Failure Intensity Function Research Articles

Reliability modelling and evaluating of wind turbine considering imperfect repair

To model and evaluate the reliability of wind turbine (WT) under imperfect repair, an improved Log-linear Proportional Intensity Model (LPIM)-based method was proposed. Initially, using the three-parameter bounded intensity process (3-BIP) as the benchmark failure intensity function of LPIM, an imperfect repair effect-aware WT reliability description model was developed. Among them, the 3-BIP was used to describe the evolution process of the failure intensity in the stable operation stage with running time, while the LPIM reflected the repair effect. Second, the estimation problem for model parameters was transformed into a minimum solution problem for a nonlinear objective function, which was then solved using the Particle Swarm Optimization algorithm. The confidence interval of model parameters was finally estimated using the inverse Fisher information matrix method. Key reliability indices interval estimation based on the Delta method and point estimation was derived. The proposed method was applied to a wind farm’s WT failure truncation time. The proposed method has a higher goodness of fit based on verification and comparison. As a result, it can bring the evaluated reliability closer to engineering practice.

수리 가능한 체계에 대한 Upside-Down 욕조 곡선 형태의 삼분할된 고장 강도 모형

Purpose: This study proposes an upside-down bathtub-shaped three-segmented failure intensity model for repairable systems. The procedure for estimating the parameters for the proposed model is presented under certain assumptions regarding the change points of the model.BRMethods: The proposed model comprises three failure intensity functions - one for each of the three model segments. The model is therefore a P-H-P model, with the power law process model, the homogeneous Poisson process model, and the power law process model that follows the non-homogeneous Poisson process as the failure intensity functions. The change points and the parameters of each failure intensity function were determined using maximum likelihood estimation and least squares estimation.BRResults: The case study shows that compared with other extant models, the proposed P-H-P model is more suitable in terms of log-likelihood function value, Akaike information criterion corrected, and mean squared error.BRConclusion: The proposed P-H-P model is expected to better explain the failure intensities of similar systems and to allow for more accurate reliability analysis.

Bayesian Statistical Method Enhance the Decision-Making for Imperfect Preventive Maintenance with a Hybrid Competing Failure Mode

The study aims to provide a Bayesian statistical method with natural conjugate for facilities’ preventive maintenance scheduling related to the hybrid competing failure mode. An effective preventive maintenance strategy not only can improve a system’s health condition but also can increase a system’s efficiency, and therefore a firm needs to make an appropriate strategy for increasing the utilization of a system with reasonable costs. In the last decades, preventive maintenance issues of deteriorating systems have been studied in the related literature, and hundreds of maintenance/replacement models have been created. However, few studies focused on the issue of hybrid deteriorating systems which are composed of maintainable and non-maintainable failure modes. Moreover, due to the situations of the scarcity of historical failure data, the related analyses of preventive maintenance would be difficult to perform. Based on the above two reasons, this study proposed a Bayesian statistical method to deal with such preventive maintenance problems. Non-homogeneous Poisson processes (NHPP) with power law failure intensity functions are employed to describe the system’s deterioration behavior. Accordingly, the study can provide useful ways to help managers to make effective decisions for preventive maintenance. To apply the proposed models in actual cases, the study provides solution algorithms and a computerized architecture design for decision-makers to realize the computerization of decision-making.

Emergency shutdowns of propylene production plants: Root cause analysis and availability modeling

Unplanned shutdown events in chemical process plants cause revenue losses due to production curtailments, repair costs, and harmful environmental and safety effects on plant personnel and the surrounding community. Several recent studies have used news articles and databases to perform statistical analyses and modeling of the causes and consequences of chemical process accidents, but these studies do not analyze the operating deviations that led to shutdowns. This work structures narratives about unplanned shutdown events into data, analyzes the causes of those events, and uses the collected data to model the failure probability of process plants. A case study comparing two propylene production technologies, steam cracking and propane dehydrogenation is developed. We use a set of 118 shutdown events reported in four sources across a five-year span for 7 propylene production plants. Using this data, the three leading causes for unplanned shutdowns in both propylene production technologies were determined to be: equipment trips/shutdowns, utility supply interruptions, and weather-related events. A power law process (PLP) for data from multiple repairable systems is used to model the failure behavior for both technologies. For the data collected, this procedure indicated an increasing failure intensity function for both technologies, with propane dehydrogenation increasing more significantly. In addition, both maximum likelihood estimates (MLEs) and confidence intervals for the PLP parameters are presented. Since these are repairable systems, an estimated inherent availability is determined for both technologies. Finally, recommendations that address how to reduce the occurrence of these events and mitigate their consequences are discussed.

