Dependent Competing Failure Processes Research Articles

Dependent Competing Failure Processes in Reliability Systems

Dependent Competing Failure Processes in Reliability Systems

Joint optimization of maintenance and spares inventory policy for a series-parallel system considering dependent failure processes

This paper investigates the joint optimization of condition-based opportunistic maintenance and spare inventory policies for a series-parallel system consisting of software and components. Software failure follows a homogeneous Poisson process. Components are subject to mutually dependent competing failure processes. When the software failure occurs, an opportunistic inspection will be implemented for the components. Besides the maintenance policy, the (s, S) inventory policy is applied for components. The maintenance and order decisions will be made according to the conditions of the components and inventory level at each inspection. The state transition probabilities and expected sojourn times can be obtained by the formulated semi-Markov decision process. The optimal inspection interval, the preventive replacement threshold of the component, and the order point can be derived by minimizing the expected average cost rate. Finally, the effectiveness and superiority of the proposed joint optimization model are verified by an illustrative example.

Reliability assessment models for competing failure processes with two types of correlative thresholds

AbstractThe two dependent competing risks are soft failure due to aging degradation and fragmentation caused by shocks and hard failure due to spring breakage caused by the same shock process. Considering the complexity of the product itself and the instability of the working environment, this study proposed a generalized reliability model for systems experiencing dependent competing failure processes (DCFPs) of degradation and random shocks, which considered two kinds of DCFP: (1) shock process could affect soft failure thresholds; (2) degradation process could affect hard failure thresholds. In case (1), we considered the effect that a cumulative number of shocks above a certain magnitude could have on the change in the soft failure threshold. In case (2), we considered not only the shock process's impact on the soft failure threshold but also the total degradation (including continuous degradation and sudden degradation caused by shock) on the hard failure threshold. The model captures the features that the shocks experienced by the system affect the degradation process, accelerating the system degradation and causing soft failures; the degradation process of the system affects the shock process, making the system more susceptible to failure from external shocks. Finally, an example using micro‐electro‐mechanical systems devices illustrates the effectiveness of the proposed approach with sensitivity analysis.

Reliability modeling for dependent competing failure processes considering random cycle times

AbstractIn this paper, a novel model is proposed for the reliability analysis of systems subjected to dependent competing failure processes at random cycle times. The model takes into account the effect of random cycle time on degradation rate and hard failure threshold. Random cycle time is the time required for the system to complete a run. With the continuous operation of the system in a period of cycle time, the degradation rate of the system is accelerated, and its resistance to random shocks is decreased, so the degradation rate and hard failure threshold are supposed to vary with the number of cycles. When the overall degradation exceeds the soft failure threshold, soft failure is triggered. When the shock magnitude is larger than the hard failure threshold, hard failure occurs. Combined with the stress‐strength interference model, the reliability function of the system is derived. Finally, a Micro‐Electro‐Mechanical System is used to verify the validity of the proposed model. The validity of the model is demonstrated by sensitivity analysis.

Modeling for dependent competing failure processes of subsea pipelines considering parameter uncertainty based on dynamic Bayesian network

Leakages in subsea pipelines can have serious environmental and economic consequences, making it essential to develop reliable evaluation methods to prevent failures. Up to now, no comprehensive assessment methods focusing on parameter uncertainty of lifetime distribution functions in the dependent competing failure of subsea pipelines has been developed. This paper proposes a novel method for evaluating the reliability of subsea pipelines with dependent competing failure processes and parameter uncertainty, using dynamic Bayesian network (DBN). The independent variables and dependent variables of physical models are converted into parent nodes and child nodes of DBNs, respectively. Uncertain parameters of the degradation failure and sudden failure equations are denoted by root nodes and assigned to probability distributions in the DBN model. The interaction between degradation failure and sudden failure of subsea pipelines is studied, and two DBNs of competing failure based on variable degradation increment and variable degradation rate are established. Mutual information analysis finds out the important parameters affecting the reliability of subsea pipelines. The parameters in degradation failure model have little effects on the failure of subsea pipelines at first, but their impact is increasing over time. According to 3-sigma rule, three different situations are defined to perform uncertainty analysis of parameters in the developed DBN model. It shows that increasing the values of uncertain parameters, the reliability of the subsea pipelines would have obvious decrease earlier.

