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.     

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.     

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.     

Reliability analysis for multi-state systems subject to distinct random shocks

This paper analyzes the competing and dependent failure processes for multi-state systems suffering from four typical random shocks. Reliability analysis for discrete degradation is conducted by explicitly modeling the state transition characteristics. Semi-Markov model is employed to explore how the system vulnerability and potential transition gap affect the state residence time. The failure dependence is specified as that random shocks can not only lead to different abrupt failures but also cause sudden changes on the state transition probabilities, making it easier for the system to stay at the degraded states. Reliability functions for all the exposed failure processes are presented based on the corresponding mechanisms. Interactions between different failure processes are also taken into account to evaluate the actual reliability levels in the context of degradation and distinct random shocks. An illustrative example of a multi-state air conditioning system is studied to demonstrate how the proposed method can be applied to the engineering practice.     

Time-based replacement policies for a fault tolerant system subject to degradation and two types of shocks

A single component nonrepairable system suffering from both an internal stochastic degradation process and external random shocks is investigated in this paper. More specifically, the Wiener process with a positive drift coefficient is introduced to describe the gradual deterioration and the arrival number of external shocks is counted with a nonhomogeneous Poisson process (NHPP). Meanwhile, fault tolerant design is incorporated into the stochastically deterioration system so as to protect it from shock failures to some extent and is consummately addressed via a generalized m − δ shock model. From the actual engineering point of view, external shocks are typically classified into two distinct categories in this current research, that is, a minor shock (Type I shock) increasing the damage load on current degradation level and a traumatic shock (Type II shock) resulting in system catastrophic failure immediately. The closed-form expression of system survival function is derived analytically and is viewed as the generalization of existing reliability function for systems subject to dependent and competing failure processes. Based on which, two time-based maintenance (TBM) policies including an age replacement model and a block replacement model are scheduled, where the expected long-run cost rate (ELRCR) in each model is, respectively, optimized to seek the optimal replacement interval. In the illustrative example part, a subsea blowout preventer (BOP) control system is arranged to validate the theoretical results numerically. To compare which policy is more profitable under different conditions, the relative gain on optimal maintenance cost rate of the two TBM policies is presented.     

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.     

Reliability Analysis and Condition‐based Maintenance for Failure Processes with Degradation‐dependent Hard Failure Threshold

In this study, we introduce reliability models for a device with two dependent failure processes: soft failure due to degradation and hard failure due to random shocks, by considering the declining hard failure threshold according to changes in degradation. Owing to the nature of degradation for complex devices such as microelectromechanical systems, a degraded system is more vulnerable to force and stress during operation. We address two different scenarios of the changing hard failure threshold due to changes in degradation. In Case 1, the initial hard failure threshold value reduces to a lower level as soon as the overall degradation reaches a critical value. In Case 2, the hard failure threshold decreases gradually and the amount of reduction is proportional to the change in degradation. A condition‐based maintenance model derived from a failure limit policy is presented to ensure that a device is functioning under a certain level of degradation. Finally, numerical examples are illustrated to explain the developed reliability and maintenance models, along with sensitivity analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

Degradation‐shock‐based Reliability Models for Fault‐tolerant Systems

Reliability modeling of fault‐tolerant systems subject to shocks and natural degradation is important yet difficult for engineers, because the two external stressors are often positively correlated. Motivated by the fact that most radiation‐induced failures are contributed from these two external stressors, a degradation‐shock‐based approach is proposed to model the failure process. The proposed model accommodates two kinds of failure modes: hard failure caused by shocks and soft failure caused by degradation. We consider a generalized m–δ shock model for systems with fault‐tolerant design: failure occurs if the time lag between m sequential shocks is less than δ hours or degradation crosses a critical threshold. An example concerning memory chips used in space is presented to demonstrate the applicability of the proposed model. Copyright © 2015 John Wiley & Sons, Ltd.     

A failure mechanism consistency test method for accelerated degradation test

Accelerated degradation test (ADT) is generally used to accelerate degradation processes in products to estimate their lifespan and to assess their reliability in a short period of time. How to perform the failure mechanism consistency test is crucial in the application of the ADT method. Existing failure mechanism consistency test methods assume that degradation rates among individual products are the same. However, these methods do not take degradation dispersions caused by manufacturing technologies into consideration. To address this issue, a failure mechanism consistency test method for ADT based on the activation energy invariant method and the likelihood ratio test is proposed. First, a degradation modeling method for ADT is introduced. Then, the logarithmic maximum likelihood function values of the degradation models are estimated based on the two-step maximum likelihood estimation (MLE) method. Finally, the decision rule is proposed based on the likelihood ratio test. The method mentioned above is, then, used on the real degradation data of carbon-film resistors and bullet O-rings, and its effectiveness is verified. Furthermore, based on the failure mechanism change point in RTV5370 siloxane rubbers, the simulated degradation data are degenerated to compare the proposed method with the method not considering individual differences in different ADT programs and degradation dispersions.     

