Stochastic Breakdown Research Articles

Impact of overvoltage on the mode transition of the spark gap switch: from edge breakdown to stochastic breakdown

Impact of overvoltage on the mode transition of the spark gap switch: from edge breakdown to stochastic breakdown

Modeling the Breakdown of Dielectrics Loaded With Conducting Particles

This study addresses the electrical breakdown of dielectrics loaded with randomly dispersed conducting particles. A simple stochastic breakdown model is proposed and used to provide information on the tree structure and dielectric breakdown strength. Parametric simulations suggest an important role of the particle fraction and microstructure (regular versus aggregated) on the breakdown strength while the particle size and size dispersity have limited effects. The obtained results have been recast in terms of geometrical parameters describing the particle structure and the minimum-gap path (path having the shortest length of dielectrics) is found to correlate quite well with numerical results. This suggests that simple geometrical quantities are relevant to provide quantitative predictions of breakdown strength for such materials.

Prediction of Energy Storage Performance in Polymer Composites Using High-Throughput Stochastic Breakdown Simulation and Machine Learning.

Polymer dielectric capacitors are widely utilized in pulse power devices owing to their high power density. Because of the low dielectric constants of pure polymers, inorganic fillers are needed to improve their properties. The size and dielectric properties of fillers will affect the dielectric breakdown of polymer‐based composites. However, the effect of fillers on breakdown strength cannot be completely obtained through experiments alone. In this paper, three of the most important variables affecting the breakdown strength of polymer‐based composites are considered: the filler dielectric constants, filler sizes, and filler contents. High‐throughput stochastic breakdown simulation is performed on 504 groups of data, and the simulation results are used as the machine learning database to obtain the breakdown strength prediction of polymer‐based composites. Combined with the classical dielectric prediction formula, the energy storage density prediction of polymer‐based composites is obtained. The accuracy of the prediction is verified by the directional experiments, including dielectric constant and breakdown strength. This work provides insight into the design and fabrication of polymer‐based composites with high energy density for capacitive energy storage applications.

Ramp metering control under stochastic capacity in a connected environment: A dynamic bargaining game theory approach

This paper presents a dynamic predictive and cooperative ramp metering approach that considers stochastic breakdowns at merging bottlenecks. A stochastic microscopic model is used to estimate traffic state parameters based on speed, location, and travel time information from connected vehicles. Traffic state predictions are obtained on a lane by lane basis using an adaptive Kalman filter (AKF) that fuses fixed detector measurements with the model; the AKF then produces multiple step ahead predictions. The ramp metering problem in this paper is modeled as a stochastic distributed model predictive control (SDMPC) approach. The SDMPC problem is solved based on a bargaining game approach where each controller, a player in the game, receives traffic state and control decision information from other controllers to solve the local optimization problem based on expected local costs and constraints. The performance of the proposed model is evaluated for three aspects of efficiency: short-term and long-term equity and effectiveness compared to multiple control scenarios. The outcomes indicate that the proposed cooperative model with stochastic capacity considerations outperforms the deterministic capacity-based models in regard to effectiveness and equity properties. However, the centralized approach performs slightly better in respect to system-wide efficiency.

A Stochastic Model Based on Fiber Breakage and Matrix Creep for the Stress-Rupture Failure of Unidirectional Continuous Fiber Composites 2. Non-linear Matrix Creep Effects

Stress rupture (sometimes called creep-rupture) is a time-dependent failure mode occurring in unidirectional fiber composites under high tensile loads sustained over long times (e. g., many years), resulting in highly variable lifetimes and where failure has catastrophic consequences. Stress-rupture is of particular concern in such structures as composite overwrapped pressure vessels (COPVs), tension members in infrastructure applications (suspended roofs, post-tensioned bridge cables) and high angular velocity rotors (e.g., flywheels, centrifuges, and propellers). At the micromechanical level, stress rupture begins with the failure of some individual fibers at random flaws, followed by local load-transfer to neighboring intact fibers through shear stresses in the matrix. Over time, the matrix between the fibers creeps in shear, which causes lengthening of local fiber overload zones around previous fiber breaks, resulting in even more fiber breaks, and eventually, formation clusters of fiber breaks of various sizes, one of which eventually grows to a catastrophically unstable size. Most previous models are direct extension of classic stochastic breakdown models for a single fiber, and do not reflect the micromechanical detail, particularly in terms of the creep behavior of the matrix. These models may be adequate for interpreting experimental, composite stress rupture data under a constant load in service; however, they are of highly questionable accuracy under more complex loading profiles, especially ones that initially include a brief “proof test” at a “proof load” of up to 1.5 times the chosen service load. Such models typically predict an improved reliability for proof-test survivors that is higher than the reliability without such a proof test. In our previous work relevant to carbon fiber/epoxy composite structures we showed that damage occurs in the form of a large number of fiber breaks that would not otherwise occur, and in many important circumstances the net effect is reduced reliability over time, if the proof stress is too high. The current paper continues our previous work by revising the model for matrix creep to include non-linear creep whereby power-law creep behavior occurs not only in time but also in shear stress level and with differing exponents. This model, thus, admits two additional parameters, one determining the sensitivity of shear creep rate to shear stress level, and another that acts as a threshold shear stress level reminiscent of a yield stress in the plastic limit, which the model also admits. The new model predicts very similar behavior to that seen in the previous model under linear viscoelastic behavior of the matrix, except that it allows for a threshold shear stress. This threshold allows consideration of behavior under near plastic matrix yielding or even matrix shear failure, the consequence of which is a large increase in the length-scale of load transfer around fiber breaks, and thus, a significant reduction in composite strength and increase in variability. Derivations of length-scales resulting from non-linear matrix creep are provided as Appendices in the Supplementary Material.

