Reliability analysis for systems with interactive competing degradation processes and mixed shock effects

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.

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.

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.

The 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.

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.

In reliability literature, shock models and multi-state systems have both been discussed extensively. Shock models have attracted a great deal of attention due to their important role in engineering systems. In the δ-shock model, a system fails if the interval time between two successive shocks is less than a pre-fixed threshold δ. In this study, a new version of mixed δ-shock models is defined by combining δ-shock and extreme shock models, thus causing the failure of a multi-state system in two ways: first, when k interarrival times between two consecutive shocks with magnitude larger than the critical threshold γ are in and second, when the interarrival time between two consecutive shocks is less than δ 1. The survival function is obtained for three cases: (i) system’s lifetime, (ii) when the system performs completely, and (iii) when the system performs partially. A Monte Carlo simulation study is carried out to validate the analytical results established here.

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.

Reliability evaluation of Markov renewal shock models with multiple failure mechanisms

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

EDUNDANCY management for the purpose of enhaning reliability is performed in three stages: failure detection in which the presence of a failure is discovered, failure isolation in which the failed instrument is identified, and failure correction in which a suitable reorganization of the system is accomplished. Many different failure detection, isolation, and correction (FDIC) algorithms for inertial navigators have appeared in the literature. Eight FDIC algorithms for the dodecahedron configuration *'2 of six strapdown gyros and 6 strapdown accelerometers have been compared in a previous study.3 We shall limit our discussion to the strapdown dodecahedron inertial navigation case although the methods to be developed are applicable to other cases in which the outputs of redundant devices are combined by least squares. All 8 of the FDIC algorithms previously mentioned require a finite period of time to isolate a failure. If the failure causes a large enough error in the instrument output, it can be isolated in less than a minor cycle time so that no erroneous output is used and will be referred to as a hard failure. A failure that causes a smaller error in the instrument output cannot be isolated in less than a minor cycle time so that erroneous output is used. It will be referred to as a soft failure. Thus soft failures degrade system performance while hard failures do not. An algorithm is desired that retroactively removes the effects of soft failures from the navigational solution at the time that the failure is finally isolated. Ideally, only the errors contributed by the instrument since the time of failure would be removed. However the time of failure is unknown, so all of the errors contributed by the failed instrument since initialization of the navigate mode will be removed. Since the FDIC cannot distinguish hard from soft failures, all of the error of the failed instrument is removed even if, in the case of hard failures, no error was introduced by the failure itself. Through the action of the least squares estimator, elimination of the error of one instrument magnifies the effects of the errors of the remaining unfailed instruments to the level they would have reached if the failed instrument had never been present. However this increase in error will usually be less

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 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.

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.

Generalized mixed [formula omitted]-shock models with random interarrival times and magnitude of shocks

Degradation process has been successfully applied in modeling the deterioration failure modes like wearout and corrosion for reliability assessment. However, deterioration failure modes are different from each other due to different physical mechanisms with different products operated under different environments, and specific attentions should be paid for non-standard circumstances. As it is well known, the failure with fatigue crack is composed of two sequential stages: the crack initiation and the crack propagation. The lifetime distribution models have been applied for the crack initiation, and the degradation process is well modeled by degradation process. Intuitively, a lifetime delayed degradation process (LDDP) would provide a general framework for such typical mixture failure mode composed of hard and soft ones sequentially. In this study, a general reliability inference approach has been proposed for the LDDP based on the maximum likelihood method, with numerical simulations and practical application with real testing data. Furthermore, the inspection planning issue is also studied for LDDP, with the first inspection time addressed which can increase the efficiency of inspection.