A reliability evaluation method for phased-mission system considering multi-mechanism coupling within phases

Due to the difference of environmental stress and system configuration, as well as the coupling between phases, the phased-mission system (PMS) has significant disparity in the failure modes and mechanisms of components in different phases. From the perspective of failure mechanism, an initial independent one will affect or be affected by other failure mechanisms during a task, and eventually leads to the failure of system. Therefore, the coupling of failure mechanisms in PMS is considered in this paper, and the recursive quantitative analysis of coupling from failure mechanism level to system level and phase level are accomplished by means of the basic rules of reliability physics. Furthermore, taking a core circuit from an aircraft electronic system as an example, the reliability modeling and analysis are performed. The results show that after considering the coupling relationship between failure mechanisms within each phase, the reliability and lifetime of components are reduced compared with the mechanism- independence situation, however, the cumulative failure probability of the system is increased. It reveals that it is very important to involve the coupling relationship between failure mechanisms in the reliability analysis of PMS, which can improve the accuracy of the prediction.     

Trading reliability targets within a supply chain using Shapley's value

The development of complex systems involves a multi-tier supply chain, with each organisation allocated a reliability target for their sub-system or component part apportioned from system requirements. Agreements about targets are made early in the system lifecycle when considerable uncertainty exists about the design detail and potential failure modes. Hence resources required to achieve reliability are unpredictable. Some types of contracts provide incentives for organisations to negotiate targets so that system reliability requirements are met, but at minimum cost to the supply chain. This paper proposes a mechanism for deriving a fair price for trading reliability targets between suppliers using information gained about potential failure modes through development and the costs of activities required to generate such information. The approach is based upon Shapley's value and is illustrated through examples for a particular reliability growth model, and associated empirical cost model, developed for problems motivated by the aerospace industry. The paper aims to demonstrate the feasibility of the method and discuss how it could be extended to other reliability allocation models.     

Structural reliability assessment of cracked pipes: The role of probability of detection data

The structural reliability of industrial pipes, including those in the nuclear, oil, and gas industries, has a significant impact on the safety of people and the environment. This work aims to develop a computational structural reliability model method in conjunction with the failure assessment diagram method and the user‐defined probability of detection curves of non‐destructive testing are used. The concept of “reliability factor of a repair” is proposed. Then, the effects of the pipe inspection considering different user‐defined probability of detection curves and different values of the reliability factor of a repair on probability of failure are discussed. The main results include the identification of cases where performing repairs do not guarantee an improved reliability, as well as the consequences of considering the repair as a “perfect process” which result in non‐conservative assessments.     

Random Hazard in Reliability Problems

A class of models for system reliability is presented which (a) introduces the notion of random variability of environment, and hence of instantaneous failure rate or “hazard,” (b) leads to exponentially distributed system time to failure, and to exponentially distributed component time to failure when components are exposed to the environment in isolation, but (c) does not lead to a prediction of series system failure rate based on the usual procedure of adding component failure rates. If the usual procedure is followed, it is shown that underestimates of system reliability are obtained. A simple spares provisioning problem is investigated when such a model is assumed to hold.     

A method for reliability estimation of logical structures

In this paper we give a procedure for estimating the reliability of a structural system when failure data on either the structure, its components, or on both are available. We first develop procedures for structures whose components are assumed to operate independently of each other. We then prove that the reliability estimates thus obtained provide meaningful inequalities for the reliability of the structure when its components are dependent in a specified manner.     

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.     

Optimization of system reliability in the presence of common cause failures

The redundancy allocation problem is formulated with the objective of maximizing system reliability in the presence of common cause failures. These types of failures can be described as events that lead to simultaneous failure of multiple components due to a common cause. When common cause failures are considered, component failure times are not independent. This new problem formulation offers several distinct benefits compared to traditional formulations of the redundancy allocation problem. For some systems, recognition of common cause failure events is critical so that the overall system reliability estimation and associated design resembles the true system reliability behavior realistically. Since common cause failure events may vary from one system to another, three different interpretations of the reliability estimation problem are presented. This is the first time that mixing of components together with the inclusion of common cause failure events has been addressed in the redundancy allocation problem. Three non-linear optimization models are presented. Solutions to three different problem types are obtained. They support the position that consideration of common cause failures will lead to different and preferred “optimal” design strategies.     

