Weibull Failure Distribution Research Articles

Reliability prediction of a 30 kW power electronics converter

This paper describes the challenges involved for predicting reliability of power electronics converter systems and provides recommendations. To this aim, a case study for modelling a 30 kW inverter platform for power quality applications is presented. The converter is based on different circuit boards that were analysed by electronics reliability prediction. In addition, fans and an IGBT module were modelled by a Weibull failure distribution. The study underlines that the reliability assessment of complex electronics is a persisting challenge.

Optimal post-warranty replacement policy based on number of product failures for the second-hand product

This paper deals with a post-warranty maintenance model for the second-hand product as follows. The second-hand product of age [Formula: see text], which is assumed to be positive, is purchased with a fixed length of non-renewing warranty, during which the product is given a fixed number of preventive maintenances periodically by the dealer. At each preventive maintenance, the failure rate of the product is adjusted to some extent for the purpose of reducing the likelihood of product failure. At the expiration of warranty, the user starts to self-maintain the product until a pre-determined number of failures occur, at which time the product is replaced by another one. For each post-warranty failure, only a minimal repair is taken to restore the failed product to its previous functioning state. This paper aims to determine an optimal number of post-warranty product failures that minimizes the expected cost rate during the second-hand product’s life cycle. To this end, we derive a formula to evaluate the expected cost rate during the second-hand product’s life cycle by assuming a certain cost structure for maintaining the product during the life-span of the product and determine an optimal number of post-warranty product failures from the user’s perspective. And we provide a numerical example to illustrate our proposed optimal maintenance model by assuming a Weibull failure distribution. The main contribution of this work is to use the number of post-warranty failures to propose a maintenance model for the second-hand product, where the number of failures is in general easier to observe than the failure times.

Improving the availability of Australian hospitals’ critical medical devices

Maintenance of Australian hospitals’ Critical Medical Devices (CMDs) can be somewhat more demanding than conventional assets from other industries. This is primarily driven by the requirement for CMDs to operate with exceptional levels of reliability. This study proposes a combined Reliability Centred Maintenance (RCM) and prioritisation maintenance strategy with the objective of improving the availability of CMDs. Reliability functions were used in this study as CMDs exhibit Weibull failure distributions identical to general products. The Analytical Hierarchy Process (AHP) was chosen as the maintenance prioritisation strategy because of its ability to analyse complex decisions using subjective and objective criteria. An online survey targeted at hospital managers and Biomedical Engineering Technicians (BMET) was developed to determine the priority of Preventive Maintenance (PM) activities for certain CMD and propose a range of optimal PM intervals for a variety of reliabilities. Results from the prioritisation study have shown that the external environmental effects from COVID-19 had significantly increased the priority for PM of ventilators over other CMDs. Ventilator manufacturers recommend conducting PM once over 12 months or every 5000 hours of operation. The proposed study has revealed that the PM of ventilators can be scheduled once every 14 months to obtain reliabilities close to 100%. Similar outcomes were observed for other CMDs as well. The aftermath of this study will ensure better availability of CMDs, as well as will help to alleviate complications with PM scheduling for managers and BMET departments.

Computing the Number of Failures for Fuzzy Weibull Hazard Function

The number of failures plays an important factor in the study of maintenance strategy of a manufacturing system. In the real situation, this number is often affected by some uncertainties. Many of the uncertainties fall into the possibilistic uncertainty, which are different from the probabilistic uncertainty. This uncertainty is commonly modeled by applying the fuzzy theoretical framework. This paper aims to compute the number of failures for a system which has Weibull failure distribution with a fuzzy shape parameter. In this case two different approaches are used to calculate the number. In the first approach, the fuzziness membership of the shape parameter propagates to the number of failures so that they have exactly the same values of the membership. While in the second approach, the membership is computed through the α-cut or α-level of the shape parameter approach in the computation of the formula for the number of failures. Without loss of generality, we use the Triangular Fuzzy Number (TFN) for the Weibull shape parameter. We show that both methods have succeeded in computing the number of failures for the system under investigation. Both methods show that when we consider the function of the number of failures as a function of time then the uncertainty (the fuzziness) of the resulting number of failures becomes larger and larger as the time increases. By using the first method, the resulting number of failures has a TFN form. Meanwhile, the resulting number of failures from the second method does not necessarily have a TFN form, but a TFN-like form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification (GMVD) method. The results show that for certain weighting factor of the GMVD, the cores of these fuzzy numbers of failures are identical.