Reliability modeling for consecutive k-out-of-n: F systems with local load-sharing components subject to dependent degradation and shock processes

Traditional k-out-of-n models assume that the components are independent, while recent research studies assume that the components are dependent caused by global load-sharing characteristic. In this paper, we investigate the consecutive k-out-of-n systems with dependent components by local load-sharing characteristic. The work load and shock load on failed components will be equally shared by adjacent components, so the components tend to fail consecutively. Consequently, the components degradation processes may be diverse, since their degradation rate (dependent on work load) and abrupt degradation (dependent on shock load) become unequal because of local load-sharing effect. Furthermore, the system failure will be path-dependent on the failure sequences of components, which results in that the same system states may have different system failure probabilities. This new dependence makes the system reliability model more complex. In this work, an analytical model that can be solved numerically is derived to compute the reliability with this complex dependence. The developed model is demonstrated by a cable-strut system in the suspension bridge. The results show that the reliability decreases significantly when the new dependence is considered.     

Reliability analysis of shock-based deterioration using phase-type distributions

This paper presents a model to estimate the lifetime of degrading infrastructure systems subject to shocks based on the family of Phase-type (PH) distributions. In particular, the paper focuses on damage accumulation when both the inter-arrival time of shocks and their sizes are random. PH distributions are applied to approximate any probability distribution with positive support; furthermore, their matrix-geometric properties allow to handle problems involving the calculation of convolutions (e.g., sum of shock sizes). The proposed PH shock model relaxes the identically distributed assumption for the inter-arrival times and/or shock sizes. Besides, the model provides easy-to-evaluate expressions for important reliability quantities such as the density function and the moments of the lifetime, and the mean and moments of the cumulative shock deterioration at any time. In order to fit data or theoretical distributions to PH, the paper compares and discusses two PH fitting algorithms: the Moment Matching (MM) and the Expectation Maximization (EM) methods in terms of accuracy, computational efficiency and the available information of the random variables to fit. Then, it provides an algorithm for the reliability estimation of infrastructures along with a study of its accuracy and efficiency; the results show acceptable execution times for most practical applications. Finally, the use of PH to handle degradation is illustrated with several examples of engineering interest; i.e., deterioration due to crack growth, corrosion, aftershocks sequences, among others.     

δ冲击条件下相关性竞争失效过程的系统可靠性建模

研究系统受到δ冲击时,考虑系统自然退化和冲击两个竞争性失效过程间具有相关性时,系统可靠性的建模问题。相关性一方面表现为冲击造成系统退化量的增加,另一方面表现为系统的自然退化程度对冲击结果的影响。假设系统因冲击而失效的过程是δ冲击过程,通过系统自然退化过程和冲击过程的分布函数,导出了系统的可靠度函数,建立了系统可靠度模型的一般形式,并给出一种特例的具体形式,最后利用文献中的具体参数进行仿真,以验证模型的正确性和有效性。     

Reliability evaluation and opportunistic maintenance policy based on a novel delay time model

The delay time concept is widely adopted in literature to model the two‐stage failure process of most industrial systems which can be divided into normal stage (from new to an initial point of a defect) and defective stage (from defect arrival point to failure). Most existing delay time models assume that the normal and defective stages are independent. A generalized delay time model is proposed in this paper by considering the dependence between the normal and defective stages which is reflected in the fact that they share the same external shock process. According to the definition of shot‐noise process, external shocks will incur random hazard rate increments in the two stages. The failure state is self‐announcing, whereas the defective state can only be detected by block‐based inspection or opportunistic inspection offered by unexpected shutdown due to unavoidable external factors. The system is correctively replaced upon the occurrence of a system failure or preventively replaced at the detection of a defective state. Based on the stochastic failure model and maintenance policy, this paper evaluates system reliability performance and average long‐run cost rate via a Markov‐chain based approach. Finally, a case study on a steel convertor plant is given to demonstrate the applicability of the proposed model.     

Integrated Approach for Field Reliability Prediction Based on Accelerated Life Testing

ABSTRACT

To predict field reliability using analytical modeling, several important reliability activities should be conducted, including failure mode and effect analysis, stress and usage condition analysis, physics of failure analysis, accelerated life testing and modeling, and cumulative damage modeling if needed. With all of the mentioned activities and results, the field reliability confidence limit can be predicted at a certain confidence level, if a modeling framework can be established. This article builds such an integrated process and comprehensive modeling framework, especially with cumulative damage rules when the certain field stresses are random processes. An engineering product is provided as an application to illustrate the effectiveness of proposed method.     

