Qianmei Feng

Reliability and maintenance modeling for systems subjected to multiple dependent competing failure precesses

For complex systems that experience Multiple Dependent Competing Failure Processes (MDCFP), the dependency among the failure processes presents challenging issues in reliability modeling. This article, develops reliability models and preventive maintenance policies for systems subject to MDCFP. Specifically, two dependent/correlated failure processes are considered: soft failures caused jointly by continuous smooth degradation and additional abrupt degradation damage due to a shock process and catastrophic failures caused by an abrupt and sudden stress from the same shock process. A general reliability model is developed based on degradation and random shock modeling (i.e., extreme and cumulative shock models), which is then extended to a specific model for a linear degradation path and normally distributed shock load sizes and damage sizes. A preventive maintenance policy using periodic inspection is also developed by minimizing the average long-run maintenance cost rate. The developed reliability and maintenance models are demonstrated for a micro-electro-mechanical systems application example. These models can also be applied directly or customized for other complex systems that experience multiple dependent competing failure processes.

Reliability Analysis for Multi-Component Systems Subject to Multiple Dependent Competing Failure Processes

For complex multi-component systems with each component experiencing multiple failure processes due to simultaneous exposure to degradation and shock loads, we developed a new multi-component system reliability model, and applied two different preventive maintenance policies. This new model extends previous research, and is different from related previous research by considering an assembled system of degrading components with s-dependent failure times resulting from shared shock exposure. Previous research primarily pertained to a single component or simple system, or systems with s-independent failure processes and failure times. In our new system model, the individual failure processes for each component and the component failure processes are all s-dependent. These models can be applied directly, or customized for many complex systems with multiple components that experience s-dependent competing failure processes. In this model, each component can fail due to a soft failure process, or a hard failure process. These two component failure processes are mutually competing and s-dependent. If one component fails relatively frequently, it is likely that the number of shocks is relatively large, and these shocks impact all components potentially causing them to fail more often as well. Therefore, failure processes of all components are also s-dependent. An age replacement policy and an inspection-based maintenance policy are applied for a system with multiple components. The optimal replacement interval or inspection times are determined by minimizing a cost rate function. The model is demonstrated on several examples.

Reliability and Maintenance Modeling for Dependent Competing Failure Processes With Shifting Failure Thresholds

We present reliability and maintenance models for systems subject to multiple s-dependent competing failure processes with a changing, dependent failure threshold. In our model, two failure processes are considered: soft failure caused by continuous degradation together with additional abrupt degradation due to a shock process, and hard failure caused by the instantaneous stress from the same shock process. These two failure processes are correlated or s-dependent in two respects: 1) the arrival of each shock load affects both failure processes, and 2) the shock process impacts the hard failure threshold level. In previous research, the failure thresholds are fixed constants, which is appropriate for most design and reliability problems. However, the nature of the failure threshold has become a critical issue for certain classes of complex devices. When withstanding shocks, the system is deteriorating, and its resistance to failure is weakening. In this case, it becomes more sensitive to hard failure. In this paper, three cases of dependency between the shock process and the hard failure threshold level are studied. The first case is that the hard failure threshold value changes to a lower level when the first shock is recorded above a critical value, or a generalized extreme shock model. The second case is that the hard failure threshold value decreases to a lower level when the time lag between two sequential shocks is less than a threshold δ, or a generalized δ-shock model. The third case is that the hard failure threshold value reduces to a lower level right after m shocks whose magnitudes are larger than a critical value, or a generalized m-shock model. Based on degradation and random shock modeling, reliability models are developed for these two s-dependent failure processes with a shifting failure threshold. Two preventive maintenance policies are also applied and compared to decide which one is more beneficial. Then a Micro-Electro-Mechanical System example is given to demonstrate the reliability models and maintenance polices.

Reliability modeling for dependent competing failure processes with changing degradation rate

This article proposes reliability models for devices subject to dependent competing failure processes of degradation and random shocks with a changing degradation rate according to particular random shock patterns. The two dependent failure processes are soft failure due to continuous degradation, in addition to sudden degradation increases caused by random shocks, and hard failure due to the same shock process. In complex devices such as Micro-Electro-Mechanical Systems the degradation rate can change when the system becomes more susceptible to fatigue and deteriorates faster, as a result of withstanding shocks. This article considers four different shock patterns that can increase the degradation rate: (i) generalized extreme shock model: when the first shock above a critical value is recorded; (ii) generalized δ-shock model: when the inter-arrival time of two sequential shocks is less than a threshold δ; (iii) generalized m-shock model: when m shocks greater than a critical level are recorded; and (iv) generalized run shock model: when there is a run of n consecutive shocks that are greater than a critical value. Numerical examples are presented to illustrate the developed reliability models, along with sensitivity analysis.

Reliability for systems of degrading components with distinct component shock sets

This paper studies reliability for multi-component systems subject to dependent competing risks of degradation wear and random shocks, with distinct shock sets. In practice, many systems are exposed to distinct and different types of shocks that can be categorized according to their sizes, function, affected components, etc. Previous research primarily focuses on simple systems with independent failure processes, systems with independent component time-to-failure, or components that share the same shock set or type of shocks. In our new model, we classify random shocks into different sets based on their sizes or function. Shocks with specific sizes or function can selectively affect one or more components in the system but not necessarily all components. Additionally the shocks from the different shock sets can arrive at different rates and have different relative magnitudes. Preventive maintenance (PM) optimization is conducted for the system with different component shock sets. Decision variables for two different maintenance scheduling problems, the PM replacement time interval, and the PM inspection time interval, are determined by minimizing a defined system cost rate. Sensitivity analysis is performed to provide insight into the behavior of the proposed maintenance policies. These models can be applied directly or customized for many complex systems that experience dependent competing failure processes with different component shock sets. A MEMS (Micro-electro mechanical systems) oscillator is a typical system subject to dependent and competing failure processes, and it is used as a numerical example to illustrate our new reliability and maintenance models.