Failure Rate Prediction of Belt Conveyor Systems using 2-parameter Weibull distribution

Abstract: The conveyor belt is one of the most operational critical equipment’s in the mining industry, they are mostly used in the transportation of crushed materials from the crushing station to where there’ll be further processed. Due to the increasing complexity of belt conveyor systems, managing their integrity has become even more difficult, as they are now used across various industries, environments and carry materials of different weight variations, leaving them susceptible to failures (1). This paper provides an industry specific knowledge on how Weibull analysis can be used to predict the failure rate of a conveyor belt system, using parameters such as the time to failure (TTF), installation and failure dates, as determinant parameters for the predictions. Several Weibull failure distributions and functions have been used to establish accuracy of results and to create comparisons on the different ways in which risk, unreliability and availability are quantified, using calculated values such as the Shape and scale parameter. The paper utilizes real world case studies in the area of mining, which sheds light on key component failures and their cut sets within the conveyor belt system (2) Keywords: TTF, TTR, Threshold parameter, Repair date, Shape parameter, B10, B15, B20, Scale parameter, ECA, CDF, PDF

Reliability Assessment of a Base Transceiver Station Using 2-Parameter Weibull Distribution Method

About 80% interruptions of cellular network availability occur due to power outage on BTS stations and reliability analysis of these systems is yet to receive exhaustive studies. Most network providers solely depend on generating power on their BTS sites using diesel generators since the grid power is least reliable, but the frequency of power outages from the diesel generators is alarming, hence, the need to analyse the reliability of these generators and their maintenance routine in relation to the site availability.
 In this study, the reliability of a Base Transceiver Station (BTS) is assessed by analysis of data obtained within a period of six months from four BTS sites used as case study using 2-parameter Weibull failure distribution method. The failure times of each BTS site were rank-ordered and the estimates of Weibull parameters θ and β were obtained from Weibull least-squares plots.
 The Weibull plots for the four BTS sites had a good index of fit which shows that a strong linear relationship exists. The value of the shape parameter (β) was found to be between the range of 1< β < 3 for all the BTS sites studied. This means that the probability density function is skewed and the failure rate of the BTS sites is increasing. The reliability of each BTS site was successfully computed. The reliability of the four BTS sites was found to be increasing as their values of scale parameter, θ increases. From the results obtained, BTS site RV0144 had the highest reliability while BTS site RV0248 had the lowest reliability.

Stochastic modeling of non-identical redundant systems with priority, preventive maintenance, and Weibull failure and repair distributions

The ever-increasing demand of automation in appliances and economic constraints in purchasing capacity of consumers motivate to analyse the non-identical redundant system. For this analysis, a stochastic model has been designed for a non-identical redundant system having two units: one operative and other cold standby. Each unit has two possible states: either operative or failure. Original unit gets priority for repair over repair and preventive maintenance of duplicate unit. The repairs, preventive maintenance, and switches used to shift standby unit into operation are perfect. All failure and repair time random variables are arbitrary distributed. The system is observed using SMP and RPT to obtain various characteristics of interest to system designers. At last, some numerical results have been obtained by considering exponential, Rayleigh, and Weibull distributions, and compared with the results obtained by Kumar et al. (Rev Invest Oper 37(3):247–257, 2016a; Cogent Math 3(1):1135721, 2016b).