Reliability Analysis of Military Vehicles Based on Censored Failures Data

The paper proposes a methodology of reliability testing as applied to vehicles used in military transport systems. After estimating the value of the reliability function using the Kaplan–Meier estimator, reliability models were developed and analysed. The neural model, which achieved the value of the correlation coefficient R exceeding 0.99, was determined to fit the empirical data the best. On the basis of the approximated reliability function of several models, the reliability characteristics of the tested sample of vehicles were determined. Plots of the failure probability density function for all three models had similar courses over a significant part of the function domain. A failure intensity function was also determined, which varied between models. For the exponential and Weibull model, the expected mileage between failures was calculated, which proved impossible for the neural model. The proposed methodology is capable of modelling reliability characteristics based on the observation of an assumed period of the exploitation process of the selected group of military vehicles.

Estimation of Parameters of PTRC SRGM using Non-informative Priors

Reliability is an essentially important characteristic of software. The reliability of software has been assessed by considering Poisson Type occurrence of software failures and the failure intensity of one parameter say (η_1 ) Rayleigh class. Here, it is assumed that the software contains fixed number of inherent faults say (η_0 ). The scale parameter of Rayleigh density (η_1 ) and fixed number of inherent faults contained in software are the parameters of interest. The failure intensity and mean failure function of this Poisson Type Rayleigh Class (PTRC) Software Reliability Growth Model (SRGM) have been studied. The estimates of above parameters can be obtained by using maximum likelihood method. Bayesian technique has been used to about estimates of η_0 and η_1 if prior knowledge about these parameters is available. The prior knowledge about these parameters is considered in the form of non- informative priors for both the parameters. The proposed Bayes estimators are compared with their corresponding maximum likelihood estimators on the basis of risk efficiencies under squared error loss. The Monte Carlo simulation technique is used for calculating risk efficiencies. It is seen that both the proposed Bayes estimators can be preferred over corresponding MLEs for the proper choice of the values of execution time.

A generalized model for recurrent failures prediction

There is a variety of models available for repairable systems with general repairs. Most popular are the Kijima models (reflecting the generalized renewal process of recurrent failures) and the Lam model (reflecting the geometric process). The Kijima models relating system's real and virtual ages can be thought of as the time shift transformation, whereas the Lam model – as the time scale transformation. In this paper, a new model is proposed that combines these two fundamental transformations within a new probabilistic formulation. Besides probabilistic aspect of the model, the maximum likelihood estimation of model parameters is discussed, and its performance is illustrated through several numerical examples using both simulated and real–life data. The efficient Monte Carlo calculation method is suggested for the expected number of recurrent events, unavailability, and the failure intensity function.

Optimal sequential preventive maintenance policy for a repairable system with maintenance windows

Optimization of sequential preventive maintenance has been widely studied. However, some issues need further discussion when considering certain real factors. Hence, an sequential preventive maintenance policy for a mono-unit repairable system with maintenance windows is proposed. The load strength and catastrophic failures of a system are considered in the reliability model, and an optimization of the SPM policy is rigorously proven by an analytical method. The existence and uniqueness of the optimal solution with a monotone increasing failure intensity function are presented in detail. The proof of theory indicates that the length of the maintenance window has an upper bound. Finally, a numerical example and some sensitivity analyses are given to illustrate the proposed sequential preventive maintenance policy. Results show that waste may occur when performing the general sequential preventive maintenance policy and may increase along with the length of the maintenance windows.

