Weibull Failure Probability Estimation Based on Zero-Failure Data

Jiang, Ping; Xing, Yunyan; Jia, Xiang

doi:10.1155/2015/681232

Cited by 20 publications

(20 citation statements)

References 7 publications

(12 reference statements)

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“…The number of the new probability distribution curves is 5000. The curves are obtained by using Equation (21) according to the 5000 groups' new samples. In this case, the 5000 groups' estimations of reliability can be calculated under the mission time.…”

Section: Mrementioning

confidence: 99%

“…Then, the reliability of the product was estimated. The method distributes the lifetime probability distribution curve was widely adopted because better results can be obtained . Although the results of the reliability assessment can be recognized, only the point estimates of distribution parameters were given.…”

Section: Introductionmentioning

confidence: 99%

“…The method distributes the lifetime probability distribution curve was widely adopted because better results can be obtained. [20][21][22][23] Although the results of the reliability assessment can be recognized, only the point estimates of distribution parameters were given. The basic purpose of the bootstrap method is to expand the number of samples.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reliability assessment of high‐quality and long‐life products based on zero‐failure data

Xie

et al. 2018

Quality & Reliability Eng

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For a period of mission time, only zero‐failure data can be obtained for high‐quality long‐life products. In the case of zero‐failure data reliability assessment, the point estimates and confidence interval estimates of distribution parameters cannot be obtained simultaneously by the current reliability assessment models, and the credibility of the assessment results may be reduced if they are obtained at the same time. A new model is proposed for consistency problem in this paper. In the proposed model, the point estimates of reliability can be obtained by the lifetime probability distribution derived from matching distribution curve method, while the confidence interval estimates of reliability can be obtained by using new samples generated from the lifetime probability distribution according to parameter bootstrap method. By analyzing the zero‐failure data of the torque motors after real operation, the results show that the new model not only meets the requirements of reliability assessment but also improves the accuracy of reliability interval estimation.

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Section: Mrementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reliability assessment of high‐quality and long‐life products based on zero‐failure data

Xie

et al. 2018

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…e method can be said to be a standard solution to the zero-failure reliability assessment for NC machine tools. Jiang et al [18] presented a method to estimate the intervals of the failure probability for the Weibull distribution by using the concavity and the property of the distribution function and validated the effectiveness and robustness of the method. Xu and Zhixin [19] proposed a fuzzy Bayesian-based zero-failure accelerated degradation demonstration (ADD) test method.…”

Section: Introductionmentioning

confidence: 99%

Vibration Reliability Evaluation of Main Fan Spindle Bearings

Pang

Qiu

Liang

et al. 2019

Shock and Vibration

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Based on an analysis of failure causes, the axial force is the main reason why spindle bearings vibrate abnormally and cause frequent failures of the main fans in mines. In this paper, the probability density function of the spindle bearing vibration was established through the bootstrap maximum entropy method, the Lagrangian multiplier and the empirical coefficient were introduced, and models of the upper- and lower-bound functions of the probability density and the true value function of the failure probability were established. The true value function and interval estimation values of vibration reliability were obtained on the basis of maximum entropy. The analysis results showed that the estimation true values of vibration decreased with an increase in the empirical coefficient. When the empirical coefficient was less than 0.1, the estimated true value decreased sharply. When the empirical coefficient was greater than 0.1, the vibration value decreased linearly with the empirical coefficient. When the empirical coefficient was 0.1, the estimated true value was 0.85 mm/s2, which is consistent with the change in the actual vibration value. Therefore, when the main fan is fault predicted, the vibration value should be 0.85 mm/s2 as the basis for judgment and then the theoretical basis for the fault diagnosis of the spindle bearing are provided.

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“…e prediction problem for accuracy reliability involves the interaction between internal factors and the external environment [1][2][3][4][5]. According to the existing research, the reliability theory of rolling bearings is primarily concerned with fatigue failure and static reliability problems and assumes that the lifetime data obey the Weibull distribution or lognormal distribution [6][7][8]. However, in practical applications, the lifetime evaluation index of an SPRB rests on accuracy rather than fatigue, which means that the bearing may be far from reaching its fatigue lifetime, while the accuracy has failed.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Prediction for Accuracy Maintaining Reliability of Superprecision Rolling Bearing in Service

Liang

Xia

Chang³

2018

Shock and Vibration

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A dynamic prediction method for accuracy maintaining reliability (AMR) of superprecision rolling bearings (SPRBs) in service is proposed by effectively fusing chaos theory and grey system theory and applying stochastic processes. In this paper, the time series of a vibration signal is used to characterize the state information for SPRB, and four runtime data points can be predicted in the future, which depends on four chaotic forecasting models to preprocess the time series. Using the grey bootstrap method and sampling from the four runtime data, a large amount of generated data (GD) are gained to analyze the changes in information on bearing service accuracy. Then, using a predefined accuracy threshold to match the Poisson count for the GD, the estimated value of variation intensity is obtained. Subsequently, with the help of the Poisson process, the dynamic evolution process is forecast in real time for AMR of the SPRB for each step in the future. Finally, according to a novel concept for maintaining relative reliability in an SPRB, the failure degree of a bearing maintaining an optimum accuracy status (BMOAS) is effectively described. Experimental investigation shows that multiple chaotic forecasting methods are accurate and feasible with all relative errors below 15%; the reliability of each step in the future can truly be described, and the prediction results for AMR over the same subseries show good consistency; dynamic monitoring of the health status of SPRB can be realized by the degree to which a BMOAS fails.

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Weibull Failure Probability Estimation Based on Zero-Failure Data

Cited by 20 publications

References 7 publications

Reliability assessment of high‐quality and long‐life products based on zero‐failure data

Reliability assessment of high‐quality and long‐life products based on zero‐failure data

Vibration Reliability Evaluation of Main Fan Spindle Bearings

Dynamic Prediction for Accuracy Maintaining Reliability of Superprecision Rolling Bearing in Service

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