Two-stage Failure Process Research Articles

The installation behavior and capacity of piggy-backed anchors for offshore wind turbine

Piggy-backed anchors present a promising solution to address the limitations of single Drag Embedment Anchors (DEAs). A series of centrifugal model tests were performed on the installation of piggy-backed anchors with varying spacings and attachment points in saturated sand using a magnetometer system. The experimental results validated the proposed theoretical prediction model, which can identify the trajectory, capacity, orientation, and soil failure wedge slip surface. Key findings include: (1). the embedment depth of the second anchor in piggy-backed anchors is significantly greater than that of a single anchor, resulting in the total capacity of piggy-backed anchors exceeding twice that of a single anchor at appropriate spacing; (2). investigating spacing effects shows that capacities are less than twice that of the single anchors when spacing is less than 1Lf due to overlapping failure soil wedges; optimal spacing was found to be 2Lf to 3Lf; (3). piggy-backed anchors with attachment points at the back of fluke exhibit better embedment performance and capacity stability compared to those with attachment points at the padeye. Finally, the prediction model explored the capacity performance of piggy-backed anchors at different loading angles at the final embedment depth, revealing a two-stage failure process compared to single drag anchors.

Optimal Condition-Based Maintenance Strategy via an Availability-Cost Hybrid Factor for a Single-Unit System During a Two-Stage Failure Process

This paper develops an optimal condition-based maintenance (CBM) strategy for a single-unit system during two-stage failure, a process that includes a normal stage and delay-time stage. Both stages are divided into the in-control state and out-of-control state. In the in-control state, the items are always produced with 100% quality, whereas in the out-of-control state, the item quality deteriorates, and minor repairs are arranged accordingly to fix this problem. This causes the optimal CBM strategy for system production to exhibit four different scenarios, where different calculations are carried out using renewal reward theory to determine the system profit. Then, the system profit is optimized by an availability-cost hybrid factor that balances the “cost per unit time” and “availability”. Finally, to investigate the effects of different decision objectives on the optimization results, a sensitivity study of the cost parameter and availability-cost weight factor is conducted on the optimized results through numerical simulations. According to the simulation results, this availability-cost hybrid factor, as well as the “cost per unit time” and “availability” factors, become less sensitive when it exceeds 0.6.

Two-stage failure modeling and optimal periodic inspection policy during the extended warranty period

ABSTRACTThe increased complexity of products and failure-induced costs add more pressure on the dealers of extended warranty (EW) contracts. In such conditions, conducting periodic inspection over the EW time-span may provide an opportunity to identify and repair defects before product failure. In this study, for a product with a two-stage failure process, the delay time model is applied to derive the failure process of the product. Considering a periodic inspection policy, the effects of identifying and removing defects on the failure process of the product and its corresponding cost are modeled. Then, a mathematical optimization model is derived to minimize the expected servicing cost for the dealer over the EW period. In the presented model, the number of inspections is assumed to be the dealer’s decision variable. Adopting a real case study from the literature, a numerical example is presented to clarify the model. Moreover, an extensive sensitivity analysis is conducted to study the effect of parameters on the optimal solution. The results show that considering periodic inspection may help pinpoint and remove defects, reduce failures, and minimize the expected servicing cost for the dealer.

Compressive failure of woven fabric reinforced thermoplastic composites with an open-hole: An experimental and numerical study

This research presents a detailed experimental and numerical study on the compressive failure of woven fabric reinforced thermoplastic composites, with an open-hole and with a pinned open-hole. The experimental evaluations are performed on the composite specimens using the Combined Loading Compression (CLC) evaluation method. Experimental results, including load response and damage morphology, are obtained and analysed. A novel meso-scale damage model is developed, based on Continuum-Damage-Mechanics (CDM), for predicting damage in woven fabric reinforced composites. The developed model, which can capture fibre fracture and matrix cracking, as well as the nonlinear response within the woven composite materials, is employed to conduct virtual Combined Loading Compression (CLC) tests. Numerical simulation results are compared with the extracted experimental results for model validation. Good correlation is achieved between experimental and computational results for both the open-hole and the pinned open-hole, with a two-stage failure process being observed for the pinned open-hole.

