scholarly journals Accelerated Lifetime Data Analysis with a Nonconstant Shape Parameter

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Guodong Wang ◽  
Zhanwen Niu ◽  
Zhen He
Keyword(s):  
Shape Parameter ◽  
High Reliability ◽  
Least Square Method ◽  
Least Square ◽  
Accelerated Life Test ◽  
Stress Factors ◽  
Likelihood Method ◽  
Accelerated Life ◽  
Lifetime Data Analysis ◽  
Accelerated Lifetime

Accelerated life test is commonly used for the estimation of high-reliability product. In this paper, we present a simple and efficient approach to estimate the coefficients of acceleration models. Assuming that both scale and shape parameters of Weibull lifetime distribution vary with stress factors, we estimate the parameters of Weibull distribution using maximum likelihood method and reduce the bias of shape parameter estimator. Considering the heteroscedasticity, we compute the estimates of the coefficients of acceleration models through weighted least square method. Additionally, we obtain the confidence interval of low percentile via bootstrapping. We compare the proposed method with other methods using a real lifetime example. Finally, we study the performance of the proposed method by simulation. The simulation results show that our proposed method is effective.

scholarly journals Weibull accelerated life testing analysis with several variables using multiple linear regression

DYNA ◽  
2015 ◽  
Vol 82 (191) ◽  
pp. 156-162 ◽  
Author(s):  
Manuel R. Piña-Monarrez ◽  
Carlos A. Ávila-Chávez ◽  
Carlos D. Márquez-Luévano
Keyword(s):  
Life Stress ◽  
Shape Parameter ◽  
Accelerated Life Testing ◽  
Accelerated Life Test ◽  
Likelihood Method ◽  
Test Analysis ◽  
Operational Level ◽  
Accelerated Life ◽  
Response Variance ◽  
Joint Form

In Weibull accelerated life test analysis (ALT) with two or more variables (<em>X<sub>2</sub>, X<sub>3</sub>, ... X<sub>k</sub></em>), we estimated, in joint form, the parameters of the life stress model r{X(t)} and one shape parameter β. These were then used to extrapolate the conclusions to the operational level. However, these conclusions are biased because in the experiment design (DOE) used, each combination of the variables presents its own Weibull family (β<sub>i</sub>, η<sub>i</sub>). Thus the estimated β is not representative. On the other hand, since (β<sub>i</sub>, η<sub>i</sub>) is determined by the variance of the logarithm of the lifetime data σ<sub>t</sub><sup>2</sup> , the response variance σ<sub>y</sub><sup>2</sup> and the correlation coefficient R<sup>2</sup>, which increases when variables are added to the analysis, β is always overestimated. In this paper, the problem is statistically addressed and based on the Weibull families (β<sub>i</sub>, η<sub>i</sub>) a vector Y<sub>η</sub> is estimated and used to determine the parameters of r{X(t)}. Finally, based on the variance σ<sub>y</sub><sup>2</sup> of each level, the variance of the operational level σ<sub>op</sub><sup>2</sup> is estimated and used to determine the operational shape parameter β<sub>op</sub>. The efficiency of the proposed method is shown by numerical applications and by comparing its results with those of the maximum likelihood method (ML).

Machining Efficiency Model Based on the Multiple Regression Theory in Turning Glass Ceramics

2012 ◽  
Vol 201-202 ◽  
pp. 1092-1095
Author(s):  
Lian Jie Ma ◽  
Ai Bing Yu ◽  
Ya Dong Gong
Keyword(s):  
Prediction Model ◽  
Multiple Regression ◽  
Removal Rate ◽  
High Reliability ◽  
Cutting Speed ◽  
Glass Ceramics ◽  
Least Square Method ◽  
Least Square ◽  
Feed Speed ◽  
Tools Wear

The materials removal rate (V/VB) was selected to be objective function. It is comprehensive parameter about materials and tools wear. Through turning glass ceramics experimentation, the materials removal influence of cutting speed, cutting depth and feed speed were study. Based on least square method, the multiple regression prediction model of materials removal rate was built. And the model was tested. It was applied to predictive and control. The results indicated: this model was well to express materials removal law in turning glass ceramics. The multiple regression prediction model is high remarkable. The prediction value was coincident with measure value. This model is high reliability. So, expect materials removal rate can been obtained by this model, and choosing the technological parameter can been guided.

