The asymptotic distribution for the time to failure of a fiber bundle

1979 ◽  
Vol 11 (1) ◽  
pp. 153-187 ◽  
Author(s):  
S. Leigh Phoenix
Keyword(s):  
Asymptotic Distribution ◽  
Fiber Bundle ◽  
Failure Time ◽  
Constant Load ◽  
Static Strength ◽  
Process Approach ◽  
Time To Failure ◽  
Failure Model ◽  
Load History ◽  
Asymptotically Normal

A model is developed for the failure time of a bundle of fibers subjected to a constant load. At any time, all surviving fibers share the bundle load equally while all failed fibers support no load. The bundle may collapse immediately or fibers may fail randomly in time, possibly more than one at a time. The failure time of the bundle is the failure time of the last surviving fiber. For a single fiber, the c.d.f. for the failure time is assumed to be a specific functional of an arbitrary load history. The model is developed using a quantile process approach. In the most important case the failure time of the bundle is shown to be asymptotically normal with known parameters. The bundle failure model has the features of both static strength and fatigue failure of earlier analyses, and thus is more realistic than earlier models.

The asymptotic distribution for the time to failure of a fiber bundle

1979 ◽  
Vol 11 (01) ◽  
pp. 153-187 ◽  
Author(s):  
S. Leigh Phoenix
Keyword(s):  
Asymptotic Distribution ◽  
Fiber Bundle ◽  
Failure Time ◽  
Constant Load ◽  
Static Strength ◽  
Process Approach ◽  
Time To Failure ◽  
Failure Model ◽  
Load History ◽  
Asymptotically Normal

A model is developed for the failure time of a bundle of fibers subjected to a constant load. At any time, all surviving fibers share the bundle load equally while all failed fibers support no load. The bundle may collapse immediately or fibers may fail randomly in time, possibly more than one at a time. The failure time of the bundle is the failure time of the last surviving fiber. For a single fiber, the c.d.f. for the failure time is assumed to be a specific functional of an arbitrary load history. The model is developed using a quantile process approach. In the most important case the failure time of the bundle is shown to be asymptotically normal with known parameters. The bundle failure model has the features of both static strength and fatigue failure of earlier analyses, and thus is more realistic than earlier models.

The time to failure of fiber bundles subjected to random loads

1979 ◽  
Vol 11 (03) ◽  
pp. 527-541 ◽  
Author(s):  
Howard M. Taylor
Keyword(s):  
Simple Model ◽  
Power Law ◽  
Failure Time ◽  
Constant Load ◽  
Asymptotic Distributions ◽  
Asymptotic Independence ◽  
Time To Failure ◽  
Random Load ◽  
The Mean ◽  
Wave Induced

The effect on cable reliability of random cyclic loading such as that generated by the wave-induced rocking of ocean vessels deploying these cables is examined. A simple model yielding exact formulas is first explored. In this model, the failure time of a single fiber under a constant load is assumed to be exponentially distributed, and the random loadings are a two-state stationary Markov process. The effect of load on failure time is assumed to follow a power law breakdown rule. In this setting, exact results concerning the distribution of bundle or cable failure time, and especially the mean failure time, are obtained. Where the fluctuations in load are frequent relative to bundle life, such as may occur in long-lived cables, it is shown that randomness in load tends to decrease mean bundle life, but it is suggested that the reduction in mean life often can be restored by modestly reducing the base load on the structure or by modestly increasing the number of elements in the bundle. In later pages this simple model is extended to cover a broader range of materials and random loadings. Asymptotic distributions and mean failure times are given where fibers follow a Weibull distribution of failure time under constant load, and loads that are general non-negative stationary processes subject only to some mild condition of asymptotic independence. When the power law breakdown exponent is large, the mean time to bundle failure depends heavily on the exact form of the marginal probability distribution for the random load process and cannot be summarized by the first two moments of this distribution alone.

The time to failure of fiber bundles subjected to random loads

1979 ◽  
Vol 11 (3) ◽  
pp. 527-541 ◽  
Author(s):  
Howard M. Taylor
Keyword(s):  
Simple Model ◽  
Power Law ◽  
Failure Time ◽  
Constant Load ◽  
Asymptotic Distributions ◽  
Asymptotic Independence ◽  
Time To Failure ◽  
Random Load ◽  
The Mean ◽  
Wave Induced

The effect on cable reliability of random cyclic loading such as that generated by the wave-induced rocking of ocean vessels deploying these cables is examined. A simple model yielding exact formulas is first explored. In this model, the failure time of a single fiber under a constant load is assumed to be exponentially distributed, and the random loadings are a two-state stationary Markov process. The effect of load on failure time is assumed to follow a power law breakdown rule. In this setting, exact results concerning the distribution of bundle or cable failure time, and especially the mean failure time, are obtained. Where the fluctuations in load are frequent relative to bundle life, such as may occur in long-lived cables, it is shown that randomness in load tends to decrease mean bundle life, but it is suggested that the reduction in mean life often can be restored by modestly reducing the base load on the structure or by modestly increasing the number of elements in the bundle.In later pages this simple model is extended to cover a broader range of materials and random loadings. Asymptotic distributions and mean failure times are given where fibers follow a Weibull distribution of failure time under constant load, and loads that are general non-negative stationary processes subject only to some mild condition of asymptotic independence. When the power law breakdown exponent is large, the mean time to bundle failure depends heavily on the exact form of the marginal probability distribution for the random load process and cannot be summarized by the first two moments of this distribution alone.

