Competing Failure Processes Research Articles

Reliability Analysis for Degradation-Shock Processes with State-Varying Degradation Patterns Using Approximate Bayesian Computation (ABC) for Parameter Estimation

The degradation of products is an integral part of their life-cycle, often following predictable trajectories. However, sudden, unexpected events, termed ’shocks’, can substantially alter these degradation paths. Shocks can significantly influence the pace of degradation, leading to accelerated system failure. Moreover, they may initiate changes in degradation patterns, transitioning from linear to non-linear or random trajectories. To address this challenge, we present a novel multi-state reliability model for competing failure processes that account for degradation-shock dependencies by considering the state-varying degradation pattern. The degradation process is divided into s-states, with each state treated according to its pattern based on the time-transform Wiener process. The reliability function is derived based on soft failure caused by continuous degradation involving the s-states, the sudden increase in degradation caused by random shocks, and hard failure due to some shock processes. Additionally, we performed a sensitivity analysis to determine which parameters have the most significant impact on product reliability. Due to the complexity of the likelihood function, we adopted the ABC method to estimate the model parameters. A simulation study and a practical application with micro-electro-mechanical systems (MEMS) degradation results are used to demonstrate the efficiency and effectiveness of the proposed approach.

Statistical Reliability Evaluation of a k-out-of-n: G System Subject to Competing Failure Process

Many systems in real life can experience failure in two categories such as a soft failure process or a catastrophic failure process. Therefore, failure processes are competing since either failure can cause the system to fail. In this study, a reliability analysis of a k-out-of-n G system which is exposed to a competing failure process is investigated based on different distribution assumptions for a shock magnitude, a damage size, and a wear volume due to continuous degradation. Besides, unlike the research in this field, in a more statistical frame, the reliability results are also examined in detail by considering normal distribution assumption. The reliability results are discussed based on a change in parameters, number of shocks and time. Graphical illustrations are also provided to observe the parameter effects explicitly on the reliability of the system.

Novel condition-based opportunistic maintenance policy for series systems with dependent competing failure processes

This paper investigates a novel condition-based opportunistic maintenance model for a two-component series system. The system comprises two non-identical components, that is, Component 1 and Component 2, suffering from shocks with different intensities. The two components are subject to dependent competing failure processes, that is, soft and hard failures. The component fails whichever type of failure process occurs. At each inspection, the replacement decision for components is made according to the condition of both components. In addition, when Component 1 is preventively replaced and Component 2 reaches the opportunistic maintenance threshold, opportunistic maintenance (OM) is implemented on Component 2. The optimal inspection interval, preventive replacement (PR) threshold, and OM threshold are derived by minimizing the long-run expected maintenance cost rate. Finally, the superiority of the proposed maintenance model is verified by an illustrative example.

Modeling coupling impacts of self-healing mechanisms and dynamic environments on systems subject to dependent failure processes

Modern smart products are endowed with the capability to autonomously repair damage from random shocks, thereby highlighting the critical necessity to incorporate this self-healing attribute in reliability assessments. This paper investigates periodically inspected self-healing systems that are exposed to dependent competing failure processes within dynamically evolving environments. The impact of environmental changes is manifested in that both the natural degradation process and the self-healing behavior are governed by distinct laws in varying environments. Explicit formulas for the system reliability and availability are analytically derived using the stochastic process theory, and their correctness is verified by proposed simulation algorithms respectively. Meanwhile, the inspection period is optimized by minimizing the long-run average cost rate. Lastly, a practical example of semiconductor lasers is applied to showcase the application of the presented methods. The sensitivity analysis reveals that increasing the self-healing time threshold or the shock arrival rate can improve the system performance while lowering the long-run average cost rate.

Dependent Competing Failure Processes in Reliability Systems.

This paper deals with a reliability system hit by three types of shocks ranked as harmless, critical, or extreme, depending on their magnitudes, being below H1, between H1 and H2, and above H2, respectively. The system's failure is caused by a single extreme shock or by a total of N critical shocks. In addition, the system fails under occurrences of M pairs of shocks with lags less than some δ (δ-shocks) in any order. Thus, the system fails when one of the three named cumulative damages occurs first. Thus, it fails due to the competition of the three associated shock processes. We obtain a closed-form joint distribution of the time-to-failure, shock count upon failure, δ-shock count, and cumulative damage to the system on failure, to name a few. In particular, the reliability function directly follows from the marginal distribution of the failure time. In a modified system, we restrict δ-shocks to those with small lags between consecutive harmful shocks. We treat the system as a generalized random walk process and use an embellished variant of discrete operational calculus developed in our earlier work. We demonstrate analytical tractability of our formulas which are also validated, through Monte Carlo simulation.

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.