Simultaneous Quality and Reliability Optimization for Microengines Subject to Degradation

Micro-electro-mechanical systems (MEMS) represent an exciting new technology, but to achieve more widespread usage and wider adoption within more industrial applications, they must be highly reliable, and manufactured to stringent quality standards. Many challenging manufacturing issues are of concern during the fabrication of MEMS, such as precise dimensional inspection, reliability modeling, burn-in scheduling, avoiding stiction, and maintenance strategies. However, only limited mathematical tools for improving MEMS reliability, quality, and productivity are currently available. This paper proposes a mathematical model to jointly determine inspection & preventive replacement policies for surface-micromachined microengines subject to wear degradation, which is a major failure mechanism for certain MEMS devices. The optimal specification limits for inspection, and the replacement interval are determined by simultaneously optimizing MEMS quality and reliability. The proposed model can be used as a tool for decision-makers in MEMS manufacturing to make sound economical and operational decisions on reliability, quality, and productivity. While illustrated considering one specific microengine design, the proposed model can be applied to a broader range of MEMS devices that experience wear degradation between rubbing surfaces.

Component Reliability Criticality or Importance Measures for Systems With Degrading Components

This paper proposes two new importance measures: one new importance measure for systems with -independent degrading components, and another one for systems with -correlated degrading components. Importance measures in previous research are inadequate for systems with degrading components because they are only applicable to steady-state cases and problems with discrete states without considering the continuously changing status of the degrading components. Our new importance measures are proposed as functions of time that can provide timely feedback on the critical components prior to failure based on the measured or observed degradation. Furthermore, the correlation between components is considered for developing these importance measures through a multivariate distribution. To evaluate the criticality of components, we analysed reliability models for multi-component systems with degrading components, which can also be utilized for studying maintenance models. Numerical examples show that the proposed importance measures can be used as an effective tool to assess component criticality for systems with degrading components.

Economic development of specifications for 100% inspection based on asymmetric quality loss functions

As a means of providing protection for both the producer and the consumer, for example as in airport security, 100% inspection plays an important role in todays environment. The same is true for some industrial or other decision-making processes where the consequences of excessive deviations from target values are very high. Motivated by Demings “all or none” inspection rule and associated philosophy for quality improvement, we develop an inspection strategy by considering the costs to both the producer and the customer, and thus to the whole system. A general optimization model is formulated to determine whether 100% inspection is to be performed or no inspection to be performed. If complete inspection is chosen then the optimal specification limits can be determined at the same time. Specifically, we consider two types of asymmetric quality loss functions for the “target the best” quality characteristic: the asymmetric quadratic quality loss function, and the asymmetric piecewise linear loss function. For each loss function, we propose an optimization model to determine the optimal process mean and specification limits. Numerical examples are given to illustrate the proposed models that can be used to improve the quality of the output of any process.

A physics-of-failure based reliability and maintenance modeling framework for stent deployment and operation

Reliability study of stents becomes extremely important due to the high demand on these devices to counteract the effects of atherosclerosis. Based on the physics-of-failure mechanisms, we propose a probabilistic reliability and maintenance modeling framework for stent deployment and operation. The fracture-mechanics-based approach in literature provides a rational basis for quantitative evaluation of damaging effects from two dominating failure modes of stents: (1) delayed failures or fatigue crack growth due to cyclic stresses, and (2) instantaneous failures due to single-event overloads. We develop the system reliability function using probabilistic degradation and random shock models. The developed system reliability model of stents is then incorporated in the optimization of a unique two-phase maintenance policy for achieving persistent patient outcomes. A numerical example is used to illustrate the results, where data in literature are used to analyze the reliability and optimize the maintenance schedule for stents. The developed reliability and maintenance models and analysis tools for stents provide fundamentally new perspectives on the application of reliability concepts to evolving medical devices.

Modeling zoned shock effects on stochastic degradation in dependent failure processes

This article studies a system that experiences two dependent competing failure processes, in which shocks are categorized into different shock zones. These two failure processes, a stochastic degradation process and a random shock process, are dependent because arriving shocks can cause instantaneous damage on the degradation process. In existing studies, every shock causes an abrupt damage on degradation. However, this may not be the case when shock loads are small and within the tolerance of system resistance. In the proposed model, only shock loads that are larger than a certain level are considered to cause abrupt damage on degradation, which makes this new model realistic and challenging. Shocks are divided into three zones based on their magnitudes: safety zone, damage zone, and fatal zone. The abrupt damage is modeled using an explicit function of shock load exceedances (differences between load magnitudes and a given threshold). Due to the complexity in modeling these two dependent stochastic failure processes, no closed form of the reliability function can be derived. Monte Carlo importance sampling is used to estimate the system reliability. Finally, two application examples with sensitivity analyses are presented to demonstrate the models.