GIBBS SAMPLING AND BAYESIAN ESTIMATORSFOR TIME CENSORING CONSTANT STRESS RELIABILITY/LIFE PREDICTION

Salma Omar Bleed

doi:10.59743/jbs.v28i.53

المؤلفون

Salma Omar Bleed College of Science, Statistics Department, Al-asmarya University, Libya

DOI:

https://doi.org/10.59743/jbs.v28i.53

الكلمات المفتاحية:

Accelerated Life Test، Constant Stress، Time Censoring، Power Law Function، Bayesian Method، Generalized Logistic Distribution، Markov Chain Monte Carlo، Gibbs Samples، Win-Bugs

الملخص

The main objective of this paper is to develop the Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under time censoring scheme of the Generalized Logistic (GL) Failure times. The power law function is used to represent the relationship between the stress and the scale parameters of a test unit. Bayes estimates are obtained using Markov Chain Monte Carlo (MCMC), simulation algorithm based on Gibbs sampling. Then, Monte Carlo error (MC error), credible intervals, and predicted values of the two scale parameters and the reliability function under design stress are obtained. Numerical illustration is addressed for illustrating the theoretical results. Win-Bugs software package is used for implementing Markov Chain Monte Carlo (MCMC) simulation and Gibbs sampling.

المراجع

A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin, Bayesian Data Analysis, 2nd Edition. New York: Chapman & Hall/CRC, 2003.

A. M. Mathai and S. B. Provost, On the distribution of order statisticsfrom generalized logistic samples, International Journal of Statistics,62(1),(2004), 63-71.

Aly, H., M., and Bleed, S., O. Bayesian Estimation for the Generalized Logistic Distribution Type-II Censored Accelerated Life Testing. Int. J. Contemp. Math. Sciences, Vol. 8, 2013, no. 20, 969 – 986, 2013.

G. Molenberghs and G. Verbeke, On the Weibull-gamma frailty model,its infinite moments, and its connection to generalized log-logistic, logistic,Cauchy, and extreme-value distributions, Journal of Statistical Planning andInference, 14, 861-868, 2011.

H. He You, Bayesian statistical analysis of random censored exponential life data under accelerated life testing, Journal of Shanghai University, 2, 360-365, 1996.

J. A. Achcar, Approximate Bayesian inference for accelerated life tests, Applied Statistical Science, 1, 223-237, 1994.

Mann, N. R., Schafer, R. E., and Singurwalla, N. D. Methods for Statistical Analysis of Reliability and Life Data. Wiley, New York, 1974.

W. Luo, Reliability Characterization and Prediction of High K DielectricThin Film, Doctoral dissertation, Department of Industrial Engineering,Texas A and M Uni., Texas, USA, 2004.

X. Liu and L. Tang, A sequential constant stress accelerated life testing scheme and its Bayesian inference, Quality and Reliability Engineering International, 25, 91-109, 2009.

Y. Zhong and W. Meeker, Bayesian methods for planning accelerated life tests, Technometrics, 48, 49-60, 2007.