A generalized system reliability model based on survival signature and multiple competing failure processes

Degradation-based system reliability analysis has been extensively conducted, but the components in a system are assumed to experience similar degradation and shock processes, neglecting actual failure mechanisms. However, multiple types of components in a system may work under different operational conditions and break down due to different failure mechanisms. Hence, a new generalized reliability model is proposed for systems with arbitrary structures experiencing multiple degradation and shock processes, including pure degradation processes (DPs), independent and dependent competing failure processes (CFPs). In this work, the Tweedie exponential-dispersion (TED) process is utilized to describe multiple degradation processes of the components, which contains the Wiener, Gamma, inverse Gaussian, and other processes as special cases. Based on multiple DPs and CFPs, a generalized reliability model is established by utilizing the structure analysis method, the survival signature, which allows the proposed method to be applied to various structural systems. Finally, an example of an automotive braking system with four types of components experiencing multiple DPs and CFPs is applied to illustrate the proposed model.

Reliability modeling of dependent competing failure processes based on time‐dependent threshold level δ and degradation rate changes

AbstractA new reliability model for dependent competing failure processes is proposed. The reliability model uses the generalized Polya process (GPP) to model the arrival of shocks and considers the degradation rate change. Most systems fail due to performance degradation and external environment shocks. On the one hand, soft failure occurs when the total amount of degradation, including continuous degradation and sudden degenerate increment, exceeds the soft failure threshold level. On the other hand, hard failure occurs when the time interval between two successive shocks is less than the recovery time. As time progresses and natural degradation, the time for a system to recover from damage due to shocks tends to increase gradually. However, conventional models usually regard recovery time as a constant, unrealistic in many practical situations. For this purpose, an increment‐dependent shock process is considered. A hard failure reliability model with recovery time is calculated using the GPP to describe the shock arrival process. On this basis, combined with the deduced soft failure function, the analytical solution of the reliability model is obtained. Finally, a numerical example based on the micro‐electro mechanical systems is conducted to illustrate the effectiveness of the proposed model.

Optimal condition‐based maintenance policy for systems with mutually dependent competing failure

AbstractIn this paper, a novel condition‐based maintenance (CBM) policy for systems with mutually dependent competing failure processes (DCFPs) is studied. The cumulative random shocks contribute to the increased rate of degradation, meanwhile, the hard failure threshold is reduced when the amount of degradation reaches a threshold. The degradation process is simulated by a non‐stationary Gamma process and random shocks are modeled as a homogeneous Poisson process. Preventive replacement (PR) and corrective replacement (CR) are accounted for in the developed maintenance strategy. The optimal periodic inspection interval, PR threshold, and the number of cumulative random shocks can be derived by minimizing the average long‐term maintenance cost rate. In the end, a numerical case is applied to demonstrate the availability of the developed models.

Modeling coupled effects of dynamic environments and zoned shocks on systems under dependent failure processes

In this paper, we focus on systems suffering from multiple dependent competing failure processes under coupled effects of zoned shocks and dynamic environments. A reliability and maintenance model is developed for a real-time inspected system subject to linear degradation and random shocks, in which the internal degradation rate and shock arrival rate are affected by a dynamic environment. Shocks are classified into four zones based on their magnitude, including the safety zone, probability damage zone, damage zone, and fatal zone. Explicit formulas for calculating reliability indexes of systems are derived, including the reliability function, availability function, and steady-state availability. Meanwhile, simulation algorithms for calculating these reliability indexes are provided based on the Monte Carlo method, which is beneficial to the verification of the analytical method. Finally, a case study of micro-engine systems is given to illustrate the proposed models and obtained results, exhibiting that zoned shocks and dynamic environments have a significant effect on system performance.

Reliability analysis for [formula omitted]-out-of-[formula omitted](G) systems subject to dependent competing failure processes

In this paper, reliability analysis for k-out-of-n(G) systems suffering from interdependent competing failure processes is conducted. The system consisting n different components fails if and only if the number of operating components is less than k. Each component degrades linearly with time. A soft failure happens if the total degradation performance exceeds the soft failure threshold of the corresponding component. All components in the system are influenced by random shocks which arrive according to a homogeneous Poisson process. The hard failure of a component occurs when a single shock with large shock load arrives (extreme shock model), or the accumulated shock load of a sequential shocks surpasses the hard failure threshold of the component (cumulative shock model). A component fails if a hard failure or a soft failure occurs. Since the external shock may cause an abrupt degradation increment to a component, the hard failure and soft failure processes of each component are relevant. Moreover, because a shock has impact on all working components in the system, the failure processes of these components are also relevant. Using multivariate analysis methods and techniques, the closed forms of the reliability functions of the k-out-of-n(G) system under the extreme shock model and the cumulative shock model are obtained. Monte Carlo simulation is used as an auxiliary method to compute the system reliability. As a numerical example, the reliability of the micro-electro-mechanical systems is calculated to illustrate the developed theory.