A Nonlinear Preventive Maintenance Model with an Environmental Factor Based Weibull Distribution

Most of the Preventive maintenance (PM) reliability modeling research has focused on the relationship between two adjacent failure intensity functions, while few real case studies have demonstrated the application of these PM models. Thinking from this vision, a nonlinear PM model with scale and shape adjustment parameters is proposed based on a Weibull distribution, and two adjustment parameters can describe each PM effect. Meanwhile, the proposed model can separate the influence of an environmental factor from the failure intensity function of the new system when it operates under a new condition. The environmental parts in the failure intensity function can be improved or removed after several PM actions. Finally, one real case study is exhibited to illustrate the proposed model. The results indicate that the proposed model exhibits good fitting performance in reliability modeling and can describe the PM effect quantitatively as well as reveal the influence of the environmental factor on the system reliability.

Development of software reliability models using a hybrid approach and validation of the proposed models using big data

This article proposes three software reliability models based on a hybrid approach combining NHPP models, Weibull model, and exponential model. The software failure is first categorised into three categories, namely pure software failures, hardware-induced software failures, and user-induced software failures. Based on the failure behaviour, NHPP models were adapted for pure software failures, Weibull model for hardware-induced failures, and exponential model for user-induced software failures. The failure intensity function, mean value function, and reliability function were determined. The proposed models are validated using big data analysis. From the data collected during the testing phase, the optimal values of parameters were estimated using maximum likelihood estimation and genetic algorithm. The expected number of failures and the cumulative number of failures were calculated, and comparison was made between the observed values to show the performance of the proposed models. A comparison criterion was also proposed to confirm the estimation accuracy. Finally, a t test was conducted to test the significance of the difference between the observed and estimated values. Experimental results confirm the better estimation accuracy of the proposed models.

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications.

The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsallis’ non-extensive entropy, namely the q-Exponential and the q-Weibull distributions. The q-Exponential and Weibull distributions can model decreasing, constant or increasing failure intensity functions. However, the power law behavior of the q-Exponential probability density function for specific parameter values is an advantage over the Weibull distribution when adjusting data containing extreme values. The q-Weibull probability distribution, in turn, can also fit data with bathtub-shaped or unimodal failure intensities in addition to the behaviors already mentioned. Therefore, the q-Exponential-GRP is an alternative for the Weibull-GRP model and the q-Weibull-GRP generalizes both. The method of maximum likelihood is used for their parameters’ estimation by means of a particle swarm optimization algorithm, and Monte Carlo simulations are performed for the sake of validation. The proposed models and algorithms are applied to examples involving reliability-related data of complex systems and the obtained results suggest GRP plus q-distributions are promising techniques for the analyses of repairable systems.

Reliability Analysis of Repairable Systems Based on a Two-Segment Bathtub-Shaped Failure Intensity Function

The reliability analysis of complex repairable systems is an important but computationally intensive task that requires fitting the failure data of whole life cycles well. Because the existing reliability models are mainly based on the assumptions that systems are either unrepairable or will go through an “as good as new” type of repair which does not describe actual situations effectively and precisely, a two-segment failure intensity model based on sectional non-homogeneous Poisson process is developed. This model is capable of analyzing repairable systems with bathtub-shaped failure intensity. It considers minimal maintenance activities and preserves the time series of failures based on the whole life cycle. The advantages of this model lie in its flexibility to describe monotonic, non-monotonic failure intensities and its practicality to determine the burn-in or replacement time for repairable systems. Three real lifetime failure data sets are applied to illustrate the developed model. The results show that the model performs well regarding the Akaike information criterion value, mean squared errors, and Cramer–von Mises values.

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

AbstractThis 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.

Confidence limits for system reliability indices with increasing function of failure intensity

The problem of calculating the lower confidence limit for the reliability function and the other main indices, such as the mean time to failure (mean lifetime) and the guaranteed (gamma-percentile) lifetime of a system based on the reliability test results has been considered. The problem is solved under the general nonparametric assumption of the monotonically increasing failure intensity function (aging) of a system. A series of expressions for the lower confidence limits of the aforementioned main reliability indices has been derived.

