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

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.

A 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.

In this paper, a different generalized Pólya shock process is proposed for the modeling of dependent competing failure processes. Dependent competing failure processes are prevalent in numerous systems, and the reliability modeling of these processes has attracted considerable attention in recent years. Currently, the arrival of random shocks is usually modeled as Poisson processes or nonhomogeneous Poisson processes, which indicates a constant hazard rate for shock inter-arrival times or varies with time. The generalized Pólya shock process breaks through the above restrictions and not only expands the scope of application of Poisson and nonhomogeneous Poisson shock processes but also effectively describes case of accelerated degradation associated with the history of the system. The dependence between the soft and hard failure processes is highlighted by assuming that the degradation increment scales linearly the shock magnitude; The hard failure threshold levels of the four shock models are linear in the total degradation performance of the system. In four different hard shock failure models, the analytic form of the reliability functions is derived using the full probability formulation. Meanwhile, Monte Carlo simulation is employed to obtain a numerical solution for the system reliability. Finally, numerical examples based on a submarine Christmas-tree type hydraulic power unit are also presented to illustrate the proposed model.

In this article, we presented a reliability assessment method based on dependent competing failure model. In this model, we considered two failure processes: 1) soft failure caused by random degradation process; 2) hard failure caused by random shock process. And these two processes are dependent: 1) The shock process will accelerate degradation process; 2) After a certain number of shocks, the hard failure threshold will decrease; 3) with the degeneration of system, the probability of occurrence of the shock process will increase. In present research, most studies consider that every arriving shock will accelerate the degradation process, but because of the system resistance, not all shocks accelerate the degradation. Taking this into consideration, we research the shock process based on imperfect shock model. Finally, we verified this new method. And the results show that this method we presented is suitable to model the system failure behaviors.

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

In this article, an extended mixed shock model is investigated, in which the system suffers from mutually dependent competing soft failure and hard failure processes. The system studied degrades gradually with time and the number of shocks coming from the environment. A soft failure occurs when the overall degradation amount surpasses the soft failure threshold of the system. The extended mixed shock model is a combination of a system-state-dependent extreme shock model and a system-state-dependent δ shock model. A hard failure occurs when the magnitude of a single shock exceeds the threshold D(t), or an inter-arrival time between shocks is less than the recovery time threshold The mutual dependency between the soft failure and hard failure processes is reflected in the fact that: (1) the external shock will accelerate the degradation process of the system by causing an abrupt increment of its degradation amount; (2) the system degradation amount determines the thresholds of the extreme shock model and the δ shock model. The system fails when a hard failure or a soft failure occurs. By using the stochastic process theory, the reliability expression and some reliability indices of the system are obtained. Some special cases of the model are also discussed. Finally, a case study of the pier columns of a sea bridge is presented to illustrate the developed model.

In this study, an effective dependent competing failure model is proposed for systems suffering from shocks. Under worse system degradation, shocks with the same magnitudes can bring larger sudden degradation increments. However, this relationship was ignored in most existing research. To address this problem, in the proposed failure model, a time-dependent rate is included for the sudden degradation increments by shocks. This time-varying rate is applied for the consideration that system degradation is closely related to operation time. Two dependent competing failure processes, i.e., soft failure and hard failure, are involved in the dependent competing failure model. The distribution of the total sudden degradation increments is then deduced, and its accuracy is verified by Monte Carlo simulation. The developed reliability model is illustrated by the reliability analysis of a microelectromechanical system. The sensitivity analyses of important parameters are also performed. The analysis results show that the proposed time-varying model effectively considers the impact of system degradation on sudden degradation increments, and by using this model, the change of sudden degradation increments can be well reflected under different system performances. These advantages make the reliability model more practical and help achieve more effective maintenance policies.

In 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.

