Multi‐system reliability trend analysis model using incomplete data with application to tank maintenance

This paper focuses on the estimation of power law type reliability trend analysis model given incomplete failure data from multiple homogeneous machines. In many real situations, we encounter data having missing parts especially in the initial recording stage, so‐called left censored data. We provide a method to estimate the failure intensity function of power law process using left censored data from multiple machines. The method consists of two folds: initially estimate parameters via the law of large numbers theory and revise the estimated parameters recursively through the EM algorithm. The validity of our method is confirmed by simulation experiments. We also apply our method to the real‐world case, Korean ARMY tank maintenance data, and show that our proposed method is applicable to practical maintenance planning.     

A New Model for Repairable Systems with Nonmonotone Intensity Function

In this study, a new model based on the mixture of bounded Burr XII failure intensity and bounded intensity process is proposed to describe the failure intensity of minimally repaired systems with approximate bathtub behavior. The estimates of the model parameters are easily obtained using the maximum likelihood estimation method. The confidence intervals for the model parameters are also provided. Other existing models, such as superposed power law process, log‐linear process–power law process, and bounded bathtub intensity process are used to compare with our proposed model. Through numerical examples, the results show that our proposed model performs well regarding the Akaike information criterion value and the mean of square errors. Copyright © 2014 John Wiley & Sons, Ltd.     

Development of vertical axis wind turbines

This paper summarises the work done at the National Aeronautical Laboratory (NAL) between 1975 and 1977 on the development of vertical axis wind turbines based on the Darrieus rotor. On the analytical side, a performance analysis was developed which permits the estimation of the characteristics of such machines. A 5 m high wind turbine using curved wooden blades was designed, fabricated and tested. Both the theory and initial tests confirmed the low starting torque of the turbine. Wind tunnel tests were performed on model Savonius rotors to determine optimum starter bucket configurations. Finally a straight-bladed turbine was designed and constructed. It is concluded from our experience that darrieus burbines are likely to be useful in large systems used to generate electrical power for the grid; for direct water pumping purposes, however, these turbines are unlikely to be suitable.     

Engineering‐driven performance degradation analysis of hydraulic piston pump based on the inverse Gaussian process

As a key aircraft component, hydraulic piston pumps must be developed with high reliability. However, collecting failure time data of such pumps for reliability analysis is a big challenge. To save testing time, performance degradation data obtained from degradation tests can be used for quick reliability estimation of hydraulic piston pumps. This paper proposes an engineering‐driven performance degradation analysis method considering the nature of mechanical wear of hydraulic piston pumps. First, the failure mechanism of a type of hydraulic piston pump is investigated. By taking into account the close relationship between the degradation rate and the failure mechanism, an inverse Gaussian (IG) process model with a variable rate is developed to describe the degradation behavior of the pump. Under this model, a Bayesian statistical method is developed for degradation data analysis. The corresponding procedure for model parameter estimation and reliability evaluation is also presented. The proposed degradation analysis method is illustrated using a real experimental data. The results show that the engineering‐driven approach is quite effective in evaluating the lifetime of the hydraulic piston pump and will improve the overall reliability of aircraft operation in the field.     

TTT-based tests for trend in repairable systems data

A major aspect of analysis of failure data for repairable systems is the testing for a possible trend in interfailure times. This paper reviews some important and popular graphical methods and tests for the nonhomogeneous Poisson process model. In particular, the total time on test (TTT) plot is considered, and trend tests based on the TTT-statistic are motivated and derived. In particular, a test based on the Anderson-Darling statistic is suggested. The tests are evaluated and compared in a simulation study, both with respect to the achievement of correct significance level and rejection power. The considered alternatives to ‘no trend’ are the log-linear, power law and a class of bathtub-shaped intensity functions. The simulation study involves single systems, as well as the case where several independent systems of the same kind are observed.     

On the overhaul effect for repairable mechanical units: a Bayes approach

This paper deals with the statistical analysis, from a Bayes viewpoint, of the failure data of repairable mechanical units subjected to minimal repairs and periodic overhauls. A proportional age reduction model is assumed to model the effect of overhauls on the reliability of the unit, whereas the failure process between two successive overhaul epochs is modeled by the power law process. Point and interval estimation of model parameters, as well as of quantities of large interest, are provided on the basis of a number of suitable prior densities, which reflect different degrees of belief on the failure/repair process. Hypothesis tests on the effectiveness of performed overhauls are developed on the basis of Bayes factor, and some guidelines to perform sensitivity analysis versus the prior information are provided. Finally, a numerical application illustrates the proposed inference and testing procedures.     

Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results

In capturing visco-elastic behavior, experimental tests play a fundamental rule, since they allow to build up theoretical constitutive laws very useful for simulating their own behavior. The main challenge is representing the visco-elastic materials through simple models, in order to spread their use. However, the wide used models for capturing both relaxation and creep tests are combinations of simple models as Maxwell and/or Kelvin, that depend on several parameters for fitting both creep and relaxation tests. This paper, following Nutting and Gemant idea of fitting experimental data through a power law function, aims at stressing the validity of fractional model. In fact, as soon as relaxation test is well fitted by power law decay then the fractional constitutive law involving Caputo’s derivative directly appears. It will be shown that fractional model is proper for studying visco-elastic behavior, since it may capture both relaxation and creep tests, requiring the identification of two parameters only. This consideration is assessed by the good agreement between experimental tests on creep and relaxation and the fractional model proposed. Experimental tests, here reported are performed on two polymers having different chemical physical properties such that the fractional model may cover a wide range of visco-elastic behavior.     

Modeling the failure data of a repairable equipment with bathtub type failure intensity

The paper deals with the reliability modeling of the failure process of large and complex repairable equipment whose failure intensity shows a bathtub type non-monotonic behavior. A non-homogeneous Poisson process arising from the superposition of two power law processes is proposed, and the characteristics and mathematical details of the proposed model are illustrated. A graphical approach is also presented, which allows to determine whether the proposed model can adequately describe a given failure data. A graphical method for obtaining crude but easy estimates of the model parameters is then illustrated, as well as more accurate estimates based on the maximum likelihood method are provided. Finally, two numerical applications are given to illustrate the proposed model and the estimation procedures.     

Model for Failure Point Process of a Repairable System and Application

A engineering system is usually repairable,and failure process of a repairable system is often described by a failure point process. The power law model is a commonly used approach to model the failure point process.This paper introduces the concept and model for the failure process of repairable system. The method of parameter estimation is developed,and failure observations are fitted into a power-law model by using the least square method. Two applications of the pressent model are discussed according to the practical failure data of the central cooling system of a nuclear power plant. One application is determining the optimal overhaul time,and the other is evaluating the quality of maintenance. This paper provides references for the overhaul decision making and maintenance quality evaluation in reality.     

贴壁射流形态对跌坎消能的水力特性影响试验研究

贴壁射流形态是影响跌坎型消力池消能效果和水力特性的重要因素之一。为研究贴壁射流形态对输水工程跌坎消能效果和水流特性的影响,通过１：２０的水工模型试验对反弧贴壁射流和平抛贴壁射流情况下的跌坎消力特性进行试验观察和测试。获得不同射流形态下的主流形态、消力池底板脉动压力过程及水面波动时程曲线。试验结果表明：平抛型贴壁射流通过增加射流入水的俯角,使射流进入消力池后产生强烈紊动和翻滚,导致消力池底板的时均压力和脉动压力比反弧贴壁射流大,但平抛贴壁射流减小了消力池和稳水区的水面波动,能更好地满足输水工程下游隧洞稳定输水要求。     

Composite load models based on field measurements and their applications in dynamic analysis

The composite load model with an induction motor in parallel with a static load has been studied and applied in analysis of dynamics of power systems for a long time. However, the load parameters from field tests are still very limited. Based on the theoretical results of identifiability and estimation methodology of load parameters that have been achieved in the previous work, a project of load modelling based on field measurements is described. Eight sets of equipment for load modelling were installed in HeNan Electric Power Grid (HNEPG) Corporation, and the dynamics of the load were recorded and a dynamic index is proposed to evaluate the dynamic characteristics of the data measured. The load models derived from the field measurements are applied to stability analysis of HNEPG. The critical clearing time and power transfer capability analyses illustrate the enhancement of the stability analysis of the power grid using the load parameters derived from the field measurements and show the benefits of application of such model parameters in power system dynamic analysis.     