Estimation of exponential component reliability from uncertain life data in series and parallel systems

Estimating reliability of components in series and parallel systems from masking system testing data has been studied. In this paper we take into account a second type of uncertainty: censored lifetime, when system components have constant failure rates. To efficiently estimate failure rates of system components in presence of combined uncertainty, we propose a useful concept for components: equivalent failure and equivalent lifetime. For a component in a system with known status and lifetime, its equivalent failure is defined as its conditional failure probability and its equivalent lifetime is its expectation of lifetime. For various uncertainty scenarios, we derive equivalent failures and test times for individual components in both series and parallel systems. An efficient EM algorithm is formulated to estimate component failure rates. Two numerical examples are presented to illustrate the application of the algorithm.     

A comprehensive reliability allocation method for design of CNC lathes

In the design and development of computerized numerical control lathes, an effective reliability allocation method is needed to allocate system level reliability requirements into subsystem and component levels. During the allocation process, many factors have to be considered. Some of these factors can be measured quantitatively while others have to be assessed qualitatively. In this paper, we consider seven criteria for conducting reliability allocation. A comprehensive failure rate allocation method is proposed for conducting the task of reliability allocation. Example data from field studies are used to illustrate the proposed method.     

Research on reliability allocation technology for NC machine tool meta‐action

The reliability of machine tool is getting more and more attention. Reasonable reliability allocation is beneficial to improve the inherent reliability of machine tool. However, the existing reliability allocation methods for machine tool have some limitations. For example, static part is selected as the reliability allocation object of machine tool, which cannot reflect the characteristics “function realized by motion”; factors affecting reliability allocation are not considered comprehensively, weights of experts are treated as the same, and the allocation results are not optimized or the impact of time on enterprise is neglected in the optimization. To solve these problems, a new multiobjective optimization reliability allocation method for machine tool is proposed in this paper. Firstly, the latest achievements about meta‐action are given, and meta‐action is set as the reliability allocation object. Secondly, more reasonable and comprehensive factors affecting reliability allocation are extracted. Thirdly, expert weight coefficient is brought to reduce the subjective impact of expert scoring. Fourthly, time factor is brought to make the optimized allocation results more reasonable and accurate. Finally, a numerical control (NC) machine tool made in China is taken as an example, with a comparison on the reliability allocation results of current methods and proposed method. The results verify the applicability, rationality, and accuracy of the proposed method, which lays a foundation for the subsequent study on the quality characteristics of machine tool based on meta‐action.     

The interval estimation of reliability for probabilistic and non-probabilistic hybrid structural system

The aim of this paper is to improve evaluation of the reliability of probabilistic and non-probabilistic hybrid structural system. Based on the probabilistic reliability model and interval arithmetic, a new model of interval estimation for reliability of the hybrid structural system was proposed. Adequately considering all uncertainties affecting the hybrid structural system, the lower and upper bounds of reliability for the hybrid structural system were obtained through the probabilistic and non-probabilistic analysis. In the process of non-probabilistic analysis, the interval truncation method was used. In addition, a recognition method of the main failure modes in the hybrid structural system was presented. A five-bar statically indeterminate truss structure and an intermediate complexity wing structure were used to demonstrate the new model is more suitable for analysis and design of these structural systems in comparison with the probabilistic model. The results also show that the method of recognition of main failure modes is effective. In addition, range obtained through interval estimation is shown to be more credible than certain results of other reliability models.     

A reliability allocation method for agricultural machinery based on AHP-IFM

In the product design phase, the available product failure data are limited, and the weight allocation method is often used to assign reliability targets to each unit. The integrated factors method (IFM) can calculate the reliability allocation weights considering multiple influencing factors simultaneously, but it cannot reflect the difference in the importance of each factor and each unit. The analytic hierarchy process (AHP) can calculate the relative importance weights of each factor and each unit. Combining the AHP with the IFM can make the IFM more adaptable to the system and more accurate for reliability allocation. However, the current combination method can cause two problems: the invalidation of the influencing factor weights and the imbalance of the unit weights. To address these two shortcomings, the AHP-IFM proposed in this paper introduces a weight weakening factor and exponentially corrects the unit weights for units, which can better apply the relative importance weights of each influencing factor and each unit to the reliability allocation. The effectiveness of the AHP-IFM is verified by comparison with existing methods and data. Finally, an AHP-IFM applicable to agricultural machinery is proposed, and the reliability allocation of a no-till seeder is used as a case to verify the feasibility of the AHP-IFM.     

Multivariate performance reliability prediction in real-time

This paper presents a technique for predicting system performance reliability in real-time considering multiple failure modes. The technique includes on-line multivariate monitoring and forecasting of selected performance measures and conditional performance reliability estimates. The performance measures across time are treated as a multivariate time series. A state–space approach is used to model the multivariate time series. Recursive forecasting is performed by adopting Kalman filtering. The predicted mean vectors and covariance matrix of performance measures are used for the assessment of system survival/reliability with respect to the conditional performance reliability. The technique and modeling protocol discussed in this paper provide a means to forecast and evaluate the performance of an individual system in a dynamic environment in real-time. The paper also presents an example to demonstrate the technique.     

