Multiple Dependent Competing Failure Processes Research Articles

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.

Modeling dynamic environment effects on dependent failure processes with varying failure thresholds

Devices usually fail due to multiple dependent competing failure processes resulting from internal degradation and random shocks, whose behavior may vary in different environments. This paper focuses on systems suffering from randomly occurring shocks described by Poisson processes and internal degradation characterized by linear path models simultaneously, where the wear rate, shock arrival rate, shock load size, and shock damage amount are modulated by Markovian environments, especially the hard failure threshold differs in distinct environments. Reliability analysis is performed where analytical formulas and simulation algorithms for computing reliability indexes of systems are provided, such as the reliability function. Two maintenance models are developed for systems, including a real-time maintenance policy where the computation formula for the availability function is derived, and a periodic inspection policy in which an optimization model is proposed to find the optimal inspection interval that minimizes the average long-run cost rate. Finally, an illustrative example of floating offshore wind turbine systems is given to demonstrate possible applications of the developed models and proposed methods.

Optimal Warranty Policy for Consumer Electronics with Dependent Competing Failure Processes

This study considers warranties for consumer electronics with multiple dependent competing failure processes, including minor, over-degradation and catastrophic failure. Furthermore, the two alternative warranty programs are investigated: (1) a long-range warranty at a fixed lump-sum price and (2) a monthly warranty plan that can be either extended for the next month by continuous purchasing or terminated at the end of the current month. A designed dynamic programming approach is employed to obtain optimal solutions for warranty programs. Moreover, consumers with different attitudes toward risk are taken in consideration, and sensitivity analyses are performed to investigate the effects that the related factors have on profit. Integrating all issues, the study proposes extended warranty programs of lump-sum or monthly payment to different risk attitudes consumers with different attitudes toward risk with consideration of multiple dependent competing failure processes. The results indicate that high repair and replacement costs favor the monthly warranty program for firms. In addition, when there are more risk averse consumers in a market, there will be fewer purchases of a monthly warranty program, and it would thus be more profitable for firms to offer the one year warranty program.

A gamma process based model for systems subject to multiple dependent competing failure processes under Markovian environments

The performance rules of many products that suffer from both natural degradation and random shocks may have discrepancies in different environments during their service life. This article proposes a reliability model for systems subject to multiple dependent competing failure processes affected by Markovian environments. The effect of dynamic environment is embodied in that the natural wear behavior of the system in different environments is controlled by distinct gamma processes. A maintenance model is developed in the case where switches of environment states take place only when systems are operating. Explicit formulas for system reliability indexes including the reliability function, first failure time distribution, mean time to first failure, and system availability are analytically derived in the form of Laplace transforms. In order to verify the correctness of the analytical formula, a simulation algorithm for evaluating the reliability function is proposed. Finally, they are applied to a study case of the micro-engine system, which illustrates the applicability of proposed models and the validity of obtained results.

Reliability analysis of composite insulators subject to multiple dependent competing failure processes with shock duration and shock damage self-recovery

Recent developments in composite insulators highlight the demand for reliability analysis, and similar to most engineering products, composite insulators experience multiple dependent competing failure processes. However, two distinct characteristics of the failure processes of composite insulators—sustained shock and self-recovery mechanism—have not received attention in previous studies, resulting in inaccurate assessments of their reliability. In view of these problems, a novel shock damage model is first proposed to accurately reflect the impact of harmful random shocks on the degradation processes of composite insulators, considering both the shock magnitude and the shock duration. Subsequently, a detailed self-recovery process considering both the recovery level and the recovery time is developed to reflect the self-recovery mechanism. Furthermore, an improved practical reliability model with an analytical expression is proposed for composite insulators subject to multiple dependent competing failure processes considering degradation processes, random shocks, and self-recovery processes. Finally, a numerical study of composite insulators is conducted to illustrate the implementation of the proposed model.

Reliability and maintenance modeling for competing failures with intermission considered

There are many industrial systems experiencing multiple dependent competing failure processes, in detail degradation failure (soft failure) and catastrophic failure (hard failure). Earlier research studied failure behaviors and system reliability during operational period, but did not consider the intermission period. Some industrial systems are not always operating continuously while with intermissions or rest period. The degradation and random shock processes are different between operating period and intermissions, which caused it more challenging and complicated to establish reliability model. In this article, a new reliability model for multiple dependent competing failure processes is developed with intermission considered. The system reliability can be analyzed based on the proposed model more practically. Besides, a preventive replacement maintenance policy is studied by minimizing the average long-run maintenance cost with intermission periods considered. Finally, the availability and general applicability of presented model are demonstrated by a case in different parameter settings.