Dependability Analysis of Homogeneous Distributed Software/Hardware Systems

2015 ◽  
Vol 22 (02) ◽  
pp. 1550007
Author(s):  
G. Vijayalakshmi
Keyword(s):  
Reliability Analysis ◽  
Distributed System ◽  
Failure Time ◽  
Load Sharing ◽  
Accelerated Failure Time Model ◽  
Time To Failure ◽  
Critical Systems ◽  
Time Model ◽  
Distributed Software ◽  
Dependability Analysis

With the increasing demand for high availability in safety-critical systems such as banking systems, military systems, nuclear systems, aircraft systems to mention a few, reliability analysis of distributed software/hardware systems continue to be the focus of most researchers. The reliability analysis of a homogeneous distributed software/hardware system (HDSHS) with k-out-of-n : G configuration and no load-sharing nodes is analyzed. However, in practice the system load is shared among the working nodes in a distributed system. In this paper, the dependability analysis of a HDSHS with load-sharing nodes is presented. This distributed system has a load-sharing k-out-of-(n + m) : G configuration. A Markov model for HDSHS is developed. The failure time distribution of the hardware is represented by the accelerated failure time model. The software faults are detected during software testing and removed upon failure. The Jelinski–Moranda software reliability model is used. The maintenance personal can repair the system up on both software and hardware failure. The dependability measures such as reliability, availability and mean time to failure are obtained. The effect of load-sharing hosts on system hazard function and system reliability is presented. Furthermore, an availability comparison of our results and the results in the literature is presented.

A stochastic covariate failure model for assessing system reliability

2001 ◽  
Vol 38 (03) ◽  
pp. 761-767 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
System Reliability ◽  
Alternative Model ◽  
Failure Time ◽  
Failure Mechanisms ◽  
Failure Model ◽  
Proposed Model ◽  
Deterioration Process

Many failure mechanisms can be traced to an underlying deterioration process, and stochastically changing covariates may influence this process. In this paper we propose an alternative model for assessing a system's reliability. The proposed model expresses the failure time of a system in terms of a deterioration process and covariates. When it is possible to measure deterioration as well as covariates, our model provides more information than failure time for the purpose of assessing and improving system reliability. We give several properties of our proposed model and also provide an example.

Thin Thermally Efficient ICECool Defense Semiconductor Power Amplifiers

2017 ◽  
Vol 14 (3) ◽  
pp. 77-93 ◽  
Author(s):  
Sumeer Khanna ◽  
Patrick McCluskey ◽  
Avram Bar-Cohen ◽  
Bao Yang ◽  
Michael Ohadi
Keyword(s):  
Heat Flux ◽  
Structural Reliability ◽  
Mechanical Design ◽  
Substrate Thickness ◽  
Time To Failure ◽  
Failure Model ◽  
High Concentration ◽  
Element Analysis ◽  
Analysis Technique ◽  
Compact Design

Abstract Traditional power electronics for military and fast computing applications are bulky and heavy. The “mechanical design” of electronic structure and “materials” of construction of the components have limitations in performance under very high temperature conditions. The major concern here is “thermal management.” To be more specific, this refers to removal of high-concentration hotspot heat flux >5 kW/cm2, background heat flux >1 kW/cm2, and “miniaturization” of device within a substrate thickness of <100 μm. We report on the novel applications of contact-based thermoelectric cooling (TEC) to successful implementations of high-conductivity materials - diamond substrate grown on gallium nitride (GaN)/AlGaN transistors to keep the hotspot temperature rise of device below 5 K. The requirement for smarter and faster functionality along with a compact design is considered here. These efforts have focused on the removal of higher levels of heat flux, heat transfer across interface of junction and substrate, advanced packaging and manufacturing concepts, and integration of TEC of GaN devices to nanoscale. The “structural reliability” is a concern and we have reported the same in terms of mean time to failure (cycles) of SAC305 (96.5% tin, 3% silver, 0.5% cu) solder joint by application of Engelmaier's failure model and evaluation of stresses in the structure. The mathematical equation of failure model incorporates the failure phenomena of fatigue and creep in addition to the dwell time, average solder temperature, and plastic strain accumulation. The approach to this problem is a nonlinear finite element analysis technique, which incorporates thermal, mechanical, and thermoelectric boundary conditions.

scholarly journals Heat Transfer Behavior of Green Roof Systems Under Fire Condition: A Numerical Study