An analytical framework for reliability growth of one-shot systems

In this paper, we introduce a new reliability growth methodology for one-shot systems that is applicable to the case where all corrective actions are implemented at the end of the current test phase. The methodology consists of four model equations for assessing: expected reliability, the expected number of failure modes observed in testing, the expected probability of discovering new failure modes, and the expected portion of system unreliability associated with repeat failure modes. These model equations provide an analytical framework for which reliability practitioners can estimate reliability improvement, address goodness-of-fit concerns, quantify programmatic risk, and assess reliability maturity of one-shot systems. A numerical example is given to illustrate the value and utility of the presented approach. This methodology is useful to program managers and reliability practitioners interested in applying the techniques above in their reliability growth program.     

Development-process-of-nonlinearity-based reliability evaluation of structures

A reliability evaluation approach based on the development process of the structural nonlinearity is presented. The traditional structural system reliability theory for structural safety regarding combination of failure modes is first revisited. It is seen that it stemmed from, and was heavily affected by, the assumption of perfect elasto-plasticity of materials. This will make the number of the failure modes increase in a non-polynomial form against the number of the potential plastic hinges. Moreover, the above methodology does not work appropriately in the case of nonlinearity in general form other than perfect elasto-plasticity, as commonly encountered in engineering practice. Discussions show that total information of the structure is involved in the development process of its nonlinearity, be it a deterministic case or stochastic counterpart. The information needed for reliability evaluation of structures could be extracted, for example, by capturing the probabilistic information of the extreme value of the corresponding response, which could be obtained by using the probability density evolution method. Therefore, the reliability evaluation for structural safety could then be directly evaluated without searching the failure modes. Taking a 10-bar truss as an example, the proposed method is theoretically elaborated and numerically exemplified.     

An integrated methodology for the dynamic performance and reliability evaluation of fault-tolerant systems

We propose an integrated methodology for the reliability and dynamic performance analysis of fault-tolerant systems. This methodology uses a behavioral model of the system dynamics, similar to the ones used by control engineers to design the control system, but also incorporates artifacts to model the failure behavior of each component. These artifacts include component failure modes (and associated failure rates) and how those failure modes affect the dynamic behavior of the component. The methodology bases the system evaluation on the analysis of the dynamics of the different configurations the system can reach after component failures occur. For each of the possible system configurations, a performance evaluation of its dynamic behavior is carried out to check whether its properties, e.g., accuracy, overshoot, or settling time, which are called performance metrics, meet system requirements. Markov chains are used to model the stochastic process associated with the different configurations that a system can adopt when failures occur. This methodology not only enables an integrated framework for evaluating dynamic performance and reliability of fault-tolerant systems, but also enables a method for guiding the system design process, and further optimization. To illustrate the methodology, we present a case-study of a lateral-directional flight control system for a fighter aircraft.     

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 multi-objective discrete reliability optimization problem for dissimilar-unit standby systems

A new methodology for the reliability optimization of a k dissimilar-unit nonrepairable cold-standby redundant system is introduced in this paper. Each unit is composed of a number of independent components with generalized Erlang distributions of lifetimes arranged in a series–parallel configuration. We also propose an approximate technique to extend the model to the general types of nonconstant hazard functions. To evaluate the system reliability, we apply the shortest path technique in stochastic networks. The purchase cost of each component is assumed to be an increasing function of its expected lifetime. There are multiple component choices with different distribution parameters available for replacement with each component of the system. The objective of the reliability optimization problem is to select the best components, from the set of available components, to be placed in the standby system to minimize the initial purchase cost of the system, maximize the system mean time to failure, minimize the system variance of time to failure, and also maximize the system reliability at the mission time. The goal attainment method is used to solve a discrete time approximation of the original problem.      

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.     

APProximate Confidence Limits for the Reliability of Series and Parallel Systems

Suppose a complex mechanism, e.g., a missile, is built up from a number of different types of components, where the reliability of each of the components has been estimated by means of separate tests on each of the components. This paper gives a method for combining such data to determine approximate confidence limits for the reliability of the complete mechanism. More precisely, a method of determining approximate confidence limits for the reliability of “series,” “parallel,” and “seriesparallel” systems is given, based on observed failures of the individual components. It is assumed that the failures are independent, and that failures of a given component follow a binomial distribution with unknown parameter, the component reliability. The large-sample properties of the likelihood-ratio test are then used to construct the appropriate confidence limits for the system reliability.