Goodness-of-fit test for generalised renewal process

Goodness-of-Fit (GOF) tests for the non-repairable systems as modelled through exponential, Weibull, normal and lognormal failure distributions are well touched upon in the literature. Substantial efforts have been made in developing GOF tests for non-repairable systems and Non-Homogeneous Poisson Process (NHPP) modelled through Power-Law Process (PLP). However, the literature is found to be limited in developing GOF models for imperfect repair modelled through Generalised Renewal Process (GRP). The paper, besides reviewing six trend tests, also develops a GOF test for repairable systems modelled through GRP based on Kijima I (KI) virtual age concept. KI takes into consideration the effect of repair effectiveness along with the shape and scale parameters. The developed GOF test model is a modification of the present Cramer-Von Mises (CVM) GOF test model available for PLP. The efficacy of the model is demonstrated with the help of three failure data sets.

Influence of deformation history parameters on softening behaviour of concrete

AbstractThe aim of this study is to investigate elasticity based damage models in which the isotropic damage is driven by different history parameters under uniaxial setting. This leads to a suitable history parameter for the description of material strain‐softening realistically. Existing damage evolution laws from literatures are used to compare the results using strain and energy equivalence principles. A suitable damage evolution law which is similar to Weibull's failure distribution is proposed in the framework of energy equivalence. Numerical results exhibit good agreement with experimental results. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Adequacy of dual-variable Weibull failure distribution for oil-impregnated paper under pulsating DC voltage

This paper presents an experimental work investigating the failure data of oil-impregnated paper under pulsating DC voltage. The failure data of the oil-impregnated paper specimens were obtained through constant voltage stress tests; the Weibull distribution was used to estimate the statistical distribution of failure data. The exponential function (EF) and the inverse power function (IPF) were used to modify the Weibull distribution of failure data, so as to obtain two dual-variable Weibull failure distributions (WFDs), which were used to analyze failure data of oil-paper specimens obtained under pulsating DC and individual DC and AC voltages. Their adequacies were evaluated by using failure data obtained through the constant stress tests under various voltages. Both EF-modified and IPF-modified WFDs show more adequacy for failure data of oil-paper insulation under DC and pulsating DC voltages than AC voltages. The EF-modified WFD was more adequate than IPF-modified WFD in estimating the statistical distribution of failure data.

Scale-dependent measurements of meteorite strength: Implications for asteroid fragmentation

Measuring the strengths of asteroidal materials is important for developing mitigation strategies for potential Earth impactors and for understanding properties of in situ materials on asteroids during human and robotic exploration. Studies of asteroid disruption and fragmentation have typically used the strengths determined from terrestrial analog materials, although questions have been raised regarding the suitability of these materials. The few published measurements of meteorite strength are typically significantly greater than those estimated from the stratospheric breakup of meter-sized meteoroids. Given the paucity of relevant strength data, the scale-varying strength properties of meteoritic and asteroidal materials are poorly constrained. Based on our uniaxial failure studies of centimeter-sized cubes of a carbonaceous and ordinary chondrite, we develop the first Weibull failure distribution analysis of meteorites. This Weibull distribution projected to meter scales, overlaps the strengths determined from asteroidal airbursts and can be used to predict properties of to the 100m scale. In addition, our analysis shows that meter-scale boulders on asteroids are significantly weaker than small pieces of meteorites, while large meteorites surviving on Earth are selected by attrition. Further, the common use of terrestrial analog materials to predict scale-dependent strength properties significantly overestimates the strength of meter-sized asteroidal materials and therefore is unlikely well suited for the modeling of asteroid disruption and fragmentation. Given the strength scale-dependence determined for carbonaceous and ordinary chondrite meteorites, our results suggest that boulders of similar composition on asteroids will have compressive strengths significantly less than typical terrestrial rocks.