Modelling hybrid production systems through the ACD specification: a case study in the fibre-glass industry

This paper is aimed at formalising a model for hybrid production systems where the interactions between the continuous process parts and the manufacturing sub-systems are given by minor stoppages. The proposal is to represent the effects of the continuous process dynamics on discrete manufacturing sub-systems using autoregressive conditional duration (ACD) models originally conceived to treat high-frequency and irregularly spaced financial transaction data. The proposed methodology has been tested on a real-life fibre-glass production plant exploiting simulation techniques. The physical model of the furnace and spooling-bushing department has been run in two different conditions: (i) the fibre-glass breakings, i.e. minor stoppages, on the spooling-bushing machines are generated according to the proposed approach; (ii) historical fibre-glass breakings data are used. The comparison between the simulation results shows that for three spooling-bushing machines only out of 24, the daily throughput of completed spools and the empirical distributions for the uncompleted spools weight are dissimilar under the two different conditions. Therefore, the ACD-based model proved useful for representing the occurrence of fibre-glass breakings on the spooling-bushing machines and, in more general terms, for the logical modelling of the hybrid production systems, where the relationships between continuous and discrete parts are given by minor stoppages.     

Inference for a geometric‐poisson‐Rayleigh distribution under progressive‐stress accelerated life tests based on type‐I progressive hybrid censoring with binomial removals

Based on failures of a parallel‐series system, a new distribution called geometric‐Poisson‐Rayleigh distribution is proposed. Some properties of the distribution are discussed. A real data set is used to compare the new distribution with other 6 distributions. The progressive‐stress accelerated life tests are considered when the lifetime of an item under use condition is assumed to follow the geometric‐Poisson‐Rayleigh distribution. It is assumed that the scale parameter of the geometric‐Poisson‐Rayleigh distribution satisfies the inverse power law such that the stress is a nonlinear increasing function of time and the cumulative exposure model for the effect of changing stress holds. Based on type‐I progressive hybrid censoring with binomial removals, the maximum likelihood and Bayes (using linear‐exponential and general entropy loss functions) estimation methods are considered to estimate the involved parameters. Some point predictors such as the maximum likelihood, conditional median, best unbiased, and Bayes point predictors for future order statistics are obtained. The Bayes estimates are obtained using Markov chain Monte Carlo algorithm. Finally, a simulation study is performed, and numerical computations are performed to compare the performance of the implemented methods of estimation and prediction.     

Effects of temperature and strain level on stress relaxation behaviors of polypropylene sutures

An investigation has been conducted on stress relaxation behaviors of polypropylene sutures under different temperatures and strain levels in a temperature-controlled water bath. The study showed that the temperature and strain level significantly affected the stress relaxation behaviors of the sutures. High temperature resulted in fast stress relaxation. The stress relaxation data could be well described by two empirical formulas. For most of the test conditions, the stress relaxation tests caused limited permanent deformation in sutures. Effects of temperature on the permanent deformation may be illustrated by a power law. The tensile properties of the sutures were not affected adversely by the stress relaxation tests, indicating good properties of polypropylene sutures.     

State-space model of grid-connected inverters under current control mode

Growth of distributed generation has led to distribution systems with a mixture of rotating machine generators and inverter interfaced generators. The stability of such networks needs to be studied through the analysis of state-space models, and so suitable models of inverters are needed to complement the well-established models of rotating machines. As machine models include features such as automatic voltage regulators and wash-out functions, the inverter model also includes phase-locking functions and internal control loops. The model for voltage source inverters with an internal current control loop, an outer power regulation loop, a measurement of average power and a phase-locked loop has been developed. The model is presented in detail and is formed with a state-vector, similar to that used for rotating machines. The model includes nonlinear terms but can be linearised about an operating point. The state-space model is verified against a component-level time-step simulation in Simulink/PLECS     

Pore pressure cohesive zone modeling of hydraulic fracture in quasi-brittle rocks

Hydraulic fracturing technology has been widely applied in the petroleum industry for both waste injection and unconventional gas production wells. The prevailing analytical solutions for hydraulic fracture mainly depend on linear elastic fracture mechanics. These methods can give reasonable prediction for hard rock, but are ineffective in predicting hydraulic fractures in quasi-brittle materials, such as ductile shale and sandstone. One of the reasons is that the fracture process zone ahead of the crack tip and the softening effect should not be neglected for quasi-brittle materials. In the current work, a set of chevron-notch three point bending tests were performed on sandstone samples from an oil field in Ordos Basin, Shaanxi province, China, and the results were compared with the cohesive zone method based on finite element analysis. The numerical results fit the experimental data well and it shows that the cohesive zone model and the Traction-Separation law used in the model are effective in modeling fracture nucleation and propagation in sandstone without considering the porous effect. A 3D pore pressure cohesive zone model was developed to predict nucleation and propagation of a penny-shaped fluid-driven fracture. The predictions were compared with the analytical asymptotic solutions and a field minifrac test from the literature; it shows that the proposed method can not only predict the length and aperture of hydraulic fracture well, but also predict the bottomhole pressure with reasonable accuracy. Based on analytical asymptotic and computational solutions, parametric studies were conducted to investigate the effects of different parameters on the fracture aperture and fracture length, fracture process zone and bottomhole pressure.     