Studying the effect of stochastic breakdowns, overtime, and rework on inventory replenishment decision

This study investigates the effect of stochastic breakdowns, overtime, and rework on the inventory replenishment decision. The overtime capacity and inevitable situations during the manufacturing process, such as the production of imperfect items and random breakdowns, are often considered in advance by production manager to smoothen fabrication schedules, maintain the desired quality, and reduce the impact from undesirable interruptions. This study builds a model to characterize these real features of a manufacturing process and derive the total relevant expenses of the system. Although a closed-form solution is unobtainable, a recursive algorithm is proposed to help find the optimal runtime for the batch fabrication plan. A numerical illustration shows how the proposed procedure and algorithm function. It also demonstrates the ability of the proposed model to reveal diverse crucial information regarding the individual and combined influences of deviations in overtime factors, the mean-time-to-failure, and rework- related variables, on the optimal replenishment runtime, total operating expenses, and different cost contributors. The research results will facilitate better decision-making aimed at increasing the competitive advantages of a manufacturing firm.

Incorporating outsourcing, stochastic failure, and scrap into batch fabrication planning

In batch production planning, managers must consider the unforeseeable circumstances in the fabrication process and resources available to meet demand on time and determine the optimal replenishment policy. To address these concerns, this study examines a hybrid fabrication system incorporating outsourcing, stochastic machine failures, and random scraps. The objective is to decide the optimal uptime that minimizes the overall system expenses. Assumptions in this study include a partial outsourcing plan associated with a higher unit cost, random scrap, and stochastic breakdown under an abort/resume policy, wherein repair of a machine begins immediately after a breakdown, and the production of the interrupted batch resumes as soon as it is completed. A precise model is developed to explore this specific problem. Mathematical derivations, optimization methodology, and a recursive algorithm are used to derive the optimal replenishment policy. The applicability of the results is illustrated by a numerical example. To facilitate managerial decision making, it reveals the individual and/or combined impact of outsourcing, scrap, and machine failure on (i) the optimal policy; (ii) the system’s different cost contributors; (iii) total system expenses; (iv) machine utilization; and (v) other key parameters of the problem.

Determining the fabrication runtime for a buyer-vendor system with stochastic breakdown, accelerated rate, repairable items, and multi-delivery strategy

Determining the fabrication runtime for a buyer-vendor system with stochastic breakdown, accelerated rate, repairable items, and multi-delivery strategy

A stochastic model based on fiber breakage and matrix creep for the stress-rupture failure of unidirectional continuous fiber composites

Stress rupture is a time-dependent failure mode occurring in unidirectional fiber composites under sustained tensile loads, resulting in highly variable lifetimes. Stress-rupture is of particular concern in composite overwrapped pressure vessels (COPVs) since it is unpredictable, and has catastrophic consequences. At the micromechanical level, stress rupture begins with the breakdown of individual fibers at random flaws, followed by local load-transfer to intact neighbors through shear stress in the matrix. Over time, the matrix creeps in shear causing lengthening overload zones around fiber breaks, resulting in even more fiber breaks, and eventually, formation of a catastrophically unstable break cluster. Current reliability models are direct extensions of classic stochastic breakdown models for a single fiber, and do not reflect such micromechanical activity. These models are adequate for modeling composite stress rupture under a constant load, however, they may be unrealistic under more complex loading profiles, such as a constant load that follows a brief ‘proof test’ at a load level up to 1.5 times this constant load. For carbon fiber/epoxy COPVs, current models predict a reliability, conditioned on survival of a proof test, that is always higher than the reliability without such a proof test. Concern exists that this is incorrect, and that a proof test may result in reduced reliability over time. While the failure probability during a proof test may be very low, overwrap damage occurs nonetheless in the form of a large number of fibers breaks that would not occur otherwise based on fiber Weibull strength statistics. This phenomenon of increased fiber breakage during a proof test is captured in the model we develop and that specifically builds on the micromechanical failure process described above. For typical proof-test load ratios, the model predicts conditional reliabilities for lifetime that are typically much lower than those calculated in the absence of a proof test.

