Competing failure analysis considering cascading functional dependence and random failure propagation time

Functional dependence (FDEP) exists in many real‐world systems, where the failure of one component (trigger) causes other components (dependent components) within the same system to become isolated (inaccessible or unusable). The FDEP behavior complicates the system reliability analysis because it can cause competing failure effects in the time domain. Existing works have assumed noncascading FDEP, where each system component can be a trigger or a dependent component, but not both. However, in practical systems with hierarchical configurations, cascading FDEP takes place where a system component can play a dual role as both a trigger and a dependent component simultaneously. Such a component causes correlations among different FDEP groups, further complicating the system reliability analysis. Moreover, the existing works mostly assume that any failure propagation originating from a system component instantaneously takes effect, which is often not true in practical scenarios. In this work, we propose a new combinatorial method for the reliability analysis of competing systems subject to cascading FDEP and random failure propagation time. The method is hierarchical and flexible without limitations on the type of time‐to‐failure distributions for system components. A detailed case study is performed on a sensor system used in smart home applications to illustrate the proposed methodology.     

A new combinatorial model for deterministic competing failure analysis

Components in many engineering and industrial systems can experience propagated failures, which not only cause the failure of the component itself but also affect other components, causing extensive damage to the entire system. However, in systems with functional dependence behavior where failure of a trigger component may cause other components (referred to as dependent components) to become unusable or inaccessible, failure propagation originating from a dependent component could be isolated if the corresponding trigger component fails first. Thus, a time-domain competition exists between the failure propagation effect and the failure isolation effect, which poses a great challenge to the system reliability modeling and analysis. In this work, a new combinatorial model called competing binary decision diagram (CBDD) is proposed for the reliability analysis of systems subject to the competing failure behavior. In particular, special Boolean algebra rules and logic manipulation rules are developed for system CBDD model generation. The corresponding evaluation algorithm for the constructed CBDD model is also proposed. The proposed CBDD modeling method has no limitation on the type of component time-to-failure distributions. A memory system example and a network example are provided to demonstrate the application of the proposed model and algorithms. Correctness of the proposed method is verified using the Markov method.     

A Bayesian framework for accelerated reliability growth testing with multiple sources of uncertainty

Reliability growth tests are often used for achieving a target reliability for complex systems via multiple test‐fix stages with limited testing resources. Such tests can be sped up via accelerated life testing (ALT) where test units are exposed to harsher‐than‐normal conditions. In this paper, a Bayesian framework is proposed to analyze ALT data in reliability growth. In particular, a complex system with components that have multiple competing failure modes is considered, and the time to failure of each failure mode is assumed to follow a Weibull distribution. We also assume that the accelerated condition has a fixed time scaling effect on each of the failure modes. In addition, a corrective action with fixed ineffectiveness can be performed at the end of each stage to reduce the occurrence of each failure mode. Under the Bayesian framework, a general model is developed to handle uncertainty on all model parameters, and several special cases with some parameters being known are also studied. A simulation study is conducted to assess the performance of the proposed models in estimating the final reliability of the system and to study the effects of unbiased and biased prior knowledge on the system‐level reliability estimates.     

Reliability modeling for multistage systems subject to competing failure processes

In this paper, a novel multistage reliability model is provided as systems are often divided into many stages according to system degradation characteristics. Multistage hard failure (caused by random shock) process (MHFP) and multistage soft failure (caused by random shock and continuous degradation) process (MSFP) are introduced to describe the competing failure processes, where either the MSFP or MHFP would break down the system. The shock processes impact the system in three ways: (1) fatal load shocks cause hard failure immediately in the hard failure process; (2) time shocks cause a hard failure threshold changing; (3) damage load shocks cause degradation level increasing in the soft failure process. In this paper, a density function dispersion method is carried out to address the multistage reliability model, and the effectiveness of the proposed models is demonstrated by reliability analysis with the one-stage model. Finally, the multistage model is applied to a case study, the degradation process is divided into three stages, and the hard failure threshold can be transmitted twice. The proposed model can be applied in other multistage situations, and the calculation method can satisfy the accuracy requirements.     

A novel framework for the reliability modelling of repairable multistate complex mechanical systems considering propagation relationships

Due to the propagation, amplification, and concatenation in a failure process, the reliabilities of repairable multistate complex mechanical systems (RMCMSs) may be affected by a significant fluctuation due to a small exception associated with a reliability indicator. Focused on the problems arising from the lack of propagation relationships among fault modes, functional components, and failure causes in conventional reliability models, a novel framework for reliability modelling is proposed to comprehensively analyse the reliabilities of RMCMSs. First, the reliability models are abstracted as weighted and directed networks with five layers. Second, an improved failure mode and effects analysis (IFMEA) method combined with the D‐number method and VIKOR approach is presented to determine the importance of reliability nodes. Third, a cut set of the reliability model is generated by any exception of a reliability indicator by considering the propagation relationships, and the reliability sensibility index is defined to characterize the fluctuations in system reliability. The effectiveness of the proposed framework is demonstrated in an actual reliability modelling application. As an intuitive method, the proposed framework inherits the advantages of conventional models but overcomes the drawbacks of these existing methods. Therefore, this method can be flexibly and efficiently used in the reliability modelling of RMCMSs. Moreover, the approach provides a foundation for comprehensive and dynamic reliability analysis and the failure mechanism mining of RMCMSs, and it can be used in other engineering applications.     