Buildings ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 206
Author(s):  
Gerzhova ◽  
Blanchet ◽  
Dagenais ◽  
Côté ◽  
Ménard
Keyword(s):  
Heat Transfer ◽  
Failure Time ◽  
Numerical Study ◽  
Fire Hazard ◽  
Green Roof ◽  
Green Roofs ◽  
Heat Transfer Process ◽  
Heat Fluxes ◽  
Substrate Thickness ◽  
Time To Failure

Currently, green roof fire risks are not clearly defined. This is because the problem is still not well understood, which raises concerns. The possibility of plants catching fire, especially during drought periods, is one of the reasons for necessary protection measures. The potential fire hazard for roof decks covered with vegetation has not yet been fully explored. The present study analyzes the performance of green roofs in extreme heat conditions by simulating a heat transfer process through the assembly. The main objective of this study was to determine the conditions and time required for the roof deck to reach a critical temperature. The effects of growing medium layer thickness (between 3 and 10 cm), porosity (0.5 to 0.7), and heating intensity (50, 100, 150, and 200 kW/m²) were examined. It was found that a green roof can protect a wooden roof deck from igniting with only 3 cm of soil coverage when exposed to severe heat fluxes for at least 25 minutes. The dependency of failure time on substrate thickness decreases with increasing heating load. It was also found that substrate porosity has a low impact on time to failure, and only at high heating loads.

scholarly journals A Dynamic Failure Time Degradation-Based Model

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1532
Author(s):  
Abdulhakim A. Albabtain ◽  
Mansour Shrahili ◽  
Lolwa Alshagrawi ◽  
Mohamed Kayid
Keyword(s):  
Hazard Rate ◽  
Failure Time ◽  
Degradation Process ◽  
Residual Lifetime ◽  
Time To Failure ◽  
Lifetime Distributions ◽  
Mean Residual Lifetime ◽  
Aging Properties ◽  
Degradation Models ◽  
Characterization Property

A novel methodology for modelling time to failure of systems under a degradation process is proposed. Considering the method degradation may have influenced the failure of the system under the setup of the model several implied lifetime distributions are outlined. Hazard rate and mean residual lifetime of the model are obtained and a numerical situation is delineated to calculate their amounts. The problem of modelling the amount of degradation at the failure time is also considered. Two monotonic aging properties of the model is secured and a characterization property of the symmetric degradation models is established.

A Physics of Failure Approach to Component Placement

1992 ◽  
Vol 114 (3) ◽  
pp. 305-309 ◽  
Author(s):  
M. D. Osterman
Keyword(s):  
Operating Temperature ◽  
Threshold Temperature ◽  
Time To Failure ◽  
Failure Model ◽  
Physics Of Failure ◽  
Component Placement ◽  
Convection Cooling ◽  
The Individual ◽  
Component Temperature ◽  
Cycles To Failure

Traditionally, placement techniques have focused on improving rotability based on minimizing the total wire length between interconnected components. However, electronic card assembly (ECA) reliability, which is measured in terms of time to failure, cycles to failure, or the hazard rates of the individual components, the interconnections, and the PWB, is also affected by component placement. This paper discusses component placement for reliability based on a failure model which incorporates component temperature, a base operating temperature, a threshold temperature, and change in temperature. Placement procedures are developed so as to minimize the time to failure or the total hazard rate of the components on a PWB utilizing a forced convection cooling.

Analysis of HDPE Failure Data in Support of Development of Flaw Acceptance Criteria for Butt Fusion Joints

2020 ◽  
Author(s):  
Cheng Liu ◽  
Douglas Scarth ◽  
Douglas P. Munson ◽  
Ryan Wolfe
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Failure Time ◽  
Slow Crack Growth ◽  
Time To Failure ◽  
Acceptance Criteria ◽  
Failure Data ◽  
Criteria For Evaluation ◽  
Hdpe Pipes

Abstract There is a need for ASME B&PV Code procedures and acceptance criteria for evaluation of flaws detected by inspection of high density polyethylene (HDPE) piping items in safety Class 3 systems. To support the development of flaw acceptance criteria for butt fusion joints in HDPE pipes, a series of coupon tests have been completed for specimens cut from butt fused HDPE pipes with surface or subsurface flaws placed in the joints prior to fusion process. Specimens containing known flaw sizes were tested under axial load at accelerated stresses and temperatures until failure; or until a prescribed number of test hours was reached. The failure time from the tests has been correlated to the net section stress and the stress intensity factor, and the results showed that the failure time can be better represented by the stress intensity factor. The test results were then used to fit the Brown and Lu formula that predicts the time to failure due to the slow crack growth of flaws as a function of stress intensity factor and temperature. With the developed Brown and Lu equation, the allowable stress intensity factors for a piping lifetime of 50 years at the maximum code allowable temperature of 60°C have been proposed for both surface and subsurface flaws in HDPE butt fusion joints. Examples of what might be corresponding allowable flaw sizes in the butt fusion joints of piping are also provided.

Sign in / Sign up

Export Citation Format

Share Document