High fidelity moving Z-score based controlled breakdown fabrication of solid-state nanopore

We investigate the current transport characteristics in the electrolyte-dielectric-electrolyte structure commonly used in the in situ controlled breakdown (CBD) fabrication of solid-state nanopores. It is found that the stochastic breakdown process could lead to fidelity issues of false positives (an incorrect indication of a true nanopore formation) and false negatives (inability to detect initial nanopore formation). Robust and deterministic detection of initial physical breakdown to alleviate false positives and false negatives is critical for precise nanopore size control. To this end, we report a high fidelity moving Z-score method based CBD fabrication of solid-state nanopore. We demonstrate 100% success rate of realizing the initial nanopore conductance of 3 ± 1 nS (corresponds to size of 1.7 ± 0.6 nm) regardless of the dielectric membrane characteristics. Our study also elucidates the Joule heating is the dominant mechanism for electric field-based nanopore enlargement. Single DNA molecule sensing using nanopores fabricated by this method was successfully demonstrated. We anticipate the moving Z-score based CBD method could enable broader access to the solid state nanopore-based single molecule analysis.

Production planning incorporating issues of reliability and backlogging with service level constraint

To stay competitive in present-day turbulent business environment, managers of manufacturing firms must achieve crucial operational goals, such as maintaining product quality, reducing operating costs, and attaining customer satisfaction. In real manufacturing systems, allowing backordering sometimes can be an effective strategy to help smooth manufacturing schedules and lower operating costs. However, the consequence of excessive shortages is the undesirable service level which reduces customer satisfaction and goodwill. To cope with this unwanted result, a maximal permitted backlogging level is set as an operating constraint to achieve the minimum required service level. Also, production of scrap items and stochastic breakdown are both inevitable in the manufacturing processes. Motivated by addressing aforementioned issues and providing insight information to managers for supporting their operational decision makings, this paper investigates the optimal runtime for a fabrication system with backordering, service level constraint, stochastic breakdown, and scrap. Mathematical model was developed and optimization methods are used to decide the optimal runtime that minimizes total system costs. Various key insights relating to joint impacts of backlogging, service level, stochastic breakdown, and scrap on the optimal runtime decision are revealed through a numerical illustration along with sensitivity analyses.

Optimal maintenance plan for two-level assembly system and risk study of machine failure

This paper deals with the optimisation of two-levels assembly system planning. This system is composed of a single machine, inventories at levels 1 and 2 for stock keeping components to assembly and final assembled product. It assumed that the machine processes all assembly operations and is subject to random failure. A mathematical model is developed to incorporate a supply planning for two-level assembly systems under stochastic lead times and breakdowns machine. A preventive maintenance plan is carried out to reduce the frequency of the corrective maintenance actions. This work has double goals. The first one is to find the optimal order release dates for the different components at level 2 and the optimal preventive maintenance plan. The second one is to quantify the risk due to machine failures which have an impact on the lead-time of the finished product. To consider the maintenance actions, preventive maintenance actions are perfectly performed to restore the machine to state “as good as new”, minimal repair is considered at failure. The model minimises the total cost, which is the sum of inventory holding cost for components at levels 1 and 2, backlogging and inventory holding cost for the finished products and maintenance costs. To illustrate the effectiveness of the proposed model, different meta-heuristics are applied; the genetic algorithm shows the most suited to our analytical model, the optimal release date founded by this algorithm allows finding the optimal preventive maintenance plan. The obtained optimal maintenance planning is used in the risk assessment in order to find the threshold repair period that avoids lost profit.

Optimal unrestricted dynamic stochastic scheduling with partial losses of work due to breakdowns

In this article, we discuss the optimal scheduling problem of the recently introduced model for partial loss due to machine breakdowns, which fills up a significant gap in the existing literature. More specifically, we consider the problem of processing a number of jobs with arbitrary random processing times by a machine subject to general stochastic breakdowns, where each breakdown may cause an uncertain loss of the work achieved on the job being processed. The objective is to maximize the expected weighted discounted reward of completing the jobs in the class of unrestricted dynamic policies. We obtain the optimal dynamic polices using multi-armed bandit process methodology, which are characterized by a set of Gittins indices as solutions to a system of integral equations. Optimal solutions for a number of problems with specific loss patterns are derived. Application of the theory to the classical no-loss model is also discussed which leads to new results.