A Multi-Degradation Model Subject to Dependent Competing Failure Processes

A Multi-Degradation Model Subject to Dependent Competing Failure Processes

Reliability modeling based on multiple wiener degradation-shock competing failure process and dynamic failure threshold

Given multiple degradation failure and shock failure processes within the complex system during operation, a reliability model that combines the degradation-shock competing failure process and dynamic failure threshold is modeled. The Wiener process with random effects is considered the degradation process model, which includes random effects to account for the heterogeneity among system units. Then, the extreme shock model with a dynamic failure threshold is used to depict the random shock. The copula function is carried out to illustrate the correlation between multiple degradation processes, the reliability model is constructed further. To verify the application of this model, a numerical case and a micro-electro-mechanical system comprising two micro-mechanical resonators are employed. The parameter sensitivity of the proposed model is analyzed. The study results show that the reliability model, which combines the Wiener process with random effects and the dynamic failure threshold, more accurately reflects the actual operational state of the complex system.

A novel solution for comprehensive competing failure process considering two-phase degradation and non-Poisson shock

A novel solution for comprehensive competing failure process considering two-phase degradation and non-Poisson shock

Reliability Optimization of Uncertain Random Systems Combined With Burn-In and Preventive Maintenance

It is well-known that uncertain random systems suffered from a competing failure process have been applied in industrial applications. Extending previous studies, we optimize system cost combined with burn-in and preventive maintenance strategies. A system in burn-in process is only subject to uncertain continuous stationary degradation process while it experiences competitive degradation and shock processes simultaneously in the period of operation. The dependence assumes that shocks can accelerate the degradation by uncertain additional degradation shifts. A reliability optimization model for uncertain random systems is proposed where the reliability index is defined as a chance measure, and the optimal burn-in parameters and maintenance observation time are derived by the genetic algorithm. Finally, we conclude with a numerical example to illustrate the application of burn-in and maintenance methods.

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.

Reliability Analysis of Mining Machinery Pick Subject to Competing Failure Processes With Continuous Shock and Changing Rate Degradation

Efficient mining machinery operation is essential for coal mining enterprises to reduce production costs, improve production efficiency, and maximize profits. As a key consumable part of mining machinery, the reliability of the pick directly determines the operational performance and service life of the machinery. During the mining process, the pick can be affected by natural wear and tear caused by the coal and rock and load shocks caused by the gangue and faults—that is, the result of the competing influence of soft failure caused by natural wear and tear and hard failure caused by random load shocks. At the same time, because the gangue and faults have a certain volume and hardness, a random load shock may last for a certain period of time, producing different acceleration effects on the pick wear under different hardness conditions. In this article, the reliability modeling of the pick competing failure process under random load shocks was studied by considering the influence of continuous shocks and the accelerated degradation at changing rates for different shock durations on the pick wear. First, the pick degradation model under random load shocks was established by considering the natural wear degradation, instantaneous shock degradation, and accelerated degradation at changing rates for different shock durations. Second, the pick reliability model under the competing failure mode was established on this basis. Finally, a numerical experiment and an effectiveness analysis of the pick reliability model were conducted based on the engineering data. The results showed that the competing failure reliability model of the pick considering continuous shocks and a changing degradation rate was more in line with engineering practice, which is of great significance for pick design optimization and improved reliability.

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: combining self-healing characteristics and dynamic failure thresholds

ABSTRACT The failure threshold of a product is not always constant when affected by random shocks. Thus, this paper establishes a reliability model that combines dynamic failure threshold and self-healing characteristics, which are subjected to the competing failure process. Soft failure is caused by degradation exceeding the soft failure threshold, and hard failure occurs because of random shocks. Degradation consists of natural degradation and a degradation increment caused by shocks. The failure thresholds and degradation rate will also be affected by random shocks. Moreover, the self-healing characteristics in the degradation process, together with the degradation increment, will affect the whole degradation process. When the random shock arrives, the soft and hard failure thresholds will change simultaneously. Based on the above factors, the corresponding analytical expressions of reliability models under different shock models are derived. To confirm the effectiveness of the proposed model, an example of micro-engine is used to verify the constructed reliability model. The influences of self-healing and dynamic thresholds in micro-engines on reliability are studied. The effects of self-healing and thresholds on the models are analyzed, which can provide study basis for the maintenance and replacement of product.

Reliability Modeling of Products with Self-Recovery Features for Competing Failure Processes in Whole Life Cycle

In light of the increasing demand for the reliability analysis of self-recovery products, with features of limited storage period and multistage degradation, a reliability evaluation model in whole life cycle is proposed. The degradation process comprises one storage phase and two working phases. On the basis of the idea of competitive failure, the shock process and the feature of self-recovery were introduced into the model. Furthermore, the problem of it being difficult to add variables to a reliability model is solved with the use of the Stieltjes integral. The influences of the parameters of model reliability are analyzed, and the results demonstrate that the new model could adequately describe the competing failure process. The model also exhibited certain feasibility and theoretical reference values.

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.