Reliability-Aware Speedup Models for Parallel Applications with Coordinated Checkpointing/Restart

Speedup models are powerful analytical tools for evaluating and predicting the performance of parallel applications. Unfortunately, the well-known speedup models like Amdahl’s law and Gustafson’s law do not take reliability into consideration and therefore cannot accurately account for application performance in the presence of failures. In this study, we enhance Amdahl’s law and Gustafson’s law by considering the impact of failures and the effect of coordinated checkpointing/restart. Unlike existing analytical studies relying on Exponential failure distribution alone, in this work we consider both Exponential and Weibull failure distributions in the construction of our reliability-aware speedup models. The derived reliability-aware models are validated through trace-based simulations under a variety of parameter settings. Our trace-based simulations demonstrate these models can effectively quantify failure impact on application speedup. Moreover, we present two case studies to illustrate the use of these reliability-aware speedup models.

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.

Using group replication for resilience on exascale systems

High performance computing applications must be resilient to faults. The traditional fault-tolerance solution is checkpoint-recovery, by which application state is saved to and recovered from secondary storage throughout execution. It has been shown that, even when using an optimal checkpointing strategy, the checkpointing overhead precludes high parallel efficiency at large scale. Additional fault-tolerance mechanisms must thus be used. Such a mechanism is replication, that is, multiple processors performing the same computation so that a processor failure does not necessarily imply an application failure. In spite of resource waste, replication can lead to higher parallel efficiency when compared to using only checkpoint-recovery at large scale. We propose to execute and checkpoint multiple application instances concurrently, an approach we term group replication. For exponential failures we give an upper bound on the expected application execution time. This bound corresponds to a particular checkpointing period that we derive. For general failures, we propose a dynamic programming algorithm to determine non-periodic checkpoint dates as well as an empirical periodic checkpointing solution whose period is found via a numerical search. Using simulation we evaluate our proposed approaches, including comparison to the non-replication case, for both exponential and Weibull failure distributions. Our broad finding is that group replication is useful in a range of realistic application and checkpointing overhead scenarios for future exascale platforms.

일회성 시스템의 저장신뢰도 결정 모델에 관한 연구

Some systems such as missiles and ammunitions are used only one time in combat or emergency situation. Predicting correct storage reliability is very important for those systems which are inspected periodically. Many researches have been done for predicting the storage reliability using generally exponential or Weibull failure distribution. However, recent studies show the hazard functions follow various types of failure distributions. So in this paper, we proposed a generalized model that measures the storage reliability regardless of type of failure distributions. And this model reflects inspection error and failures that might be occurred during periodical check and within storage term as well.

RELIABILITY AND AVAILABILITY ANALYSIS OF MECHANICAL SYSTEMS USING STOCHASTIC PETRI NET MODELING BASED ON DECOMPOSITION APPROACH

Reliability and availability assessment of a complex system in a single model, considering binary states of individual components, using Markov technique is difficult due to state space explosion problem. Inclusion of various types of dependencies in the model further aggravates it. To overcome this, Stochastic Petri net (SPN) modeling based on decomposition is proposed for reliability and availability assessment of mechanical systems. The decomposition is based on three aspects of the system: Hierarchical level, basic structure and dependency. The model is demonstrated at three hierarchical levels. Individual component (level '3') SPN model is developed assuming Weibull failure distribution, while the individual subsystem (level '2') SPN model is developed considering the arrangement of components within the subsystem. The individual model at level '2' is reduced to an equivalent single net model and its equivalent transition rate is derived from its basic structure assuming the independence of components. This along with the dependencies (e.g. repair, standby redundancy) are included in the system model (level '1'). The repair distribution in this model is assumed exponential. Reachable markings are generated for the system model to obtain the reduced state space of Semi-Markov model for assessment of reliability and availability of the system. The steps of the proposed methodology are suggested and these are illustrated for a pumping system, with two pumps; one in standby.

