Synthetic Reliability Assessment Model involving Temperature–Humidity Step-Stress Based on Wiener Process

2020 ◽  
pp. 2150016
Author(s):  
Bin Suo ◽  
Liang Zhao
Keyword(s):  
Wiener Process ◽  
High Reliability ◽  
Likelihood Estimation ◽  
Degradation Process ◽  
Test Sample ◽  
Assessment Model ◽  
Engineering Practice ◽  
Accelerated Degradation ◽  
Failure Data ◽  
Newton Iteration Method

There are always some difficulties in storage reliability evaluation of high-reliability, long-life, and high-value products, such as the test sample being small, degradation speed being slow, and failure data being inadequate. Temperature–humidity step-stress accelerated degradation test (THSS-ADT) is an effective method to evaluate the reliability of this type of products, but the test data processing is an extremely complex work. The motivation of this paper is to provide a clear, effective, and convenient method to evaluate the reliability on the basis of THSS-ADT data. Considering the stochastic volatility in degradation process, Wiener process is used to modeling the accelerated degradation process. The methods to estimate the parameters of Peck accelerated model and degradation model are discussed under temperature–humidity step-stress. As ordinary optimization algorithms (such as Newton Iteration Method and impelling function method) find it difficult to get the solutions, particle swarm optimization (PSO) method is used to solve the problem of maximum-likelihood estimation. Finally, the proposed methods are demonstrated for two examples, in which one is a numerical simulation, and another is an engineering practice of a microwave power amplifier.

scholarly journals Accelerated Degradation Tests Modeling Based on the Nonlinear Wiener Process with Random Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shengjin Tang ◽  
Xiaosong Guo ◽  
Chuanqiang Yu ◽  
Haijian Xue ◽  
Zhijie Zhou
Keyword(s):  
Wiener Process ◽  
Random Effects ◽  
Process Modeling ◽  
High Reliability ◽  
Random Variable ◽  
Degradation Process ◽  
Unknown Parameters ◽  
Accelerated Degradation ◽  
Degradation Tests ◽  
Product Variation

Accelerated degradation tests (ADT) modeling is an important issue in lifetime assessment to the products with high reliability and long lifetime. Among the literature about the accelerated nonlinear degradation process modeling, the current methods did not consider the product-to-product variation of the products with the same type. Therefore, this paper proposes an accelerated degradation process modeling method with random effects for the nonlinear Wiener process. Firstly, we derive the lifetime distribution of the nonlinear Wiener process with random effects. Secondly, the nonlinear Wiener process is used to model the degradation process of a single stress, and the drift coefficient is considered as a random variable to describe the product-to-product variation. Using the random acceleration model, the random effects are incorporated into the constant stress ADT models and the step stress ADT models. Then, a two-step maximum likelihood estimation (MLE) method is presented to estimate the unknown parameters in the degradation models. Finally, a simulation study and a case study are provided to demonstrate the application and superiority of the proposed model.

scholarly journals Accelerated Degradation Process Analysis Based on the Nonlinear Wiener Process with Covariates and Random Effects

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Li Sun ◽  
Xiaohui Gu ◽  
Pu Song
Keyword(s):  
Diffusion Coefficient ◽  
Wiener Process ◽  
Random Effects ◽  
Process Analysis ◽  
Likelihood Estimation ◽  
Degradation Process ◽  
Unknown Parameters ◽  
Accelerated Degradation ◽  
Degradation Data ◽  
Drift Parameter

It is assumed that the drift parameter is dependent on the acceleration variables and the diffusion coefficient remains the same across the whole accelerated degradation test (ADT) in most of the literature based on Wiener process. However, the diffusion coefficient variation would also become obvious in some applications with the stress increasing. Aiming at the phenomenon, the paper concludes that both the drift parameter and the diffusion parameter depend on stress variables based on the invariance principle of failure mechanism and Nelson assumption. Accordingly, constant stress accelerated degradation process (CSADP) and step stress accelerated degradation process (SSADP) with random effects are modeled. The unknown parameters in the established model are estimated based on the property of degradation and degradation increment, separately for CASDT and SSADT, by the maximum likelihood estimation approach with measurement error. In addition, the simulation steps of accelerated degradation data are provided and simulated step stress accelerated degradation data is designed to validate the proposed model compared to other models. Finally, a case study of CSADT is conducted to demonstrate the benefits of our model in the practical engineering.

scholarly journals Reliability Assessment for Very Few Failure Data and Weibull Distribution

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Lulu Zhang ◽  
Guang Jin ◽  
Yang You
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Weibull Distribution ◽  
Failure Probability ◽  
Evaluation Method ◽  
High Reliability ◽  
Point Estimation ◽  
Engineering Practice ◽  
Reliability Parameters ◽  
Failure Data

