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In reliability analysis and life-testing experiments, the researcher is often interested in the effects of changing stress factors such as “temperature”, “voltage” and “load” on the lifetimes of the units. Step-stress (SS) test, which is a special class from the well-known accelerated life-tests, allows the experimenter to increase the stress levels at some constant times to obtain information on the unknown parameters of the life models more speedily than under usual operating conditions. In this paper, a simple SS model from the exponentiated Lomax (ExpLx) distribution when there is time limitation on the duration of the experiment is considered. Bayesian estimates of the parameters assuming a cumulative exposure model with lifetimes being ExpLx distribution are resultant using Markov chain Monte Carlo (M.C.M.C) procedures. Also, the credible intervals and predicted values of the scale parameter, reliability and hazard are derived. Finally, the numerical study and real data are presented to illustrate the proposed study
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- Abd El-monem, G. H. and Jaheen, Z. (2017). Bayesian estimation for a multistep-stress accelerated generalized exponential model with Type II censored data, Journal of mathematics and computer sciences, 7, 292-306.
- Bai, S. D., Lee, H. S. and Kim, M. S. (1989). Optimum simple step-stress accelerated life tests with censoring, IEEE Transactions on reliability, 38, 528-532
- Chandra N. and Khan M. A. (2016): Classical and Bayesian inference on 3-Step step-stress accelerated life test plan for Weibull model under modified progressive Type-I censoring, International Journal of Performability Enginnering, 12(2), 131-142
- DeGroot and Goel (1979). Bayesian estimation and optimal designs in partially accelerated life testing. Naval Research Logistics, 26, 223-235.
- Drop, J., Mazzuchi, T., Fornell, G. and Pollock, L. (1996). A Bayesian approach to step-stress accelerated life testing. IEEE Transactions on Reliability, 45, 491-498.
- El-bassiouny,A. H., Abdo, N. F. and Shahen, H. S. (2015). Exponential Lomax Distribution, International Journal of Computer Applications, 121, 24-30.
- Gelman, A. and Rubin, D. (1992). Inference from iterative simulation using multiple sequences, Statistical Science, I, 451-511.
- Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2003). Bayesian data analysis, the 2nd Edition. New York, Chapman and Hall/CRC.
- Ismail, A. (2017). Planning step-stress life tests for the generalized Rayleigh distribution under progressive Type-II censoring with binomial removals, 49, 292-306.
- Lee, J. and Pan, R. (2010). Analyzing step-stress accelerated life testing data using generalized linear models. Journal IEEE Transactions on Reliability, 42, 589-598.
- Lee, J. and Pan, R. (2011). Bayesian analysis of step-stress accelerated life test with exponential distribution. Quality reliability engineering international. 28, 353-361.
- Li, T. F. (2002). Bayesian empirical Bayesian approach to estimation of the failure rate in exponential distribution. Communications in Statistics-Theory and Methods, 31, 1457-1465.
- Lin, T. (2002). Bayesian empirical Bayesian approach to estimation of the FR in exponential distribution, communication in statistics theory and method, 31, 1457-1465.
- Miller, R. and Nelsen, W. (1983). Optimum simple step-stress plans for accelerated life testing, IEEE Transactions on reliability, R-32, 59-63.
- Murthy, D., Xie, M. and Jiang, R. (2004). Weibull models. John Wiley and Sonc, Inc.
- Nelson, W. B. (1990). Accelerated testing statistical models, test plans and data analysis. John Wiley and Sons, Inc.