A degradation-shock dependent competing failure processes based method for remaining useful life prediction of drill bit considering time-shifting sudden failure threshold

• A dependent competing failure model is established for drill lifetime estimation. • The effect of wear degradation on the sudden failure threshold is considered. • Reliability functions and useful life expression of the drill are derived. • A drilling experiment is provided for validating the proposed method. Accurate remaining useful life (RUL) prediction of the drill bit is central to ensuring the processing quality of products and enhancing processing safety and reliability. However, the majority of current methods are confined to considering the wear degradation during the drilling and ignore the combined effect of wear degradation and random shock on RUL. Therefore, it is difficult to the sudden failure prediction of the drill bit. To address this limitation, a degradation-shock dependent competing failure processes (DCFPs) based method considering time-shifting sudden failure threshold is proposed in this paper for RUL prediction. First, a degradation-shock DCFPs model is established based on the processing characteristics of the drill bit. Further, the expressions of reliability function and useful life taking into account the time-shifting sudden failure threshold are derived. Then, based on the Bayesian method, a two-step maximum likelihood estimation (MLE) is designed for parameter estimation, and the crucial parameters are updated utilizing a local gaussian importance resampling particle filter. Finally, a carbon composite laminate drilling experiment is provided for demonstration. Experimental results demonstrate the superiority of the proposed method for drill bit RUL prediction, especially when the drill bit is chipped.

Reliability modeling for dependent competing failure processes based on planar mechanism

Considering the influence of external random shock on the kinematic accuracy of mechanism, a new reliability model of dependent competing failure processes (DCFP) is proposed in this paper. The kinematic accuracy of the mechanism is limited by the original errors such as the dimension error and joint clearance error, and it is also affected by aging and wear-out during service life, thus eventually leading to functional failure. Meanwhile, according to the magnitude of the external random shock, the random shock has different effects on the degradation process of the mechanism. In this study, a DCFP model with accuracy degradation process and multi-type mixed shock is considered. The time-dependent kinematic accuracy reliability model of the planar mechanism is established based on the Gamma degradation theory, effective length model, mechanism kinematic error theory and the fourth moment technique. Moreover, the magnitude of random shock is divided into different regions when the extreme shock, cumulative shock, and δ-shock on mechanism reliability are considered. Finally, a numerical example of the pantograph mechanism is conducted to demonstrate the feasibility and effectiveness of the proposed model. The results show that the kinematic accuracy reliability of the pantograph mechanism reduces with the increasing of wearing capacity and external shocks. According to sensitivity analysis, an effective way to improve the reliability of the planar mechanism is to optimize its strength of the mechanism. The proposed method can be used to evaluate the reliability of planar mechanisms with dependent competing failure modes.

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

AbstractMost 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.

Reliability analysis of dependent competing failure processes with time-varying δ shock model

The dependent competing failure process model has received increasing research attention in recent years due to its essential role in describing system reliability. For the δ shock model, as a main type of shock in dependent competing failure process, the system fails if the interval of time between two sequential shocks is less than a threshold δ. As the operation of systems, the aging effect will gradually increase. Thus, systems affected by shocks need more time to recover from damages. In the time-varying δ shock model, if damage shocks occur, the degradation rate and δ value will change multiple times simultaneously. Three failure processes consisting of a soft process induced by a degradation process and two sudden failure processes due to random shocks. Sudden failure processes include fatal shocks and damaged shocks. Damaged shocks affect systems in three different ways: (1) impacting systems by causing the degradation increment, (2) increasing the degradation rate of systems, and (3) impairing systems’ performance by increasing the δ value. A real-world example of a microelectromechanical system is presented to show the applicability of the reliability model. Sensitivity analysis is evaluated to demonstrate how parameters affect reliability.

Reliability model of series systems with multiple shock sources subject to dependent competing failure processes using phase-type distribution

ABSTRACT In this paper, we introduce the concept of a series system with two components and three shock sources considering degradation to build a reliability model. Sources 1 and 2 affect components 1 and 2, respectively. Source 3 covers both components. Both components are subject to dependent competing failure processes (DCFPs). A general reliability model of the n-component series system with m-shock sources subject to DCFPs is derived. The phase-type distribution method is applied to calculate the reliability of the hard failure process. The time lag among shocks follows the continuous phase-type distribution (PH c ). The lifetime and system reliability properties are discussed based on the phase-type distribution. The dependence of shock sources is also considered according to the proposition of phase-type distribution (PH). Finally, an application example and sensitivity analysis of micro-electro-mechanical systems (MEMS) oscillators subject to various shock models are presented to illustrate the developed reliability models.