Bimodal Weibull Distribution of Metal/High-$\kappa$ Gate Stack TDDB—Insights by Scanning Tunneling Microscopy

We provide new insights, via nanoscale TDDB testing, into the bimodal Weibull failure distribution obtained from area scaling of high-κ (HK) gate stack. Time-to-breakdown (BD) statistics for grain boundary (GB) and grain in a polycrystalline HK gate stack are obtained individually from localized constant voltage stressing via a scanning tunneling microscope. In spite of an initial difference in the preexisting defect density, no apparent difference in the Weibull slope is observed for the two sets of BD statistics. The bimodal Weibull distribution is shown to be a combined effect: 1) The steep Weibull slope of the lower percentile, arising from large-area devices, is related to BD at GBs, and 2) the upper percentile, arising from small-area devices, is mostly related to grain BDs. In this case, the Weibull slope is reduced by a small fraction of these devices exhibiting early failures due to GB BDs. We show directly that structural defects in an HK dielectric, particularly GBs, play an important role on its BD distribution.

Gate oxide reliability at the nanoscale evaluated by combining conductive atomic force microscopy and constant voltage stress

The gate oxide integrity of different thin films (silicon dioxide, silicon nitride, and hafnium oxide) was analyzed by constant voltage stress (CVS) at the nanoscale using conductive atomic force microscopy (cAFM) with the probe tip directly in contact to the dielectric layer. The results were evaluated assuming a Weibull failure distribution for the dielectrics under voltage stress, and a good fit was obtained for the measurement data. This indicates that CVS measurements at the nanoscale can be applied for inline characterization of as-deposited dielectrics without the need for gate electrodes. In addition, time-to-breakdown extracted from the CVS using cAFM was compared to data retrieved from CVS measurements using conventional current-voltage measurements on samples with gate electrodes. In particular, area scaling of CVS data over eight orders of magnitude using cAFM was performed for the first time. The evaluation indicates a decent match between macroscopic and nanoscale CVS measurements for the hafnium oxide and silicon dioxide samples. In contrast, significant discrepancies are evident for the silicon nitride samples, which may be related to charge trapping effects.

Guaranteeing Service Availability in SLAs; a Study of the Risk Associated with Contract Period and Failure Process

Service Level Agreements (SLAs) are a common means to define the obligations of network/service providers and users in business relationships. The terms that define the guaranteed availability for a given period are an important element of these contracts. The appropriate selection values is difficult due to the large number of variables involved, the complexities of the network and service provision and the computational challenge posed by the transient solution, as opposed to a steady state, that is needed. A common policy taken to solve it, is using the steady state availability as a reference. Nevertheless this simplification may put on risk the contract fulfillment as stochastic variation of the measured availability is significant over a typical contract period. This paper analyzes the relevance that the interval availability analysis has on SLAs, and provides suggestions to the network providers on the selection of adequate availability guarantees. The interval availability of unprotected and shared protected connections is studied under exponential and Weibull failure and repair distributions. It is observed that for a single path scenario, a small reduction of the guaranteed availability below the steady state value improve the probability to meet the requirements considerably. The same is the case for connections with shared backup protection. However performing this analysis in the transient domain is quite demanding. Hence, to simplify it, it is proposed to obtain the steady state results and introduce a safeguard factor to control that the availability guarantee is meet. For the Weibull distributed times between failures, where the shape factor is less than one, as observed in operational networks, the the probability of meeting a guaranteed availability over a finite contract period, decrease more radically than for the commonly assumed Poisson failure process. This increases the importance of making a transient analysis.

Optimal accelerated life tests under interval censoring with random removals: the case of Weibull failure distribution

In this paper, optimal accelerated life test (ALT) plans are investigated under progressive Type I interval censoring with random removals when lifetimes are Weibull distributed. The optimal ALT plans which minimize the asymptotic variance of the estimated qth quantile for different combinations of total number of inspections and removal probability are presented. For implementation convenience, the practical plans, which adopt the same optimality criterion but the inspection times are determined based on the ideas of equally spaced or equal probability scheme at each stress level, are also derived. Numerical studies are conducted to evaluate the relative efficiency of a practical plan to the corresponding optimal ALT plan. Some suggestions are given to experimenters for selecting an appropriate practical plan in designing an ALT under the proposed censoring scheme.