Reliability evaluation based on a dependent two-stage failure process with competing failures

This paper evaluates system reliability performance based on a dependent two-stage failure process with competing failures. The failure process of the system can be divided into two stages, i.e., the defect initialization stage, and the defect development stage. Dependence between these two stages is reflected in the fact that they share the same shock process modeled by a nonhomogeneous Poisson process. The impact of shock damage on system failure behavior is characterized by random hazard rate increments of the two stages. Based on practical failure behavior of industrial systems, we consider two typical and competing failure modes, defect-based failure and duration-based failure. Defect-based failure occurs when a defect reaches the damage threshold and duration-based failure is triggered when the duration in defective state is larger than a time threshold. We derive some results on system reliability and show that, with different parameter settings, our model reduces to several classic competing risk models. Finally, a detailed illustrative example of an oil pipeline system is given to demonstrate the applicability of the proposed model.

Joint Optimization of Jobs Sequence and Inspection Policy for a Single System With Two-Stage Failure Process

We will discuss the joint optimization of the jobs sequence as well as inspection policy for a single system expected to process n jobs with different processing times. The system has a two-stage failures process, i.e., first a defect arises in the system, and if the defect is not detected, the system eventually fails. The interrupted job due to failure should be restarted after corrective replacement of the system. The possibility of inspecting the system before starting a job is considered to detect a potential defect. We develop two models to find the optimal policy based on either total expected makespan, or total expected cost. In the cost optimization model, we assume a common due date for all jobs and incur a penalty cost per unit time that the makespan exceeds the due date. We develop a recursive formula to obtain the expected makespan, and the number of failures and preventive replacements and present the application of our proposed models to a system, which is supposed to process four jobs. We compare the results of the direct calculation (recursive formula) with a Monte Carlo simulation model, and discuss how changing the models’ parameters can impact the optimal policy.

Reliability and maintenance policies for a two-stage shock model with self-healing mechanism

In this paper, a two-stage shock model with self-healing mechanism is proposed as an extension of cumulative shock and delta-shock models. A change point is introduced to describe the two-stage failure process of a system and defined as the moment when the cumulative number of valid shocks reaches d. Before the change point, the system can heal the damage caused by a valid shock when the number of delta-invalid shocks reaches k in the trailing run of invalid shocks. Equivalently, the damage caused by previous i valid shocks can be healed when the number of delta-invalid shocks falls in [ik,(i+1)k) in the run of invalid shocks. The system loses self-healing ability when it reaches the change point, and then fails when the cumulative number of valid shocks reaches a prefixed value n (n > d). Based on the established model, the finite Markov chain imbedding approach is employed to obtain the probability mass function, the distribution function and the mean of shock length. Three preventive maintenance policies are proposed for the system under different monitoring conditions, and corresponding optimization models are constructed to determine the optimal quantities. Finally, numerical examples are given for the proposed model.

Optimal inspection and replacement strategy for systems subject to two types of failures with adjustable inspection intervals

The inspection activities are often carried out to detect possible indication of failures in plant systems. This paper considers a single unit system subject to two types of failures, where one failure mode is the traditional 0-1 logic failure and the other failure mode is described by a two-stage failure process. Adjustable inspections are used to detect the defective stage of the latter. We assume that the inspection duration gets shorter and shorter with a constant ratio. At the same time, preventive replacement is used to avoid the possible failure due to the former failure mode. The renewal process of this system is analyzed and the expected long-run cost per unit time (ELRCUT) is derived. The optimal inspection period and the preventive replacement interval to minimize ELRCUT are studied. At last, a numerical example is presented to illustrate the proposed model.

Optimal maintenance strategy for systems with two failure modes

This paper considers a single-unit system subject to two types of failures: a traditional catastrophic failure and a two-stage delayed failure. Periodic inspections are carried out to identify the defective stage of the two-stage failure process, whereas preventive replacements are implemented to avoid any potential failure due to the catastrophic failure mode. We construct a basic maintenance model and then extend it to the cases of imperfect inspections (i.e., inspections that do not always notice a defective state). We analyze the renewal process of the system and establish the expected long-run cost rate (ELRCR). The optimal inspection period and preventive replacement interval are determined by minimizing the ELRCR. A case study on infusion pumps is presented to illustrate the proposed model.