Reliability modeling for competing failure systems with instant-shift hard failure threshold

Many researchers have modeled systems under multiple dependent competing failure processes (MDCFP) in recent years. Typically, those failure processes consist of degradation (soft failure) and random shock (hard failure). In previous papers the threshold of hard failure has been a fixed value, which does not reflect engineering practices. Threshold refers to the ability to resist external random shocks, which shifts with time as the system is used. Thus, this paper establishes a model for MDCFP with instant-shift hard threshold. The hard failure threshold changes with time instantaneously, and it is also influenced by external shocks. This paper also presents a system reliability model. The effectiveness of the presented model is demonstrated by a reliability analysis of the micro-engine at Sandia National Laboratories. In addition, a sensitivity analysis is performed for specific parameters.

Reliability Modeling for Humidity Sensors Subject to Multiple Dependent Competing Failure Processes with Self-Recovery.

Recent developments in humidity sensors have heightened the need for reliability. Seeing as many products such as humidity sensors experience multiple dependent competing failure processes (MDCFPs) with self-recovery, this paper proposes a new general reliability model. Previous research into MDCFPs has primarily focused on the processes of degradation and random shocks, which are appropriate for most products. However, the existing reliability models for MDCFPs cannot fully characterize the failure processes of products such as humidity sensors with significant self-recovery, leading to an underestimation of reliability. In this paper, the effect of self-recovery on degradation was analyzed using a conditional probability. A reliability model for soft failure with self-recovery was obtained. Then, combined with the model of hard failure due to random shocks, a general reliability model with self-recovery was established. Finally, reliability tests of the humidity sensors were presented to verify the proposed reliability model. Reliability modeling for products subject to MDCFPs with considering self-recovery can provide a better understanding of the mechanism of failure and offer an alternative method to predict the reliability of products.

Reliability modeling for dependent competing failure processes of damage self-healing systems

Systems experiencing multiple dependent competing failure processes (MDCFP) have attracted much attention in the recent years. Similar to the biological systems, which have the ability to heal after being wounded; damage self-healing exists in many systems and products due to the intrinsic resistance to abrupt damage. The earlier research assumed the dependence between shock process and random shock but didn’t take the damage self-healing process into consideration, which occurs in many engineering systems. In the paper, a new reliability model subject to MDCFP by considering the damage self-healing phenomenon is developed. For each random shock, we propose healing time and healing level concept to describe the self-healing process. The model is practical and realistic for many complex systems such as electrical devices or microelectronic polymeric components. Due to complexity of the model, there is no analytical form of the reliability function. However, we estimate the system reliability efficiently by using simulation method. Furthermore, it is shown that the proposed model is general model that can be transformed into many classical degradation and shock models in different parameter settings.

Sensor-based calibrations to improve reliability of systems subject to multiple dependent competing failure processes

Reliability models with sensor-based calibrations are presented for systems or devices subject to dependent competing failure processes of soft failure due to degradation process and hard failure according to shock process. Shock magnitudes to indicate the hard failure are considered in terms of two patterns, inter-arrival times and arrival times. The soft failure is indicated by overall degradation measurement comprising of internal continuous degradation measurement and additional degradation damage caused by the shock process. By sensors, instant calibrations are carried out to rejuvenate the additional degradation damage. Then explicit reliability expressions are derived for the dependent competing failure system whose internal degradation measurement is described by the general degradation path model. And a simulation procedure is proposed to model the internal continuous degradation measurement indicated the Wiener process. Meanwhile, the usefulness of the proposed models is demonstrated by the numerical example. The results are illustrated that the proposed model with the instant calibrations are available to improve system reliability and make the system to operate in a higher safety in applications.