Reliability assessment for systems suffering common cause failure based on Bayesian networks and proportional hazards model

The Bayesian network (BN) is an efficient tool for probabilistic modeling and causal inference, and it has gained considerable attentions in the field of reliability assessment. The common cause failure (CCF) is simultaneous failure of multiple elements in a system under a common cause, and it is a common phenomenon in engineering systems with dependent elements. Several models and methods have been proposed for modeling and assessment of complex systems with CCF. In this paper, a new reliability assessment method is proposed for the systems suffering from CCF in a dynamic environment. The CCF among components is characterized by a BN, which allows for bidirectional reasoning. A proportional hazards model is applied to capture the dynamic working environment of components and then the reliability function of the system is obtained. The proposed method is validated through an illustrative example, and some comparative studies are also presented.     

Application of discrete‐time Bayesian network on reliability analysis of uncertain system with common cause failure

With the increasing complexity of engineering systems, reliability analysis and evaluation of systems with traditional methods can't meet practical engineering requirements. Based on limited experimental conditions, lack of data, complex structure models, insufficient cognitive abilities, and many other issues, people have to consider many uncertain factors in system reliability research. Besides, common cause failure (CCF) has become an important factor of system failure. In this paper, a discrete‐time Bayesian network (DTBN) associated with an eight‐rotor unmanned aerial vehicle (UAV) system is presented to discuss above problems. In this approach, the system is assumed as a two‐state system. After that, interval analysis theory is employed to deal with uncertainty. We consider the four sets of auxiliary propellers in the auxiliary power group as a 3/8 voting system, and β factor model is used to process CCF in the auxiliary power group. The proposed methods prove the validity of proposing interval analysis theory to solve uncertain problems and it is necessary to consider reducing or avoiding CCFs in system.     

Reliability modeling for competing failure processes considering degradation rate variation under cumulative shock

Most systems experience both random shocks (hard failure) and performance degradation (soft failure) during service span, and the dependence of the two competing failure processes has become a key issue. In this study, a novel dependent competing failure processes (DCFPs) model with a varying degradation rate is proposed. The comprehensive impact of random shocks, especially the effect of cumulative shock, is reasonably considered. Specifically, a shock will cause an abrupt degradation damage, and when the cumulative shock reaches a predefined threshold, the degradation rate will change. An analytical reliability solution is derived under the concept of first hitting time (FHT). Besides, a one-step maximum likelihood estimation method is established by constructing a comprehensive likelihood function. Finally, the reasonability of the closed form reliability solution and the feasibility and effectiveness of the proposed DCFPs modeling methodology are demonstrated by a comparative simulation study.     

A multi-mode failure boundary exploration and exploitation framework using adaptive kriging model for system reliability assessment

Various adaptive reliability analysis methods based on surrogate models have recently been developed. A multi-mode failure boundary exploration and exploitation framework (MFBEEF) was proposed for system reliability assessment using the adaptive kriging model based on sample space partitioning to reduce computational cost and use the characteristics of the failure boundary in multiple failure mode systems. The efficiency of the adaptive construction of kriging model can be improved by using the characteristics of the center sample of the small space to represent the characteristics of all samples in the small space. This method proposes a failure boundary exploration and exploitation strategy and a convergence criterion based on the maximum failure probability error for a system with multiple failure modes to adaptively approximate the failure boundary of a system with multiple failure modes. A multiple-failure-mode learning function was used to identify the optimal training sample to gradually update the kriging model during the failure boundary exploration and exploitation stages. In addition, a complex failure boundary-oriented adaptive hybrid importance sampling method was developed to improve the applicability of the MFBEEF method to small failure probability assessments. Finally, the MFBEEF method was proven to be effective using five system reliability analysis examples: a series system, a parallel system, a series–parallel hybrid system, a multi-dimensional series system with multiple failure modes, and an engineering problem with multiple implicit performance functions.     