Reliability Assessment of Degradable Systems under Imperfect Maintenance and Utilisation Rate: A Case Study

Medical equipment is the biggest capital investment of every healthcare industry and ensuring the reliability and maintenance for critical devices is vital for Patient/user safety and better availability of services. To keep the medical device in a good operational condition, Inspection based maintenance activities have been the most usual means. The purpose of this study is to establish an improved delay time framework to model the two-stage failure process taking into account the influence of the utilization rate on the system’s degradation on the assumption of imperfect maintenance at inspection. This proportional delay time model is seldom considered in DTMs widely used in literature. A complete framework, for Parameters estimation method and the test for goodness of fit is given. To illustrate the model capabilities, a reel case study from the healthcare domain is presented, the model parameters are estimated entirely using the collected maintenance data. Then, the maximum likelihood estimation of the reliability parameters is achieved by Genetic Algorithms.

Preventive replacement for systems with condition monitoring and additional manual inspections

Condition monitoring (CM) and manual inspection are increasingly used in industry to identify a system's state so that necessary preventive maintenance (PM) decisions can be made. In this paper, we present a model that considers a single-unit system subject to both CM and additional manual inspections. There are two preset control limits: an inspection threshold and a preventive replacement (PR) threshold. When a CM measurement is equal to or greater than the inspection threshold but is less than the PR threshold, a manual inspection activity is initiated. When a CM measurement is greater than the PR threshold, a PR activity should be carried out. The system's degradation process evolves according to a two-stage failure process: the normal working stage, which is from new to the initial point that a defect occurs, with the CM measurement coming from a stochastic process; and the delay-time stage, which is from the initial point that a defect occurs until the point of failure, with the CM measurement coming from an increasing stochastic process. We assume that a manual inspection is perfect in that it can always identify which of these two stages the system is in. In our study, the decision variables are the CM interval and the inspection threshold, and we aim to minimize the expected cost per unit time. We provide a numerical example to demonstrate the applicability and solution procedure of the model.

A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems

When complex systems are monitored, multi-observations from several sensors or sources may be available. These observations can be fused through Bayesian theory to give a posterior probabilistic estimate of the underlying state which is often not directly observable. This forms the basis of a Bayesian control chart where the estimated posterior probability of the state can be compared with a preset threshold level to assess whether a full inspection is needed or not. Maintenance can then be carried out if indicated as necessary by the inspection. This paper considers the design of such multivariate Bayesian control chart where both the transition between states and the relationship between observed information and the state are not Markovian. Since analytical or numerical solutions are difficult for the case considered in this paper, Monte Carlo simulation is used to obtain the optimal control chart parameters, which are the monitoring interval and the upper control limit. A two-stage failure process characterised by the delay time concept is used to describe the underlying state transition process and Bayesian theory is used to compute the posterior probability of the underlying state, which is embedded in the simulation algorithm. Extensive examples are shown to demonstrate the modelling idea.

The availability model and parameters estimation method for the delay time model with imperfect maintenance at inspection

The delay time model (DTM) is widely used to model the two-stage failure process and is helpful for developing cost-effective inspection/maintenance plans. Imperfect maintenance is common in practice, but seldom considered in DTM. An improved DTM with imperfect maintenance at inspection has been developed based on the assumption of imperfect inspection maintenance and perfect failure maintenance. The model of the long-run availability for the improved DTM is established. Parameters estimation method and the test for goodness of fit method are given. Numerical simulations are performed to study the influence of imperfect maintenance on the long-run availability and to validate the credibility of the parameters estimation method. The results show that imperfect maintenance will decrease the long-run availability. The existence of the optimal inspection interval regarding the maximum long-run availability is tightly related to the improvement factor, which denotes the maintenance effect. The parameters estimation method proves credible. The maximum likelihood estimations of the reliability parameters can be easily achieved by the Genetic Algorithms (GAs) searching tool.

