Many mechanical systems are subject to degradation and random shock processes, which are dependent and competing. The two processes are soft failure process and hard failure process, either of which occurs will cause the system to fail. In this paper, a hard failure model of the gear system is established based on the Stress-Strength Interference model, and a soft failure model of the system is also proposed. To consider the dependence between the two failure processes, the copula function is adopted. Then, the reliability model of the system subject to degradation and shocks is developed, and an expression of the system reliability is derived. Finally, a planetary gear transmission system is taken as a numerical example to demonstrate the effectiveness of the proposed model, which is considered a k-out-of-n system experiencing the processes of degradation and random shocks. Moreover, the effect of model parameters on reliability is evaluated through sensitivity analysis.

In this paper, a system reliability model subject to Dependent Competing Failure Processes (DCFP) with phase-type (PH) distribution considering changing degradation rate is proposed. When the sum of continuous degradation and sudden degradation exceeds the soft failure threshold, soft failure occurs. The interarrival time between two successive shocks and total number of shocks before hard failure occurring follow the continuous PH distribution and discrete PH distribution, respectively. The hard failure reliability is calculated using the PH distribution survival function. Due to the shock on soft failure process, the degradation rate of soft failure will increase. When the number of shocks reaches a specific value, degradation rate changes. The hard failure is calculated by the extreme shock model, cumulative shock model, and run shock model, respectively. The closed-form reliability function is derived combining with the hard and soft failure reliability model. Finally, a Micro-Electro-Mechanical System (MEMS) demonstrates the effectiveness of the proposed model.

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.

Many systems are usually subjected to the combined effects of degradation and random shocks at the same time. Their failures are the competitive result of soft failure caused by degradation and hard failure caused by shocks. For operating machinery, wear failure is the main failure mechanism, and the machine is also subject to shock during the wear process. This paper proposes a new generalized surface wear model in combination with dependent competing failure processes; this proposed model is different from the other wear model with independent wear increments. As a typical mechanical structure, worm gears and worms are subjected to the combined effect of two failure mechanisms: soft failure caused by performance degradation, and hard failure caused by shocks. Meanwhile, it is necessary to consider the competitiveness and correlation of these two failure mechanisms. The interdependent competitive failure model is used to describe the failure of operating machinery. In this study, the extended Archard model is used to calculate the wear depth of the tooth surface, and the wear model is established through the wear threshold. The relationship between tooth surface wear depth and duty cycle, sliding speed, and contact stress is analyzed. An iterative algorithm is used to derive a nonlinear time-varying wear degradation model considering contact stress and sliding velocity. Comparing the calculation results with the Monte Carlo simulation method, the model has high accuracy and describes the mechanism of soft and hard failures, and the mutual dependence of the two failure mechanisms has an important effect on reliability. Numerical examples are presented to illustrate the developed reliability models, along with sensitivity analysis.INDEX TERMS Archard model, dependent competing failure, hard failure threshold, system reliability, wear degradation.

No abstract

For 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

No abstract

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.