Many systems experience dependent competing failure processes (DCFP) resulting due to degradation processes and random shocks. In some complex systems, the threshold of random shocks will descend because of the degradation processes. According to previous researches, two cases of shock threshold descent will be considered. The first case is the hard failure threshold decent to a lower value when derogation exceeds the critical degradation value. The second case is the hard failure threshold decent continuously with the increasing degradation. In mutually DCFP system, the two cases of hard failure threshold decent will exist simultaneously, so they compete with each other. In this paper, a case of laser lithography machine will be introduced to verify the theory derivation. The Monte Carlo sampling method will be used to sample and simulate the case data to obtain the reliability of the system. The result showed that when shock threshold descent, the reliability of the system drops significantly.

For complex multi-unit systems whose sub-unit suffering multiple dependent competing failure processes (MDCFP) with shifting hard failure threshold, new multiple-component system models were developed in this paper. The previous studies about reliability analysis have focused on a single unit or simple system with s-independent failure processes and failure times. The new models are different from previous studies by extending unit-level degradation model to the system level. In this paper, each component in the system can be invalid owing to a hard failure process or a soft failure process. These failure processes mentioned-above are not only competing but also dependent and whichever happens first, the component fails. Moreover, the hard failure threshold can change due to the increment of the total degradation. Then, the reliability models for series, parallel, series-parallel system were derived respectively. Finally, numerical examples about Micro-electro-mechanical System (MEMS) are illustrated to verify the developed models and the results are effective. These models could be applied in MEMS or used in many other similar systems.

To identify the incidence of and common causes for cochlear implant revision. Retrospective case series. Operative records were reviewed for all cases of revision cochlear implantation from 1992 to 2006. The causes for reimplantation were classified as hard device failure, soft device failure, exposure/infection, receiver/stimulator migration, and electrode migration. Manufacturers' failure analysis of explanted devices was likewise determined. Eight hundred and six cochlear implants were performed during the study period including 44 (5.5%) revision procedures. The revision rate was 7.3% for children and 3.8% for adults and reached statistical significant difference. The most common reasons for revision were device failure (78%; 55% hard failure, 23% soft failure) followed by electrode migration (9%) and receiver/stimulator migration (7%). Manufacturers' analysis of failed devices revealed loss of hermetic seal and cracked cases to be the most common causes of failure. Bench analysis of 5/10 explanted devices that were soft failures demonstrated identifiable device defects. Revision cochlear implant surgery is an infrequent occurrence. Its incidence appears to be higher in children than in adults, although in this series does not appear to be due to increased wound complications, infections, or trauma. Explanted implants that have soft failure as the etiology may have demonstrable defects on bench testing.

This paper focuses on system reliability analysis with dependent competing failure process due to soft failure and hard failure. Some new probabilistic methods based on cumulative shock model and nonlinear Wiener process under different shifting thresholds situation are obtained. Considering that nonlinearity exists extensively in practice, the continuous soft failure process is governed by random effected nonlinear Wiener process. Firstly, reliability evaluation models for hard failure and soft failure are obtained under the cumulative shock, respectively. Furthermore, some system reliability models under different shifting thresholds situation are studied, in which failure threshold will decrease after a certain number of shocks. A real numerical example about fatigue crack growth dataset is carried out to demonstrate the proposed procedure. Numerical results indicate that both random shocks and shifting threshold have significant effect on system reliability. Finally, some sensitivity analysis are also been given.

Modeling dependent competing failure processes with degradation-shock dependence

In this paper, we develop a novel selective maintenance framework for optimizing the reliability or economic performance of a multi-component system subject to multiple failure modes. We classify the failure modes into soft failures and hard failures (possibly dependent). Soft failures are defined as occurring when a degradation process under condition monitoring surpasses a predefined threshold while hard failures are spontaneous failures that cannot be monitored. To optimize the system performance, different levels of maintenance actions on multiple components are considered. In particular, imperfect maintenance actions reduce the effective age and degradation level of a component while increasing the component’s frailty. We solve the optimization problem using standard Differential Evolution (DE) and Genetic Algorithm (GA) heuristics. A numerical example shows that the proposed selective maintenance framework provides an effective tool for making the optimal maintenance decisions by considering hard failures and the correlation among degradation processes.

Optimal maintenance policy for multicomponent systems with periodic and opportunistic inspections and preventive replacements