Modeling dynamic environment effects on dependent failure processes with varying failure thresholds

Devices usually fail due to multiple dependent competing failure processes resulting from internal degradation and random shocks, whose behavior may vary in different environments. This paper focuses on systems suffering from randomly occurring shocks described by Poisson processes and internal degradation characterized by linear path models simultaneously, where the wear rate, shock arrival rate, shock load size, and shock damage amount are modulated by Markovian environments, especially the hard failure threshold differs in distinct environments. Reliability analysis is performed where analytical formulas and simulation algorithms for computing reliability indexes of systems are provided, such as the reliability function. Two maintenance models are developed for systems, including a real-time maintenance policy where the computation formula for the availability function is derived, and a periodic inspection policy in which an optimization model is proposed to find the optimal inspection interval that minimizes the average long-run cost rate. Finally, an illustrative example of floating offshore wind turbine systems is given to demonstrate possible applications of the developed models and proposed methods.

Reliability modeling for multi-component system subject to dependent competing failure processes with phase-type distribution considering multiple shock sources

In this article, a reliability model for the multi-component system subject to dependent competing failure processes considering multiple shock sources is presented. For a single component, soft failure occurs when the sum of natural degradation and instantaneous degradation increment is greater than the soft failure threshold. The soft failure reliability model is established using the degradation-threshold interference model. The hard failure model is developed using the phase-type distribution survival function. Then, system reliability is derived based on the history of shocks from all shock sources. Finally, the reliability model is demonstrated by a numerical example.

Reliability analysis of load-sharing man-machine systems subject to machine degradation, human errors, and random shocks

This paper considers a load-sharing man-machine system with multiple man-machine units (MMUs) subject to machine degradation, human errors, and random shocks. Human errors affect the machine that the person operates in a MMU and contribute to dependent competing failure processes (DCFPs) of unit (DCFPsU): soft and hard failure processes. Random shocks affect all MMUs and contribute to DCFPs of system (DCFPsS): unit soft/hard failure one after another until the system failure and common cause failures. In addition, once a MMU fails, more workloads are shared on surviving MMUs due to load-sharing characteristic, which increase not only machine degradation rates but also human error intensities. We incorporate human errors into reliability analysis besides degradation processes and random shocks and develop an analytical reliability model of load-sharing man-machine system. A Poisson-type human error model considering the effects of workload is proposed first. To model the DCFPsU, DCFPsS, and load-sharing characteristic, conditional distributions of DCFPsU and conditional probability density functions of MMU failures are investigated. A system reliability model is then developed based on total probability formula through analytical derivation. Finally, a load-sharing 2-out-of-3:G lathe system and small-, medium- and large-scale examples are implemented to illustrate the effectiveness of the reliability model.

Reliability assessment of a system with multi‐shock sources subject to dependent competing failure processes under phase‐type distribution

AbstractFor a system affected by multiple shock sources, the system usually experiences not only one failure process. This paper develops a reliability model for systems with multi‐shock sources subject to dependent competing failure processes (DCFPs). DCFPs consist of two failure modes: soft and hard failures. Multiple shock sources act on the system as follows: assuming there are m shock sources in total, the kth shock source works on the system at first until the system fails, and then the next shock source re‐acts on the system. Unlike the methods in other papers, the phase‐type distribution is used to build the hard failure reliability model in this paper. We consider the time lag of impacts and assume that the impact magnitudes do not exceed the hard failure threshold as an element in the transition matrix. At the same time, consider these two situations to establish a reliability model. In addition, we divide shock magnitudes into three areas: dead, nondeadly, and safe zones. An application example of a micro‐engine is studied to describe the availability of the developed reliability model. And we conduct the sensitivity analysis to exemplify the influence of the performance of the micro‐engine with parameter changing. With the proposed model, the reliability analysis is more efficient with multi‐shock sources subject to DCFPs

Optimal Warranty Policy for Consumer Electronics with Dependent Competing Failure Processes

This study considers warranties for consumer electronics with multiple dependent competing failure processes, including minor, over-degradation and catastrophic failure. Furthermore, the two alternative warranty programs are investigated: (1) a long-range warranty at a fixed lump-sum price and (2) a monthly warranty plan that can be either extended for the next month by continuous purchasing or terminated at the end of the current month. A designed dynamic programming approach is employed to obtain optimal solutions for warranty programs. Moreover, consumers with different attitudes toward risk are taken in consideration, and sensitivity analyses are performed to investigate the effects that the related factors have on profit. Integrating all issues, the study proposes extended warranty programs of lump-sum or monthly payment to different risk attitudes consumers with different attitudes toward risk with consideration of multiple dependent competing failure processes. The results indicate that high repair and replacement costs favor the monthly warranty program for firms. In addition, when there are more risk averse consumers in a market, there will be fewer purchases of a monthly warranty program, and it would thus be more profitable for firms to offer the one year warranty program.