Analysis of correlated multivariate degradation data in accelerated reliability growth

Modern engineering systems have become increasingly complex and at the same time are expected to be developed faster. To shorten the product development time, organizations commonly conduct accelerated testing on a small number of units to help identify failure modes and assess reliability. Many times design changes are made to mitigate or reduce the likelihood of such failure modes. Since failure-time data are often scarce in reliability growth programs, existing statistical approaches used for predicting the reliability of a system about to enter the field are faced with significant challenges. In this work, a statistical model is proposed to utilize degradation data for system reliability prediction in an accelerated reliability growth program. The model allows the components in the system to have multiple failure modes, each associated with a monotone stochastic degradation process. To take into account unit-to-unit variation, the random effects of degradation parameters are explicitly modeled. Moreover, a mean-degradation-stress relationship is introduced to quantify the effects of different accelerating variables on the degradation processes, and a copula function is utilized to model the dependency among different degradation processes. Both a maximum likelihood (ML) procedure and a Bayesian alternative are developed for parameter estimation in a two-stage process. A numerical study illustrates the use of the proposed model and identifies the cases where the Bayesian method is preferred and where it is better to use the ML alternative.     

A Dependent Competing Risks Model for Technological Units Subject to Degradation Phenomena and Catastrophic Failures

This paper proposes a dependent competing risks model for the reliability analysis of technological units that are subject both to degradation phenomena and to catastrophic failures. The paper is mainly addressed to the reanalysis of real data presented in a previous work, which refer to some electronic devices subject to two failure modes, namely the light intensity degradation and the solder/Cu pad interface fracture, which in previous papers, were considered independent. The main reliability characteristics of the devices, such as the probability density functions, the cause‐specific cumulative distribution function and hazard rate of each failure mode in the presence of both modes, are estimated. Likewise, the fraction of failures caused by each failure mode during the whole life of the devices or their residual life is derived. Finally, the results obtained under the proposed dependent competing risks model are compared to those obtained in previous papers. Copyright © 2015 John Wiley & Sons, Ltd.     

Impacts of networking effects on software reliability growth processes: A multi‐attribute utility theory approach

Software reliability growth models, which are based on nonhomogeneous Poisson processes, are widely adopted tools when describing the stochastic failure behavior and measuring the reliability growth in software systems. Faults in the systems, which eventually cause the failures, are usually connected with each other in complicated ways. Considering a group of networked faults, we raise a new model to examine the reliability of software systems and assess the model's performance from real‐world data sets. Our numerical studies show that the new model, capturing networking effects among faults, well fits the failure data. We also formally study the optimal software release policy using the multi‐attribute utility theory (MAUT), considering both the reliability attribute and the cost attribute. We find that, if the networking effects among different layers of faults were ignored by the software testing team, the best time to release the software package to the market would be much later while the utility reaches its maximum. Sensitivity analysis is further delivered.     

System Reliability with Multiple Failure Modes and Time Scales

Lifetime of some systems can be measured based on multiple time scales. For instance, the lifetime of an airplane may be affected by its mileage or number of landings. Furthermore, most systems are exposed to competing risks. In this regard, time scales can accelerate the failure mechanism of these systems. In this paper, the behavior of systems is investigated under competing risks and multiple time scales. The time scales follow independent Poisson processes. As it is not straight forward obtaining closed‐form relations for the system reliability, we have provided a parametric upper bound. Also, the upper bound can be tightened by considering an error function. The error function can be built by regression on a sample containing real values of system reliability for given time units. Performance of the upper bound is studied in two numerical examples and a case study. Results show that the obtained upper bound is very tight. Copyright © 2015 John Wiley & Sons, Ltd.     

Uncertain process–based reliability and maintenance modeling for systems under mutually dependent degradation and shock processes

For the systems that experience competing failure processes, an uncertain process–based degradation model is developed to describe the systems. The competing degradation process is composed of internal continuous degradation and external shocks, and the mutual dependence between them is considered. When the magnitude of the internal degradation exceeds the threshold, the soft failure occurs. While for the shock processes involving the randomness and the subjective information, we adopt the uncertain random renewal reward process to characterize it. Hard failure occurs when the damage of the shock process exceeds the strength threshold of the system. By using the belief reliability metric, the reliability of the degraded system is defined as the chance measure that neither soft failure nor hard failure occurs. And the effect of the degradation-shock dependence on the system reliability is performed by the parametric studies. Then the proposed degradation model is introduced into the preventive maintenance strategy to minimize the average maintenance cost. Using the microelectromechanical systems as an example, the effectiveness of the constructed degradation model and maintenance strategy is illustrated, and the proposed model can characterize the system degradation process in a superior way to the stochastic process model. These methods can be applied to other similar degraded systems and provide support for maintenance decisions.     

