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 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>

Double-Crossed Step-Stress Accelerated Life Testing for Pneumatic Cylinder

2011 ◽  
Vol 121-126 ◽  
pp. 1274-1278 ◽  
Author(s):  
Juan Chen ◽  
De Yi Wang ◽  
Yong Ling Fu ◽  
Xiao Ye Qi
Keyword(s):  
Stress Testing ◽  
Estimation Error ◽  
Accelerated Life Testing ◽  
Constant Stress ◽  
Pneumatic Cylinder ◽  
Average Lifetime ◽  
Life Testing ◽  
Failure Data ◽  
Accelerated Life ◽  
Step Down

This paper discusses the principle and method of Double-Crossed Step-Down-Stress Accelerated Life Testing (DCSDS-ALT) for pneumatic cylinders. As to pneumatic cylinder, the step-down-stress testing failure physics can be described as cumulative degradation model. Temperature and frequency are normally chosen as the test stresses. The failure data obtained under DCSDS-ALT testing steps can be converted to those under constant stress testing. And the reliability specifications can be derived accordingly. To compare Double-stress ALTs with traditional constant stress testing shows Double-stress ALTs can meet the accuracy demand. The 5% of average lifetime estimation error and 1.85% of the characteristic lifetime error are very satisfying for pneumatic industrial lifetime prediction.

scholarly journals Bayesian Estimation and Prediction Based on Constant Stress-Partially Accelerated Life Testing for Topp Leone-Inverted Kumaraswamy Distribution

2021 ◽  
pp. 11-36
Author(s):  
G. R. Al-Dayian ◽  
A. A. El-Helbawy ◽  
R. M. Refaey ◽  
S. M. Behairy
Keyword(s):  
Loss Function ◽  
Accelerated Life Testing ◽  
Constant Stress ◽  
Type Ii ◽  
Life Testing ◽  
Bayes Estimators ◽  
Kumaraswamy Distribution ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests

Accelerated life testing or partially accelerated life tests is very important in life testing experiments because it saves time and cost. Partially accelerated life tests are used when the data obtained from accelerated life tests cannot be extrapolated to usual conditions. This paper proposes, constant–stress partially accelerated life test using Type II censored samples, assuming that the lifetime of items under usual condition have the Topp Leone-inverted Kumaraswamy distribution. The Bayes estimators for the parameters, acceleration factor, reliability and hazard rate function are obtained. Bayes estimators based on informative priors is derived under the balanced square error loss function as a symmetric loss function and balanced linear exponential loss function as an asymmetric loss function. Also, Bayesian prediction (point and bounds) is considered for a future observation based on Type-II censored under two samples prediction. Numerical studies are given and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied to real data sets.

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