Dependent Failure Modes Research Articles

Reliability Model of Mechanical Components with Dependent Failure Modes

A mechanical component may fail in many modes that are usually not independent. There is generally not a joint probability density function to describe these correlated failure modes. Thus, it is difficult to compute the reliability when considering the correlations between the failure modes. It is supposed that three or more failure modes arise synchronously to be a very small probability event. The relationship between ultimate state functions in different failure modes is established by utilizing linear regression method. A double integration model for reliability of mechanical components with dependent failure modes is built according to stress-strength interference model. In case of square, cube, or exponential relationship between two ultimate state functions, a linear transformation is made. An example of pin that may fail in shear fracture, bruise, or both is discussed. The reliability is compared with that obtained by using Monte Carlo method, which represents that the reliability model with dependent failure modes proposed is correct.

Planning of Accelerated Life Tests With Dependent Failure Modes Based on a Gamma Frailty Model

Accelerated life tests (ALT) provide timely information on product reliability. As product complexity increases, ALT often generate multiple dependent failure modes. However, the planning of an ALT with dependent failure modes has not been well studied in the literature. This article investigates the statistical modeling and planning of ALT with multiple dependent failure modes. An ALT model is constructed. Associated with each failure mode there is a latent lifetime described by a log-location-scale distribution, and the statistical dependence between different failure modes is described by a Gamma frailty model. The proposed model incorporates the ALT model with independent failure modes as a special limiting case. We obtain the c-optimal test plans by minimizing the large-sample approximate variance of the maximum likelihood estimator of a certain life quantile at use condition. The method is illustrated by developing ALT plans for field-effect transistors with competing gate oxide breakdown. A sensitivity analysis is performed to investigate the robustness of the optimal ALT plan against misspecification of model parameter values. This article has supplementary materials that are available online.

Effect of compressive loading speed and stacking sequence on mechanical characteristics of satin weave E‐glass/epoxy composites

AbstractThis article experimentally investigated the in‐plane loading speed dependent mechanical properties and failure modes of satin weave E‐glass/epoxy composite laminates [45/−45/0/90]ns. Two types of E‐glass fabric/epoxy pre‐impregnated tapes were used to manufacture the composite laminates specimens. The low strain rate tests were conducted with an INSTRON™ testing machine, and the high strain rate tests done using a pulse shape modified compressive Split Hopkinson Pressure Bar apparatus. From the experimental result, it was concluded that under different strain rate loading, compressive strength, modulus, and strain at peak stress were rate sensitive. Optical and microscopic photos of the specimens were taken to determine operative failure modes. Within the studied strain rate regimes, the failure mode changed from splitting followed by fiber kink buckling to predominantly delamination and shear fracture as strain rate increases from quasi‐static to high strain rates. Compressive properties and failure modes were severely affected by strain rate, stacking sequence, and fabric material. POLYM. COMPOS. 2012. © 2012 Society of Plastics Engineers

Maintaining Systems With Dependent Failure Modes and Resource Constraints

Many works on preventive maintenance (PM) of systems only consider either a single failure mode, or statistically independent failure modes. Here, we study the maintenance policy for systems with two statistically dependent failure modes (namely maintainable, and nonmaintainable), and resource constraints. Assume (i) the nonmaintainable failures unidirectionally affect the maintainable failure rate; (ii) due to the constrained resource, only a limited number of imperfect PM actions are performed to reduce the maintainable failure; and (iii) the improvement factor due to each imperfect PM is fixed, and the maximal number before replacement is fixed. By combining a Castro model for statistically dependent failure modes with a Zhang-Jardine model for a single failure mode and imperfect PM, we propose a hybrid maintenance model for systems with statistically dependent failure modes and limited imperfect PM. To examine the maintenance policy, assume that both the nonmaintainable failures and the maintainable failures follow the same type of failure rate functions such as the increasing power law failure rate function. We discuss the relation between expected cost rate per unit-time and each decision variable, and then give a solution to a constrained optimization problem provided that the length of the interval between two successive maintenance actions cannot be too small. Numerical simulations for the increasing power law failure rate fully verify the proposed maintenance policy, which can be also extended to other increasing failure rate functions such as an exponential failure rate function.