Reliability modeling for systems subject to multiple dependent competing failure processes with shock loads above a certain level

Considering that products with high reliability have ability to resist small shock loads, a new reliability model is proposed for system experiencing dependent competing failure processes(DCFP) with shock loads above a certain level. Such shock loads are separated by the shock threshold, beyond which are fatal shocks causing sudden failure of systems. The remaining part between the certain level and shock threshold are general shock loads causing sudden degradation increments (SDI). Moreover, an explicit relationship between SDI and the magnitude of shock loads is established for reliability assessment. In this study, we consider two kinds of DCFP: (1) a shock process and a degradation process; (2) a shock process and multiple degradation processes. In case (1), we consider the dependence between shock process and degradation process with conditional probability. In case (2), we not only consider the dependence between shock process and degradation processes with conditional probability, but also the dependence between multiple degradation processes with Copulas. Finally, the effectiveness of proposed models is demonstrated by reliability analysis of the microengine developed by Sandia National Laboratories and an extended numerical example. Besides, sensitivity analysis is performed to assess the effects of model parameters on the system reliability.

Probability box as a tool to model and control the effect of epistemic uncertainty in multiple dependent competing failure processes

Engineering components and systems are often subject to multiple dependent competing failure processes (MDCFPs). MDCFPs have been well studied in literature and various models have been developed to predict the reliability of MDCFPs. In practice, however, due to the limited resource, it is often hard to estimate the precise values of the parameters in the MDCFP model. Hence, the predicted reliability is affected by epistemic uncertainty. Probability box (P-box) is applied in this paper to describe the effect of epistemic uncertainty on MDCFP models. A dimension-reduced sequential quadratic programming (DRSQP) method is developed for the construction of P-box. A comparison to the conventional construction method shows that DRSQP method reduces the computational costs required for P-box constructions. Since epistemic uncertainty reflects the unsureness in the predicted reliability, a decision maker might want to reduce it by investing resource to more accurately estimate the value of each model parameter. A two-stage optimization framework is developed to allocate the resource among the parameters and ensure that epistemic uncertainty is reduced in a most efficient way. Finally, the developed methods are applied on a real case study, a spool valve, to demonstrate their validity.

Reliability Modeling for Systems Subject to Interactional Competing Failure Processes

For complex systems or items that experience multiple dependent competing failure processes, the dependency among the failure processes presents challenging issues in reliability modeling. This article, discusses the dependence of the degradation failure processes and the traumatic failure process. On the condition of passion shock processes, a degradation failure reliability model is developed with the wiener degradation processes. By the influence of the degradation, a traumatic failure reliability model is developed under weibull failure distribution. Then, we get system reliability model deals with mutual effect of the two processes. In additional, the parameters estimation of the reliability model is solved. An applied example demonstrated the model correctness and availability.

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 systems subject to multiple dependent competing failure processes

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.

How to identify a bathtub hazard rate : Magne Vollan Aarset. IEEE Trans. Reliab.R-36, 106 (1987)

The performance rules of many products that suffer from both natural degradation and random shocks may have discrepancies in different environments during their service life. This article proposes a reliability model for systems subject to multiple dependent competing failure processes affected by Markovian environments. The effect of dynamic environment is embodied in that the natural wear behavior of the system in different environments is controlled by distinct gamma processes. A maintenance model is developed in the case where switches of environment states take place only when systems are operating. Explicit formulas for system reliability indexes including the reliability function, first failure time distribution, mean time to first failure, and system availability are analytically derived in the form of Laplace transforms. In order to verify the correctness of the analytical formula, a simulation algorithm for evaluating the reliability function is proposed. Finally, they are applied to a study case of the micro-engine system, which illustrates the applicability of proposed models and the validity of obtained results.

Propagation of T-waves in the Pacific Ocean : Wadati Kiyoo and Hideo Sato, 1965. Geophys. Mag., Tokyo, 32 (3): 255–271

The performance rules of many products that suffer from both natural degradation and random shocks may have discrepancies in different environments during their service life. This article proposes a reliability model for systems subject to multiple dependent competing failure processes affected by Markovian environments. The effect of dynamic environment is embodied in that the natural wear behavior of the system in different environments is controlled by distinct gamma processes. A maintenance model is developed in the case where switches of environment states take place only when systems are operating. Explicit formulas for system reliability indexes including the reliability function, first failure time distribution, mean time to first failure, and system availability are analytically derived in the form of Laplace transforms. In order to verify the correctness of the analytical formula, a simulation algorithm for evaluating the reliability function is proposed. Finally, they are applied to a study case of the micro-engine system, which illustrates the applicability of proposed models and the validity of obtained results.