Modeling Two-Dimensional Framework for Multi-Upgradations of a Software with Change Point

Across the globe almost every organization is dependent on information technology for increasing their business efficiency. This has led to huge demand for reliable and good quality software. Innovation is most important to attain success in software industry. Software companies need to keep bringing upgradations or add-ons in the software to compete in the market. In the present framework we propose a generalized mathematical modeling for multiple software releases. In this framework we examine the collective effect of testing time and resources using Cobb–Douglas production function for defining the failure phenomenon using a software reliability growth model (SRGM). In this paper, we consider the practical scenario where there is a possibility of change in the fault detection rate. Fault detection rate can be affected by various factors like testing environment, testing strategy and allocation of resources. Change in these factors during testing phase can lead to increase or decrease in failure intensity function. The time point at which abrupt fluctuations in fault detection rate take place is known as change point. In this paper, a generalized framework for developing a two-dimensional SRGM with change point for multiple software releases has been discussed. We have derived various existing change point models using the proposed framework. The developed models have been validated on real data set.

Reliability functions of low voltage electrical terminals made from bare wires, insulated and cables

The article presents the results of the evaluation of basic functions determining reliability characteristics of LV connections, they are a failure intensity function, function reliability and unreliability function. Based on years of follow-up LV connections operated in large electricity distribution company in the country were defined empirical waveforms mentioned features. It was also carried out an analysis of the empirical distribution of compliance with the assumed theoretical distribution. In paper was determined the expected value of lifetime to damage of LV connections.

Non-parameter Estimation of Failures Intensity of Tractor Based on Bootstrap

The failures data of tractors operating in field conditions were collected by failure tracking tests. A mathematical model is established with non-homogenous Poisson process to get the tractor failure intensity function. Bootstrap method is presented for constructing confidence regions for the failure intensity of a repairable system. Combined with fault data in tracking experiment, the early period failure intensity curves are drawn, revealing the failure regular in the initial stages of tractors. A confidence interval can be estimated by standard likelihood asymptotic theory in the parametric estimation, however in the non-parametric case it can be obtained by using the bootstrap. Comprising the MSE of cumulative intensity and cumulative number of failures between the two estimations, it is seen that the curve which was estimated by non-parameter estimation method is more realistic to the actual experiment process. Results provide the reference to improve tractor reliability, maintainability and maintenance strategy.

전동차 제동장치의 고장데이터와 비용함수를 고려한 유지보수 정책에 관한 연구

Railway vehicle equipment goes back again to the state just before when failure by the repair. In repairable system, we are interested in the failure interval. As such, a statistical model of the point process, NHPP power law is often used for the reliability analysis of a repairable system. In order to derive a quantitative reliability value of repairable system, we analyze the failure data of the air brake system of the train line 7. The quantitative value is the failure intensity function that was modified, converted into a cost-rate function. Finally we studied the optimal number and optimal interval in which the costs to a minimum consumption point as cost-rate function. The minimum cost point was 194,613 (won/day) during the total life cycle of the braking system, then the optimal interval were 2,251days and the number of optimal preventive maintenance were 7 times. Additionally, we were compared to the cost of a currently fixed interval(4Y) and the optimum interval then the optimal interval is 3,853(won/day) consuming smaller. In addition, judging from the total life, "fixed interval" is smaller than 1,157 days as "optimal interval".

The determination procedure of the onset of the object wear-out period based on monitoring of the empirical failure intensity function

The determination procedure of the onset of the object wear-out period based on monitoring of the empirical failure intensity function

Decline and repair, and covariate effects

The failure processes of repairable systems may be impacted by operational and environmental stress factors. To accommodate such factors, reliability can be modelled using a multiplicative intensity function. In the proportional intensity model, the failure intensity is the product of the failure intensity function of the baseline system that quantifies intrinsic factors and a function of covariates that quantify extrinsic factors. The existing literature has extensively studied the failure processes of repairable systems using general repair concepts such as age-reduction when no covariate effects are considered. This paper investigates different approaches for modelling the failure and repair process of repairable systems in the presence of time-dependent covariates. We derive probabilistic properties of the failure processes for such systems.