An accelerated life test plan for a two-component parallel system under ramp-stress loading using masked data

2018 ◽  
Vol 35 (3) ◽  
pp. 811-820 ◽  
Author(s):  
Preeti Wanti Srivastava ◽  
Savita Savita
Keyword(s):  
Optimality Criterion ◽  
High Reliability ◽  
Parallel System ◽  
Stress Rate ◽  
Accelerated Life Test ◽  
Cumulative Exposure ◽  
Life Test ◽  
Optimal Plan ◽  
Content Type ◽  
Accelerated Life

Purpose Most of the literature on the design of accelerated life test (ALT) plan focus on a single system (subsystem) totally disregarding its internal configuration. Many a times it is not possible to identify the components that cause the system failure or that the cause can only be identified by a subset of its components resulting in a masked observation. The purpose of this paper is to deal with the planning of ramp-stress accelerated life testing for a high-reliability parallel system comprising two dependent components using masked failure data. Such a testing may prove to be useful in a twin-engine aircraft. A ramp-stress results when stress applied on the system increases linearly with time. Design/methodology/approach A parallel system with two dependent components is taken with dependency modeled by Gumbel-Hougaard copula. The stress-life relationship is modeled using inverse power law, and cumulative exposure model is assumed to model the effect of changing stress. The method of maximum likelihood is used for estimating design parameters. The optimal plan consists in finding optimal stress rate using D-optimality criterion. Findings The optimal plan consists in finding optimal stress rate using D-optimality criterion by minimizing the reciprocal of the determinant of Fisher information matrix. The proposed plan has been explained using a numerical example and carrying out a sensitivity analysis. Originality/value The model formulated can help reliability engineers obtain reliability estimates quickly of high-reliability products that are likely to last for several years.

scholarly journals A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

2020 ◽  
Vol 8 (2) ◽  
pp. 610-630 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Emrah Altun EA ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Survival Times ◽  
New Model ◽  
Von Mises ◽  
Bootstrapping Method

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

Judge the Possible Areas in Eastern Part of Inner Mongolia where Strong Earthquakes Occur in the Future by Utilizing b-Value

2012 ◽  
Vol 518-523 ◽  
pp. 5616-5622
Author(s):  
Xiao Ming Han ◽  
Ding Xue ◽  
Bo Hu
Keyword(s):  
Inner Mongolia ◽  
Strong Earthquake ◽  
Least Square Method ◽  
B Value ◽  
Geological Structure ◽  
Least Square ◽  
Space Distribution ◽  
Likelihood Method ◽  
Time Scanning ◽  
The Future

The Zhalantun district of eastern part of Inner Mongolia is located at the northern section of Greater Khingan seismic belt, and it has complicated geological structure, with relatively dynamic moderately strong earthquake in past times and modern times. The seismic activities in this district is selected as the research object; based on the integrity analysis toward seismic sequence in the district, least square method is used to conduct time scanning calculation of b-value, and maximum likelihood method is used to conduct space scanning calculation of b-value. The b-value during the time scanning is the mean b-value of research zone in every scanning window, so its amplitude of variation is not quite great, with range of variation of b-value basically staying within 0.78-1.13, and range of error staying within 0.04-0.065. The space scanning results indicate that the space distribution range of b-value of Zhalantun district basically stays within 0.4-1.6, and the range of error is 0.045-0.085. The low b-value zone is the north central section of Alun River breakage, with b-value basically distributed within 0.5-0.7, which indicates that the earth crust medium of this zone is under the state of high horizontal stress accumulation and it is the dangerous zone where moderately strong earthquake or more occurs in the future.

The Statistics Analysis of Degradation Data Based on the Degradation Amount Distribution

2013 ◽  
Vol 791-793 ◽  
pp. 1260-1263
Author(s):  
Yi Zhou He ◽  
Jin Huang Wu ◽  
Yi Dong Wang ◽  
Wei Hua Liu
Keyword(s):  
High Reliability ◽  
Performance Degradation ◽  
Accelerated Life Test ◽  
Test Reliability ◽  
Analysis Method ◽  
Life Test ◽  
Failure Data ◽  
Degradation Data ◽  
Accelerated Life ◽  
Long Life

In order to solve the key technology and method in reliability study of the long-life products, the analysis method of degradation data based on the degradation amount distribution was proposed in this paper. On the basis of statistical model, by analyzing three models of degradation amount distribution, it can be got there is a large number of reliability information with high-reliable and long-life products in performance degradation data. In the case of not getting the failure data by life test and accelerated life test, reliability assessment and life prediction could be carried out for high reliability and long life products with performance degradation data.

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