Application of Bayesian Methods for Age‐Dependent Reliability Analysis

In this article, the authors present a general methodology for age‐dependent reliability analysis of degrading or ageing components, structures and systems. The methodology is based on Bayesian methods and inference—its ability to incorporate prior information and on ideas that ageing can be thought of as age‐dependent change of beliefs about reliability parameters (mainly failure rate), when change of belief occurs not only because new failure data or other information becomes available with time but also because it continuously changes due to the flow of time and the evolution of beliefs. The main objective of this article is to present a clear way of how practitioners can apply Bayesian methods to deal with risk and reliability analysis considering ageing phenomena. The methodology describes step‐by‐step failure rate analysis of ageing components: from the Bayesian model building to its verification and generalization with Bayesian model averaging, which as the authors suggest in this article, could serve as an alternative for various goodness‐of‐fit assessment tools and as a universal tool to cope with various sources of uncertainty. The proposed methodology is able to deal with sparse and rare failure events, as is the case in electrical components, piping systems and various other systems with high reliability. In a case study of electrical instrumentation and control components, the proposed methodology was applied to analyse age‐dependent failure rates together with the treatment of uncertainty due to age‐dependent model selection. Copyright © 2013 John Wiley & Sons, Ltd.     

Reliability assessment models for dependent competing failure processes considering correlations between random shocks and degradations

This article develops reliability models for systems subject to two dependent competing failure processes, considering the correlation between additional damage size on degradation in soft failure process and stress magnitude of shock load in hard failure process, both of which are caused by the same kth random shock. The generalized correlative reliability assessment model based on copulas is proposed, which is then extended to three different shock patterns: (1) δ‐shock, (2) m‐shock, and (3) m‐run shocks. There are some statistical works to be introduced in reliability modeling, including data separation of total degradation amount, inferring the distribution of amount of aging continuous degradation at time t, and fitting copula to the specific correlation. The developed reliability models are demonstrated for an application example of a micro‐electro‐mechanical system.     

Special issue: Reliability management of complex system

Nowadays,reliability is moving toward interdisciplinary research with ever-increasing connotations for full life-cycle system management,including system design,analysis,modeling,test,operation,optimization,etc.Meanwhile,complex systems,such as transportation system,power system,communication system and other various critical infrastructure systems,have posed a big challenge,which attracts great attention both in theory and application.Characterized by nonlinear interaction,emergent response,and high dimensional coupling,the complex systems are in the face of extremely high uncertainty and vulnerability.Therefore,failure of these complex systems could cause even more dramatic cascading impacts,leading to huge losses of life and property.All these realities put forward more urgent requirements for the fundamental theory and specific application of reliability management of complex systems.     

Identifying emerging failure phenomena in complex systems through engineering data mapping

In the past, standard reliability and risk approaches have sufficed to identify the dominant causes of failure in forensic analyses, and the dominant risk contributors for proactive risk investigations. These techniques are particularly applicable when individual or even simple common failure events of a similar type dominate the analysis. However, nowadays due to increased understanding of the ‘simple’ mechanisms and the increasing complexity of the systems we build, failures in highly dependable systems arise from unexpected interactions between subsystems and the external and internal environment.

Engineering data analysis is the process of data collection and investigation from a variety of perspectives, alternatively dissecting it into its underlying (yet often unknown) patterns; this process is becoming ever more necessary as systems become more complex. Some of the techniques employed are slicing the data sets according to known underlying variables, or overlaying data gathered from different perspectives, or imbedding data into previously established logical or phenomenological structures.

This paper addresses the issues involved in visualizing patterns in data sets by providing examples of interesting maps from the past, indicating some of the maps currently in use, and speculating on how these visual maps might be developed further and used in the future to discover problems in complex systems before they lead to failure. Guidance is proposed as to how to explore and map data from different technical perspectives in order to evoke potentially significant patterns from reliability data. The techniques presented have been developed by combining approaches to common cause failure (CCF) classification with multidimensional scaling (MDS) to produce a new method for exploratory engineering data mapping.     

Set theoretic formulation of performance reliability of multiple response time‐variant systems due to degradations in system components

This paper presents a design stage method for assessing performance reliability of systems with multiple time‐variant responses due to component degradation. Herein the system component degradation profiles over time are assumed to be known and the degradation of the system is related to component degradation using mechanistic models. Selected performance measures (e.g. responses) are related to their critical levels by time‐dependent limit‐state functions. System failure is defined as the non‐conformance of any response and unions of the multiple failure regions are required. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory can be manifest by approximating the probability of the unions by second‐order bounds. Further, for numerical efficiency probabilities are evaluated by first‐order reliability methods (FORM). The presented method is quite different from Monte Carlo sampling methods. The proposed method can be used to assess mean and tolerance design through simultaneous evaluation of quality and performance reliability. The work herein sets the foundation for an optimization method to control both quality and performance reliability and thus, for example, estimate warranty costs and product recall. An example from power engineering shows the details of the proposed method and the potential of the approach. Copyright © 2006 John Wiley & Sons, Ltd.