Condition-Based Maintenance for Systems with Dependent Failure Modes

Abstract Many complex maintainable systems are subject to multiple dependent failure modes. In this research, we introduce a new model for modeling the stochastically dependent time-to-maintenance and time-to-failure of different failure modes. The model is then utilized to obtain the optimum Condition-Based Maintenance (CBM) schedules that maximizes the system availability over its life cycle, or, minimizes the long-run cost per unit time. The proposed method efficiently solves the condition-based maintenance-scheduling problem for system with multiple dependent failure modes, which has not been well addressed in the literature.

Reliability Modeling for Degrading System with multiple Dependent Failure Modes

To adequately predict reliability and optimize the time-to-maintenance for complex system design and reliability problems, this research develops a new model for complex systems, which are subject to performance degradation and multiple dependent failure modes. In particular, the hazard rate corresponding to each failure mode depends both on time and system state. The system state stochastically degrades over time, and the degradation is described by a stochastic process. The degradation rate, in particular, depends on time and is also a function of the degradation level. This research develops a reliability model for complex systems, which are subject to performance degradation and multiple dependent failure modes. A joint model of system degradation and failure time is constructed. The system state stochastically degrades over time, and the degradation is described by a stochastic process. Unlike existing reliability models, we consider a realistic scenario where the degradation rate is, not only a function of time, but also the degradation level at that time. The goal of this research project is to develop the optimum Condition-Based Maintenance (CBM) schedules. The developed model will be used as the basis in our future research on CBM scheduling.

Cooperative Predictive Maintenance of Repairable Systems With Dependent Failure Modes and Resource Constraint

Many works on condition-based maintenance of repairable systems apply to either a single failure mode, or statistically independent failure modes. Different from these works, this paper considers the problem of predictive maintenance of repairable systems with dependent failure modes, and resource constraints. Assume that (i) a repairable system is subject to two statistically dependent failure modes bidirectionally affecting each other, (ii) imperfect maintenance actions are cooperatively performed on two dependent failure modes by allocating insufficient resources spent for maintenance, and (iii) future maintenance scheduled at the current time depend on both the predicted number of future failures and the minimization of the expected maintenance cost rate defined in the long term. To resolve the above problem, a novel cooperative predictive maintenance model is proposed. Its basis is the incorporation of the hazard-rate function, and effective age. In this model, two failure modes are statistically dependent in such a way that the hazard rate of one failure mode depends on the accumulated number of failures of the other failure mode. The effect of imperfect maintenance is interpreted in terms of how the hazard rate function and the effective age are changed by maintenance actions. The age reduction factor for each failure mode due to maintenance has some deterministic relation to the degree of resources cooperatively allocated to perform maintenance. The decision variables in the maintenance policy, namely the number of maintenance actions to be performed, the interval between successive maintenance actions, and the cooperatively allocated degree of resources, can be recursively updated when new monitored information arrives. This approach relies on both the predicted number of future failures, and the minimization of the expected maintenance cost rate defined in the long term.

Quantitative accelerated degradation testing: Practical approaches

The concept of accelerated testing by tracking degradation of samples over test time needs to be developed for reliability estimation. This paper aims at proposing practical approaches to conduct accelerated degradation testing on new and available used samples. For this purpose, product failure is related to a suitable physical property. Then, its failure time is defined as the expected time in which its property reaches the critical level. Degradation model of field samples returned from service due to a degrading failure mode has been estimated based on the least square method, and available gap between manufacturer criterion and user's claim (to report a failure) has also been discussed. For a product under some stresses, a general formula has been proposed by the superposition principle in order to estimate its degradation for independent and dependent failure modes. If used samples are available, and acceleration factor of the related test is unknown, partial aging method has been presented to considerably shorten the test time.