A Lane-Based Analysis of Stochastic Breakdown Phenomena on an Urban Expressway Section

A Lane-Based Analysis of Stochastic Breakdown Phenomena on an Urban Expressway Section

Karlstad lean factory: an instructional factory for game-based lean manufacturing training

Simulation for training lean manufacturing ranges from simple paper-based or LEGO®-based games to larger scale simulation environments, for instance push car assembly. Some models for game-based learning are discussed and a model for lean manufacturing training is adopted. Many types of simulation may be suitable for teaching some basic elements of Lean manufacturing to students, but they are often less suitable for training industry workers in applying Lean manufacturing in their work environment. The latter group is more used to intuitive learning than to formal instruction. Thus, it is important that a training environment for this group more realistically represents the work environment; otherwise training transfer will be limited. For this reason, a lean training environment that includes materials processing stations as well as assembly areas was created. The stations exhibit some realistic behaviour such as stochastic breakdowns. Based on a comparison between factory workers and university students, five hypotheses for testing in future work are proposed.

Group scheduling in hybrid flexible flowshop with sequence-dependent setup times and random breakdowns via integrating genetic algorithm and simulation

In this paper, the problem of group scheduling in hybrid flexible flowshop with sequence-dependent setup times is studied. Owning to its algorithmic complexity and since the problem belongs to NP-hard class, utilisation of meta-heuristic algorithms is justified to tackle the potential complexity of the problem considered. Moreover, to further actualise the problem, one of the practical, yet rarely used assumptions is incorporated in this study: 'stochastic breakdowns'. By releasing this assumption and thanks to dynamic nature of the problem, the structural complexity increases markedly. In this regard, to overcome this form of complexity, simulation techniques are typically employed. Eventually, since the problem possesses both types of complexities (algorithm complexity and structural complexity), simulation is integrated with one of the most widely-used meta-heuristic approaches, namely genetic algorithm, to minimise the expected average of completion times. What is more, in order to analyse the impact of both the problem characteristics and the algorithmic parameters, a set of varied test samples are generated. Consequently, the obtained results are explored using Taguchi experimental design method.

Robust scheduling for flexible job shop problems with random machine breakdowns using a quantum behaved particle swarm optimisation

This paper addresses a robust schedule for a flexible job shop scheduling problem with random machine breakdown. A multi objective framework based on quantum particle swarm optimisation (QPSO) is proposed to generate the predictive schedules that can simultaneously optimise the makespan and the robust measures. The results indicate that the proposed QPSO algorithm is quite effective in reducing makespan in the event that uncertainty is encountered in terms of stochastic machine breakdown. An exhaustive experimental study is conducted to study the effect of different proposed robustness measures on the generated schedules using benchmark problems.

Optimal Rules for Single Machine Scheduling with Stochastic Breakdowns

This paper studies the problem of scheduling a set of jobs on a single machine subject to stochastic breakdowns, where jobs have to be restarted if preemptions occur because of breakdowns. The breakdown process of the machine is independent of the jobs processed on the machine. The processing times required to complete the jobs are constants if no breakdown occurs. The machine uptimes are independently and identically distributed (i.i.d.) and are subject to a uniform distribution. It is proved that theLongest Processing Time first(LPT) rule minimizes the expected makespan. For the large-scale problem, it is also showed that theShortest Processing Time first(SPT) rule is optimal to minimize the expected total completion times of all jobs.

Optimal run time for EPQ model with scrap, rework and stochastic breakdowns: A note

In a recent study [Chiu et al., 2007. Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns. European Journal of Operational Research 180, 664–676], the perfect rework of nonconforming items was assumed in a production system that is subject to stochastic breakdown and random defective rate. However, in most real-life manufacturing systems emphasizing on quality assurance, the perfect rework of nonconforming products may not always be possible as a result of various factors. Therefore, in order to enhance the practical usages of their research outcome, this paper incorporates failure in rework factor into Chiu et al.'s model, derives the optimal replenishment run time for the amended model, and investigates the effect of the failure in rework on the optimal operating policy through this exact model.

On the exploration of convexity about the expected total cost per unit time of replenishment run time problem with machine breakdown and failure in rework

Recently, Chiu et al. [Expert Systems with Applications 39 (2012) 1291-1297] study the optimal replenishment run time for a production system with stochastic machine breakdown and failure in rework. Basically, their model is rather interesting. However, their solution procedure based on Theorem 1 of Chiu et al. (2012) has shortcomings from the fundamentals of mathematics. The main purpose of this paper not only indicates its shortcomings but also presents the correct solution procedure for Chiu et al. (2012).