Preventive maintenance policy of single‐unit systems based on shot‐noise process

This paper develops reliability and maintenance models for a single‐unit system subject to hard failures under random environment of external shocks. Motivated by the observations of shot‐noise process in practice, the impact of shock damage on system failure behavior is characterized by random hazard rate increments. To remove such negative impact, imperfect preventive repair is performed periodically, and preventive replacement is performed after several repairs. Considering the joint effects of both random shocks and imperfect repair on the system hazard rate, we derive recursive equations for the system reliability function. Furthermore, we investigate the optimal maintenance policy that minimizes the expected cost per unit time of the system. The applicability of the reliability and maintenance model is validated by a case study on a wind turbine system.     

The set-theory method for systems reliability of structures with degrading components

The times and frequencies of inspection, maintenance and replacement in structural systems are complicated by uncertain degradation rates of structural characteristics. Although degradation work at the component, or single failure mode level, is ongoing, this paper presents a method for assessing systems reliability where failure events may be described by time-variant parallel and/or series systems. Herein the models for the degradation rates contain random variables and time. For multiple failure modes and a sequence of discrete times, set theory establishes the true incremental failure region that emerges from a safe region. Probabilities via Monte-Carlo simulation require only time-invariant calculations. The cumulative failure distribution is the summation of the incremental failure probabilities. A practical implementation of the theory requires only two contiguous times. Error analysis suggests ways to predict and minimize errors so the method appears sufficiently accurate for engineering applications. Two structures with elastic-brittle material and time-invariant loads show the details of the method and the potential of the approach. It is shown that the proposed method provides a more realistic and efficient way to predict systems reliability than path-tracing methods that are available in the open literature.     

Engineering‐driven performance degradation analysis of hydraulic piston pump based on the inverse Gaussian process

As a key aircraft component, hydraulic piston pumps must be developed with high reliability. However, collecting failure time data of such pumps for reliability analysis is a big challenge. To save testing time, performance degradation data obtained from degradation tests can be used for quick reliability estimation of hydraulic piston pumps. This paper proposes an engineering‐driven performance degradation analysis method considering the nature of mechanical wear of hydraulic piston pumps. First, the failure mechanism of a type of hydraulic piston pump is investigated. By taking into account the close relationship between the degradation rate and the failure mechanism, an inverse Gaussian (IG) process model with a variable rate is developed to describe the degradation behavior of the pump. Under this model, a Bayesian statistical method is developed for degradation data analysis. The corresponding procedure for model parameter estimation and reliability evaluation is also presented. The proposed degradation analysis method is illustrated using a real experimental data. The results show that the engineering‐driven approach is quite effective in evaluating the lifetime of the hydraulic piston pump and will improve the overall reliability of aircraft operation in the field.     

A novel pseudo‐maximum likelihood estimation method for accelerated degradation tests under Wiener process

For reliability assessment based on accelerated degradation tests (ADTs), an appropriate parameter estimation method is very important because it affects the extrapolation and prediction accuracy. The well‐adopted maximum likelihood estimation (MLE) method focuses on interpolation fitting and obtains results via maximizing the likelihood of the observations. However, a best interpolation fitting does not necessarily yield a best extrapolation. In this paper, therefore, a pseudo‐MLE (P‐MLE) method is proposed to improve the prediction accuracy of constant‐stress ADTs by considering the degradation mechanism equivalence under Wiener process. In particular, the degradation mechanism equivalence is characterized by a mechanism equivalence factor which presents the proportional relationship between degradation rate and variation. Then, the mechanism equivalence factor is determined via a two‐step method. The other model parameters can be estimated by the general MLE method. The asymptotic variances of acceleration factors and the p‐quantile of product failure time under normal condition are adopted to compare the statistical properties of the proposed method and the general MLE approach. Numerical examples show that the novel P‐MLE method may not achieve a maximum likelihood but can provide more benefits regarding prediction accuracy enhancement especially when the sample size is limited.     

Reliability analysis for accelerated degradation data based on the Wiener process with random effects

On the basis of the principle of degradation mechanism invariance, a Wiener degradation process with random drift parameter is used to model the data collected from the constant stress accelerated degradation test. Small-sample statistical inference method for this model is proposed. On the basis of Fisher's method, a test statistic is proposed to test if there is unit-to-unit variability in the population. For reliability inference, the quantities of interest are the quantile function, the reliability function, and the mean time to failure at the designed stress level. Because it is challenging to obtain exact confidence intervals (CIs) for these quantities, a regression type of model is used to construct pivotal quantities, and we develop generalized confidence intervals (GCIs) procedure for those quantities of interest. Generalized prediction interval for future degradation value at designed stress level is also discussed. A Monte Carlo simulation study is used to demonstrate the benefits of our procedures. Through simulation comparison, it is found that the coverage proportions of the proposed GCIs are better than that of the Wald CIs and GCIs have good properties even when there are only a small number of test samples available. Finally, a real example is used to illustrate the developed procedures.