A model of imperfect preventive maintenance with dependent failure modes

Consider a system subject to two modes of failures: maintainable and non-maintainable. A failure rate function is related to each failure mode. Whenever the system fails, a minimal repair is performed. Preventive maintenances are performed at integer multiples of a fixed period. The system is replaced when a fixed number of preventive maintenances have been completed. The preventive maintenance is imperfect because it reduces the failure rate of the maintainable failures but does not affect the failure rate of the non-maintainable failures. The two failure modes are dependent in the following way: after each preventive maintenance, the failure rate of the maintainable failures depends on the total of non-maintainable failures since the installation of the system. The problem is to determine an optimal length between successive preventive maintenances and the optimal number of preventive maintenances before the system replacement that minimize the expected cost rate. Optimal preventive maintenance schedules are obtained for non-decreasing failure rates and numerical examples for power law models are given.

Evaluation of a Multi-Axial, Temperature- and Time- Dependent Failure Mode

To obtain a better understanding of the response of the structural adhesives used in the space shuttle's reusable solid rocket motor (RSRM) nozzle, an extensive effort has been conducted to characterize in detail the failure properties of these adhesives. This effort involved the development of a failure model that includes the effects of multi-axial loading, temperature, and time. An understanding of the effects of these parameters on adhesive failure is crucial to the prediction of safety of the RSRM nozzle. The use of this newly developed multi-axial, temperature, and time-dependent failure model for modeling failure for the adhesives TIGA 321, EA913NA, and EA946 is documented. The development of the mathematical failure model using constant load rate data for both normal and shear loading is presented. Verification of the accuracy of the failure model is shown through comparisons between predictions and measured creep and multi-axial failure data. The verification indicates that the failure model performs well for a wide range of conditions (loading, temperature, and time) for the three adhesives. The failure criterion is shown to be accurate through the glass transition for the EA946 adhesive. Though this failure model has been developed and evaluated with adhesives, the concepts should be applicable for other isotropic materials.

Computation of probabilistic stability measures for a controlled distributed parameter system

Parameter uncertainty can degrade the performance of an otherwise well-designed control system, sometimes leading to system instability. In the context of structural control, performance degradation and instability imply excessive vibration and even structural failure. The ability of a controller to maintain the stability of a system in spite of parameter uncertainty is measured by its robustness, which can be viewed as a probability measure, wherein the joint distribution is of dimension equal to the number of uncertain parameters and the failure hypersurface is defined by the onset of instability in the eigenspace. This observation has led to some recent analyses employing FORM/SORM methods and Monte Carlo simulation.The extension of these concepts to distributed parameter systems is, unfortunately, not immediate. The mere fact that these systems are infinite dimensional precludes the use of much of the machinery available for discrete systems, unless the distributed system is first discretized, which itself introduces error into the analysis, or is represented by an eigenfunction expansion, which requires truncation after some finite number of modes, also a potential source of error. In fact, the system will behave as one with an infinite number of subsystems with highly dependent failure modes in series.In Bergman and Hall, Effect of controller uncertainty on the stability of a distributed parameter system, Structural Safety and Reliability, eds. Schuëller, Shinozuka and Yao, Balkema, Rotterdam, 1993, pp. 210–220, root locus analysis was employed to assess the reliability of the system, requiring the repetitive solution of a transcendental characteristic equation over a range of the parameter under investigation. The loci then provide a mapping from the probability distribution of the random parameter to the probability distribution of the system eigenvalues. This approach was utilized over 30 years ago by Boyce, Random vibration of strings and bars, Proc. of the Fourth US National Congress of Applied Mechanics, Berkeley, 18–21 June, 1962, pp. 77–85, who examined eigenvalue distributions for undamped taut strings and Euler-Bernoulli beams, each subjected to the action of a single point actuator. He demonstrated that, for the case of uncertainty in the actuator gain alone, a simple, closed form mapping leading to the distributions of the eigenvalues of the system could be determined directly from the distribution of the actuator gain, and for uncertainty in the remaining parameters, approximate distributions could be obtained through the application of perturbation methods.In the current paper, the FORM/SORM approach is applied to the taut string problem, where the distributed nature of the system is maintained throughout the analysis. Uncertain parameters, in this case the proportional gain and time delay, are characterized by probability distributions with known mean and variance. Each is transformed to a standard normal variate via Rosenblatt transformations, and the most likely failure point in the parameter space is found using a constrained optimization procedure. The effect of distribution is shown through parameter studies, and verification is provided by Monte Carlo simulation. As expected, time delay is shown to have a pronounced effect upon system robustness.

