infrastructures such as sensor and cross-layer networks, supply chains, and other complex systems that support the essential functioning of our society and economy. The mathematical complexity of the reliability and the importance measure calculation implies that one has to rely on approximation techniques, since no analytical method for solving this problem in reasonable computation time is known to exist. This study will build upon the Permutation Monte Carlo paradigm. The major advantage of the proposed solution is that it allows us to obtain reliable estimates of both the network reliability and the Birnbaum importance measure using the same algorithmic machinery. We show that the suggested algorithm is easy to implement and that the method is scalable to meet real-life network sizes.

A Birnbaum Importance and regression analysis based heuristic algorithm for multi-type component assignment problem

In this paper, a new kind of multi-type component assignment problem (MCAP) called the two types of component of component assignment problem (TCAP) is proposed. The problem is to assign two types of components to three types of positions in a system in order to obtain high system reliability. The number of each type of components equals the number of positions in the system where the components can be placed in. A new heuristic algorithm, called the REG-ZK method, based on Birnbaum Importance and regression analysis for solving the new MCAP, is illustrated in the paper. Comprehensive numerical experiments on small systems and large systems are conducted to evaluate the optimization effect of the method. Compared to the enumeration and randomization method, the REG-ZK method proves to be applicable and efficient with good optimization quality.

A heuristic for a special kind of multi-type component assignment problem

The multi-type component assignment problem (MCAP) is to assign more than one type of components to positions in the system to maximize system reliability. This paper proposes a two-stage Birnbaum importance-based local search heuristic to address a special kind of MCAP where positions in the system can accept up to two types of components. To evaluate the performance of the heuristic, comprehensive simulation experiments are conducted across different types of systems. The results demonstrate the heuristic’s efficiency and applicability. It shows that the Birnbaum importance is also promising in solving MCAPs.

Importance Measure of Equipment Task Based on Operational Dependency of SoS

In order to evaluate the mission success of system of systems (SoS) and to develop maintenance strategies to meet mission requirements of SoS, an importance measure method of equipment task based on operational dependency of SoS is proposed. The operational dependency network of SoS is constructed based on FDNA, and the nodes and dependency relationships in the network are determined. According to the Markov process, the reliability model of a system function is constructed, and the operability level and probability of each node in the network are obtained. Meanwhile, the algorithm of Birnbaum importance measure is introduced to effectively quantify the impact of operational dependency on the task importance of each equipment system in SoS. Finally, the feasibility and effectiveness of this method is verified by a case study.

Research of Multi-objective Component Assignment Problem for Lin/con/k/n System Considering Cost

Component assignment problem (CAP) is widely used in engineering systems, which is investigated for enhancing the system performance by assigning switchable components to several positions. However, the traditional CAP does not consider the cost factor and has limitations for improving the system reliability. Therefore, this paper focus on a multi-objective CAP for Lin/con/k/n system to find the cost-efficient maintenance scheme. Firstly, a multi-objective mathematical optimization model is developed with the aim of maximizing the system reliability and minimizing maintenance cost, which has been proved to be a Non-deterministic polynomial hard problem and should be computed by heuristics. Secondly, a comprehensive maintenance method is adopted to improve the system reliability, which integrates improving the system reliability with changing the permutation of components. To evaluate the contribution of the component reliability on both system reliability and maintenance cost, the multi-objective Birnbaum importance (MOBI) is derived. Finally, MOBI is introduced into the non-dominated sorting genetic algorithm-II (NSGA-II) to solve the optimization model. The numerical experiments for several Lin/con/k/n Systems show that MOBI is available to solve CAP considering cost, and MOBI-based-NSGA-II algorithm is more efficient to obtain higher system reliability with lower maintenance cost.

On the Use of Importance Measures in the Reliability of Inventory Systems, Considering the Cost

In order to maximize inventory benefits or minimize costs, reliability and cost of inventory control models need to be identified and analyzed. These importance measures are one important approach to recognize and evaluate system weaknesses. However, importance measures have fewer applications in inventory systems’ reliability. Considering the cost, this paper mainly discusses the reliability change of performance parameters with the importance measures in inventory systems. The calculation methods of differential importance and Birnbaum importance are studied in the inventory control model with shortages. By comparing the importance values of various parameters in the model, the optimization analysis of the inventory model can be used to identify the key parameters, so as to effectively reduce the total inventory cost. The importance order and the identification of key parameters are helpful to increase the operational efficiency of the inventory control and provide effective methods for improving the inventory management. Lastly, a case study with a shortage and limited inventory capacity is used to demonstrate the proposed model.

Research on multiple‐state industrial robot system with epistemic uncertainty reliability allocation method

AbstractReliability allocation of industrial robot (IR) system is one of the important means to improve its whole life cycle, reduce maintenance cost, and characterize weak subsystems. The IR system is not only very complex but also has strong customization; meanwhile, its sample data are small, resulting in unclear degeneration and failure. Based on the above two epistemic uncertainties, a new methodology called multiple‐state IR system reliability allocation method with epistemic uncertainty (MIRS‐RAM‐EU) is proposed. First, the Dempster‐Shafer (D‐S) evidence theory is used to quantify the epistemic uncertainty. Then, the Kolmogorov differential equations of MIR's subsystems are calculated. The reliability index of MIRS is allocated based on Birnbaum importance degree theory, and the reliability allocation coefficient of each IR subsystem is clearly expressed by this method. Finally, compared with traditional importance allocation method, the MIRS‐RAM‐EU is more efficient and accurate. This method is usefully directive for reliability evaluation of IR.