scholarly journals Statistical Inference for Burr Type X Distribution using Geometric Process in Accelerated Life Testing Design for Time censored data

2020 ◽  
pp. 577-586
Author(s):  
Ahmadur Rahman ◽  
Tabassum Naz Sindhu ◽  
Showkat Ahmad Lone ◽  
Mustafa Kamal
Keyword(s):  
Censored Data ◽  
Life Stress ◽  
Asymptotic Variance ◽  
Accelerated Life Testing ◽  
Likelihood Method ◽  
Type I ◽  
Life Testing ◽  
Statistical Point ◽  
Geometric Process ◽  
Accelerated Life

In accelerated life testing researcher generally use a life stress relationship between life characteristic and stress to estimate the parameters of failure time distributions at use condition which is just a re-parameterization of original parameters but from statistical point of view it is easy and reasonable to deal with original parameters of the distribution directly instead of developing inference for the parameters of the life stress relationship. So, an attempt is made here to estimate the parameters of Burr Type X life distribution directly in accelerated life testing by assuming that the lifetimes at increasing stress levels forms a geometric process. A mathematical model for the analysis of constant stress accelerated life testing for type-I censored data is developed and the estimates of parameters are obtained by using the maximum likelihood method. Also a Fisher information matrix is constructed in order to get the asymptotic variance and interval estimates of the parameters. Lastly, a simulation study is performed to illustrate the statistical properties of the parameters and the confidence intervals.

scholarly journals Bayesian estimation of the parameters of the bivariate generalized exponential distribution using accelerated life testing under censoring data

2015 ◽  
Vol 3 (2) ◽  
pp. 215
Author(s):  
Abd El-Maseh, M. P
Keyword(s):  
Bayesian Estimation ◽  
Accelerated Life Testing ◽  
Constant Stress ◽  
Type I ◽  
Life Testing ◽  
Unknown Parameters ◽  
Numerical Studies ◽  
Inverse Power Law ◽  
Accelerated Life ◽  
Power Law Function

<p>In this paper, the Bayesian estimation for the unknown parameters for the bivariate generalized exponential (BVGE) distribution under Bivariate censoring type-I samples with constant stress accelerated life testing (CSALT) are discussed. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The parameters are estimated by Bayesian approach using Markov Chain Monte Carlo (MCMC) method based on Gibbs sampling. Then, the numerical studies are introduced to illustrate the approach study using samples which have been generated from the BVGE distribution.</p>

Study on Reliability Design of the Domestic Compressor Subjected to Repetitive Internal Stresses by Parametric Accelerated Life Testing

2022 ◽  
pp. 241-266
Author(s):  
Seongwoo Woo ◽  
Dennis L. O'Neal ◽  
Yimer Mohammed Hassen
Keyword(s):  
Life Stress ◽  
Failure Modes ◽  
Action Plan ◽  
Accelerated Life Testing ◽  
Valve Plate ◽  
Life Testing ◽  
Accelerated Life ◽  
Mechanical Products ◽  
Reed Valve ◽  
Design Defects

This chapter explains the parametric accelerated life testing (ALT) to recognize design defects in mechanical products. A life-stress model and a sample size formulation are suggested. A compressor is used to demonstrate this method. Compressors were failing in the field. At the first ALT, the compressor failed due to a fractured suction reed valve. The failure modes were similar to those valves returned from the field. The fatigue of the suction reed valves came from an overlap between the suction reed valve and the valve plate. The problematic design was modified by the trespan dimensions, tumbling process, a ball peening, and brushing process for the valve plate. At the second ALT, the compressor locked due to the intrusion between the crankshaft and thrust washer. The corrective action plan performed the heat treatment to the exterior of the crankshaft made of cast iron. After the design modifications, there were no troubles during the third ALT. The lifetime of compressor was secured to have a B1 life 10 years.

scholarly journals MCMC Method for Exponentiated Lomax Distribution based on Accelerated Life Testing with Type I Censoring

2021 ◽  
Vol 20 ◽  
pp. 319-334
Author(s):  
Refah Alotaibi ◽  
H. Rezk ◽  
Sanku Dey
Keyword(s):  
Accelerated Life Testing ◽  
Constant Stress ◽  
Estimation Methods ◽  
Model Parameters ◽  
Type I ◽  
Life Testing ◽  
Informative Priors ◽  
Lomax Distribution ◽  
Type I Censoring ◽  
Accelerated Life

Accelerated Life Testing (ALT) is an effective technique which has been used in different fields to obtain more failures in a shorter period of time. It is more economical than traditional reliability testing. In this article, we propose Bayesian inference approach for planning optimal constant stress ALT with Type I censoring. The lifetime of a test unit follows an exponentiated Lomax distribution. Bayes point estimates of the model parameters and credible intervals under uniform and log-normal priors are obtained. Besides, optimum test plan based on constant stress ALT under Type I censoring is developed by minimizing the pre-posterior variance of a specified low percentile of the lifetime distribution at use condition. Gibbs sampling method is used to find the optimal stress with changing time. The performance of the estimation methods is demonstrated for both simulated and real data sets. Results indicate that both the priors and the sample size affect the optimal Bayesian plans. Further, informative priors provide better results than non-informative priors.

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).

Sign in / Sign up

Export Citation Format

Share Document