Fault trees and Markov models for reliability analysis of fault-tolerant digital systems

Reliability analysis of fault tolerant computer systems for critical applications is complicated by several factors. In this paper, we discuss these modeling difficulties and describe and demonstrate approaches to handling them. Three important techniques characterize our approach. First, behavioral decomposition separates the system failure modes specification from the recovery process specification. Second, a fault tree representation of the system failure modes is converted to an equivalent Markov model, to which the recovery models are added automatically. Third, the fault tree to Markov chain conversion allows the definition of new dynamic fault tree gates to capture the sequence dependent failure modes that are often associated with advanced fault tolerant systems. Two advanced fault tolerant computer systems are described, and fault tree models for their analysis are presented. HARP (the Hybrid Automated Reliability Predictor) is a software package developed at Duke University and NASA Langley Research Center that is used to analyze the example systems.

Bonding, structure, and properties of metal/ceramic interfaces: Part 2 Interface fracture behaviour and property measurement

The fracture behaviour of metal/ceramic interfaces is reviewed. It is shown that fracture is a complicated process which depends on many factors such as the geometry of the test specimen and loading conditions, strength of the interfacial bond, thermal, elastic, and fracture properties of the metal and ceramic, thickness of the metal layer, and testing environment. Considerable progress has been made in understanding some of these areas while others are just beginning to be understood. Advances in this field include the development of favourable specimen geometries for measuring various interface properties and an understanding of the relationship between the phase angle of loading, the crack trajectory, and the interface fracture energy for these geometries. The major contributions of plasticity and crack bridging to the fracture resistance of metal/ceramic interfaces has been established. The detrimental effects of thermal and elastic mismatch on interface properties are also well known. Conversely, little is known about the stress corrosion and fatigue behaviour of metal/ceramic interfaces though data on these time dependent failure modes are beginning to appear in the literature. Considerably more work is needed in order to understand the fracture behaviour of metal/ceramic interfaces.

Bonding, Structure and Properties of Metal/Ceramic Interfaces

AbstractThis paper reviews the effects of chemical bonding, reaction, interfacial structure, fabrication, specimen geometry and testing conditions on the strength and fracture behavior of metal/ceramic interfaces. It is shown that a number of important properties of metal/ceramic interfaces such as the wetting behavior and work of adhesion can be qualitatively predicted from simple bonding models based on the elements in the metal and ceramic. In addition, the interfacial structure can often be predicted from principles of equilibrium thermodynamics and minimization of interfacial energy for relatively thick metal/ceramic layers. More quantitative description of interfacial structure employing atomistic calculations has been performed for simple interfaces and this area is progressing. The fracture behavior of metal/ceramic interfaces is a complicated process which depends on many factors such as the specimen geometry and loading conditions, strength of the interfacial bond, thermal, elastic and fracture properties of the metal and ceramic, thickness of the metal layer and testing environment. Advances in this area include the development of favorable specimen geometries for measuring interface properties and an understanding of the relationship among the phase angle of loading, crack trajectory and interface fracture energy for these geometries. Conversely, little is known about the stress corrosion and fatigue behavior of metal/ceramic interfaces although data on these time dependent failure modes are beginning to appear in the literature. Much progress has been made but considerably more work isneeded to understand the properties of metal/ceramic interfaces.

A dependent multiple failure mode modelling procedure

Under mild distributional assumptions,Langberg,Proshane,and Quinzi demonstrated the changing of a dependent competing failure mode system into an independent one.In this paper, their procedure is ultiized to construct dependent failure mode models.The common reliablity models, Exponential,Weibull and Extreme value, are examined with this procedure and an example is discussed.

A modification to fault tree “AND” gate

This short paper presents the fault tree “AND” gate hazard rate derivation of a parallel redundant system subject to dependent failure modes.