Reliability analysis for electronic devices using beta‐Weibull distribution

Today, in reliability analysis, the most used distribution to describe the behavior of electronic products under voltage profiles is the Weibull distribution. Nevertheless, the Weibull distribution does not provide a good fit to lifetime datasets that exhibit bathtub‐shaped or upside‐down bathtub–shaped (unimodal) failure rates, which are often encountered in the reliability analysis of electronic devices. In this paper, a reliability model based on the beta‐Weibull distribution and the inverse power law is proposed. This new model provides a better approach to model the performance and fit of the lifetimes of electronic devices. To estimate the parameters of the proposed model, a Bayesian analysis is used. A case study based on the lifetime of a surface mounted electrolytic capacitor is presented, the results showed that the estimation of the proposed model differs from the inverse power law–Weibull and that it affects directly the mean time to failure, the failure rate, the behavior, and the performance of the capacitor under analysis.     

A hierarchical modeling approach to accelerated degradation testing data analysis: A case study

In this case study, we investigate the degradation process of light‐emitting diodes (LEDs), which is used as a light source in DNA sequencing machines. Accelerated degradation tests are applied by varying temperature and forward current, and the light outputs are measured by a computerized measuring system. A degradation path model, which connects to the LED function recommended in Mitsuo (1991), is used in describing the degradation process. We consider variations in both measurement errors and degradation paths among individual test units. It is demonstrated that the hierarchical modeling approach is flexible and powerful in modeling a complex degradation process with nonlinear function and random coefficient. After fitting the model by maximum likelihood estimation, the failure time distribution can be obtained by simulation. Copyright © 2010 John Wiley & Sons, Ltd.     

Reliability Modelling of Multiple Repairable Units

This paper proposes a model selection framework for analysing the failure data of multiple repairable units when they are working in different operational and environmental conditions. The paper provides an approach for splitting the non‐homogeneous failure data set into homogeneous groups, based on their failure patterns and statistical trend tests. In addition, when the population includes units with an inadequate amount of failure data, the analysts tend to exclude those units from the analysis. A procedure is presented for modelling the reliability of a multiple repairable units under the influence of such a group to prevent parameter estimation error. We illustrate the implementation of the proposed model by applying it on 12 frequency converters in the Swedish railway system. The results of the case study show that the reliability model of multiple repairable units within a large fleet may consist of a mixture of different stochastic models, that is, the homogeneous Poisson process/renewal process, trend renewal process, non‐homogeneous Poisson process and branching Poisson processes. Therefore, relying only on a single model to represent the behaviour of the whole fleet may not be valid and may lead to wrong parameter estimation. Copyright © 2015 John Wiley & Sons, Ltd.     

A model based creep equation for 9Cr–1Mo–0·2V (P91 type) steel

Abstract

The isothermal constant stress creep tests data for a 9Cr–1Mo–0·2V (P91 type) steel were submitted for a phenomenological analysis in order to obtain the relevant creep equation for such steel. Namely, the minimum creep strain rate of P91 type steel cannot be described by the simple Arrhenius type power law constitutive model. The incorporation of the threshold stress concept in the analysis of creep data leads to a modified power law, which satisfactorily describes the creep behaviour of the examined P91 steel. However, the threshold stress is not a good material parameter, as it often varies with temperature and/or applied stress. This adds uncertainty to the extrapolation of the creep rates into ranges where experimental data are not available. Besides the fact that the physical foundation for a threshold stress is questionable from a scientific point of view, this is a serious practical limitation of the modified power law creep equation. The second creep equation proposed in the present paper is the improved stress dependent energy barrier model. The improvement of the standard model is based on two assumptions: first, on the hypothesis that the application of a stress also affects the energy barrier to be overcome when a local region transitions from the initial to the final state, and second, by applying a simple power function of stress instead of a hyperbolic sin function in the model based equation. The obtained value of stress exponent, n=5·5, is too high for entirely climb controlled creep. The apparent activation energy of approximately 510 to 545 kJ mol^?1, which is considerably higher than the activation energy for lattice diffusion, is the stress dependent activation energy of the slowest, dominant rate controlling process of the supposed multiple creep mechanisms.