Modeling and analysis of software aging and software failure

Many studies reported that system suffered from outages more due to software faults than hardware faults. Recently, the phenomenon of “software aging”, which was caused by aging-related faults, is observed in many software systems. Software aging, characterized by progressive performance degradation, is mainly caused by exhaustion of the operating system resources, such as memory leaking, unreleased-file locks, data corruption, etc. This paper mainly focuses on the modeling and analysis of software aging and software failure. A stochastic time series decomposition algorithm based on robust locally weighted regression (Loess) is presented to separate the exhaustion of system resource from the resource usage, from which aging trend is estimated. Then the model of software aging and software failure process is constructed. Experiments on a practical server system verify the effectiveness of the algorithm presented in this paper, and the two-stage failure process is also confirmed for the first time in the history of research on software aging. The conclusions drawn from this paper will greatly benefit the application of software rejuvenation technique, that is, it makes it easy to determine when to perform software rejuvenation, which is a key issue in implementation of software rejuvenation. The results for the server system employing different rejuvenation policies show that software performance can be effectively improved.

A family of weakest link models for fiber strength distribution

It is well known that the most widely used distribution function for fiber tensile strength, the two-parameter Weibull distribution, does not always adequately describe the experimentally observed fiber strength scatter and the strength dependence on fiber length. To remedy this discrepancy, modifications of the Weibull distribution have been proposed that, while providing a good empirical fit to the strength data, sometimes lack the theoretical appeal of the weakest link models. We derive a family of weakest link models based on the assumption of a two-stage failure process incorporating explicitly the probabilities of flaw initiation and the fiber fracture due to the largest flaw (i.e. the weakest link). The model is verified against a sample of E -glass fiber strength data at different gauge lengths and shown to provide a reasonably good fit to the test results.

Modelling the probability assessment of system state prognosis using available condition monitoring information

This paper reports on a model to assess the current and future states of a monitored system based on measured condition monitoring information to date. The true state of the system is unobservable, but is assumed to be related to the measured condition monitoring information in a stochastic way. We further assume that the transition of the system state follows a time-dependent Markov chain which has only three states, namely good, defective and failed. This assumption effectively defines a two-stage failure process which is widely used in delay time modelling of maintained systems. Three modelling techniques are used to establish the model. First, we use a hidden Markov model to describe the transitions between system states. Second, the transition matrix is established based on the well-known delay time concept. The last one is the use of the filtering technique to construct the relationship between measured condition information and the underlying true state of the system. We also discuss the procedure for model parameter estimation. A numerical example is presented to demonstrate the modelling ideas.

A new model family for the strength distribution of fibers in relation to their length

Based on the weakest-link model, a family of fiber strength distributions is investigated assuming a two-stage failure process. At the first stage, a weakest link is formed (instantly or gradually), but at the second one the fracture of this link takes place. The gradual accumulation of flaws is described with the aid of Markov chain theory. The adequacy of the models considered is verified by checking them against experimental strength data for E-glass and flax fibers of various lengths. It is found that the models are not less accurate, but are even better, in a number of cases, than the model based on the known modified Weibull model with a power-law relation between the fiber length and the scale parameter.

Air oxidation of commercial FeCrAlRE alloy foils between 800 and 950°C

The oxidation behaviour of 30 μm and 50 μm thick Aluchrom YHf and 50 μm thick Kanthal AF foils have been examined during discontinuous exposure (100 h cycles) to laboratory air at 800, 850, 900 and 950°C. Oxidation was continued out to 3000 h or until chemical failure ensued, whichever was the shorter. Resulting observations include two oxidation temperature domains, a two-stage oxidation process leading to a duplex (transitional-α) alumina scale and ultimately, a two-stage chemical failure process of the oxide scale leading to breakaway/non-protective attack. To unravel the underlying mechanisms involved, the scales were examined by a range of microscopy and analytical techniques, including optical and scanning electron microscopy (SEM), electron microprobe analysis (EPMA), energy dispersive X-ray analysis (EDX) and X-ray diffraction (XRD).