Only very few failure data can be obtained for the time censored test of high-reliability and long-life products. For very few failure data, the current methods fail to obtain both the point estimation and confidence interval of reliability parameters. If the point estimation and confidence interval of reliability parameters are obtained based on different methods, the results tend to be unreliable. In this study, based on the existing research, a Bayesian reliability evaluation method for very few failure data under the Weibull distribution was proposed. First, the range of failure probability was limited based on the convexity and self-features of the Weibull distribution function. Second, based on the background of the sample with very few failure data, the pretest distribution function and parameters were set and solved. The point estimation and confidence interval model of failure probability based on the Bayesian formula was established. The improved match distribution curve method was used to compute both the point estimation and confidence interval of reliability parameters. Furthermore, by comparing the results of numerical examples, the calculation results obtained by the proposed method were verified as being very reasonable. Finally, taking wet friction plates as an example, the results showed the effectiveness of this method in engineering practice.

Feature Extraction for Bearing Prognostics Based on Continuous Hidden Markov Model

2014 ◽  
Vol 541-542 ◽  
pp. 1483-1486
Author(s):  
Jian She Kang ◽  
Xing Hui Zhang ◽  
Jin Song Zhao ◽  
Lei Xiao
Keyword(s):  
Fault Diagnosis ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov ◽  
High Reliability ◽  
Degradation Process ◽  
Health Condition ◽  
Diagnosis And Prognosis ◽  
Failure Data ◽  
Fault Diagnosis And Prognosis

Many research papers implemented fault diagnosis and prognosis when there are many history data. However, for some capital and high reliability equipment, it is very difficult to acquire some run-to-failure data. In this case, the fault diagnosis and prognosis become very hard. In order to address this issue, continuous hidden Markov model (CHMM) is used to track the degradation process in this paper. With the degradation, the log-likelihood which is the output of CHMM will decrease gradually. Therefore, this indicator can be used to evaluate the health condition of monitored equipment. Finally, bearing run-to-failure data sets are used to validate the model’s effectiveness

Sample selection of prognostics validation test based on multi-stage Wiener process

2018 ◽  
Vol 233 (4) ◽  
pp. 605-614
Author(s):  
Zhiao Zhao ◽  
Yong Zhang ◽  
Guanjun Liu ◽  
Jing Qiu
Keyword(s):  
Wiener Process ◽  
Process Model ◽  
Failure Modes ◽  
Early Stage ◽  
Sample Selection ◽  
Degradation Process ◽  
Time Interval ◽  
Degradation Data ◽  
Multi Stage ◽  
Selection Of

Sample allocation and selection technology is of great significance in the test plan design of prognostics validation. Considering the existing researches, the importance of prognostics samples of different moments is not considered in the degradation process of a single failure. Normally, prognostics samples are generated under the same time interval mechanism. However, a prognostics system may have low prognostics accuracy because of the small quantity of failure degradation and measurement randomness in the early stage of a failure degradation process. Historical degradation data onto equipment failure modes are collected, and the degradation process model based on the multi-stage Wiener process is established. Based on the multi-stage Wiener process model, we choose four parameters to describe different degradation stages in a degradation process. According to four parameters, the sample selection weight of each degradation stage is calculated and the weight of each degradation stage is used to select prognostics samples. Taking a bearing wear fault of a helicopter transmission device as an example, its degradation process is established and sample selection weights are calculated. According to the sample selection weight of each degradation process, we accomplish the prognostics sample selection of the bearing wear fault. The results show that the prognostics sample selection method proposed in this article has good applicability.

Valuation of machinery and equipment subject to the Wiener degradation process

2021 ◽  
Vol 57 (3) ◽  
pp. 97
Author(s):  
Sergey Smolyak
Keyword(s):  
Service Life ◽  
Wiener Process ◽  
Market Value ◽  
Degradation Process ◽  
Average Value ◽  
Boundary State ◽  
Proposed Model ◽  
Negative Drift ◽  
The Mean ◽  
The Moment

We propose a model describing the decrease in the market value of machines (depreciation) with age. Usually it is characterized by the percent good factor, i.e. the ratio of machine’s value to the value of similar new machinery item. Often, appraisers know about a used machinery item only by its age, but not its performance. Therefore, for the valuation of the machinery item of a known age, they have to use the mean (for machines of this age) of percent good factor. In the proposed model, the state of the machine is characterized by the intensity of the benefits it brings. In this case, the benefits from using the machine in a certain period are defined as the market value of the work performed by it minus operating costs. We describe the change in the intensity of benefits over time by the Wiener process with negative drift. This allows us to take into account the tendency for the performance of machine to deteriorate during operation. The market value of a machine is defined as the maximum mathematical expectation of the sum of discounted benefits from its use. It is shown that it corresponds to the moment the machine reaches a certain boundary state. The parameters of the Wiener process (drift and volatility) are expressed through the known characteristics of the machine's durability, namely the average value and the coefficient of variation of the service life. The dependences of the mean percent good factor of machines on the relative age (the ratio of age to the average service life) are found. It turned out that these dependencies are almost independent of the discount rate and average service life.

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