OPTIMUM STEP STRESS ACCELERATED LIFE TESTING FOR FRECHET DISTRIBUTION
Keywords:
Accelerated Life Testing, Frechet Distribution, Asymptotic Variance, Cumulative Exposure Model, Log-Linear Relationship, Simple Step StressAbstract
Nowadays products become more reliable so these highly reliable products could take long time to fail under normal condition. To overcome this problem, accelerated life testing has been used to estimate the reliability of these products. In this paper, we propose Frechet step stress accelerated life test plan under cumulative exposure model assuming a log-linear relationship between Frechet scale parameter and stresses. The simulation study is used for estimation. Further, optimal plan is designed using real data set by minimizing the asymptotic variance of the maximum likelihood estimators at 100pthpercentile of the design stress. Finally, sensitivity analysis is designed.
Downloads
References
Abbas, K. and Tang, Y. (2013). Estimation of parameters for Frechet distribution based on type-II censored samples, Caspian Journal of Applied Sciences Research, 2(7), p. 36-43.
Alhadeed, A. A. and Yang, S. S. (2002). Optimal simple step-stress plan for Khamis-Higgins model, IEEE Transactions on Reliability, 51(2), p. 212-215.
Alhadeed, A. A., and Yang, S. S. (2005). Optimal simple step-stress plan for cumulative exposure model using log-normal distribution, IEEE Transactions on Reliability, 54(1), p. 64-68.
Chandra, N., Khan, M. A. and Gopal, G. (2016). Optimum quadratic step- stress accelerated life test plan for Weibull distribution under type-I censoring, International Journal of System Assurance Engineering and Management, 28(3), p. 1-7.
Chung, S.W. and Bai, D.S. (1998). Optimal designs of simple step-stress accelerated life tests for log-normal lifetime distributions, International Journal of Reliability, Quality and Safety Engineering, 5(04), p. 315-336.
Ebrahem, M. A. H. and Al-Masri, A. Q. (2007). Optimum simple step-stress plan for log-logistic cumulative exposure model, Metron-International Journal of Statistics, 65(1), p. 23-34.
Frechet, M. (1927). Sur la loi de probabilite de lecart maximum, In Annales de la societe Polonaise de Mathematique, 6(93), p. 110-116.
Hakamipour, N., Rezaei, S., Withers, C., Nadarajah, S., Marin-Jimnez, A. E., RoldnNofuentes, J. A. and Borzadaran, G. M. (2017). Optimizing the simple step stress accelerated life test with type I censored Frechet data, REVSTAT Statistical Journal, 15(1), p. 1-23.
Hakamipour, N. and Rezaei, S. (2015). Optimal Design for a Bivariate Simple Step-Stress Accelerated Life Testing Model with Type-II Censoring and Gompertz Distribution, International Journal of Information Technology and Decision Making, 14(06), p. 1243-1262.
Hong, Y., Ma, H. and Meeker, W. Q. (2010). A tool for evaluating time- varying-stress accelerated life test plans with log-location-scale distributions, IEEE Transactions on Reliability, 59(4), p. 620-627.
Khamis, I.H. and Higgins, J. J. (1996). Optimum3-stepstep-stress tests, IEEE transactionson reliability, 45(2), p. 341-345.
Kielpinski, T. J. and Nelson, W. (1975). Optimum censored accelerated life tests for normal and lognormal life distributions, IEEE Transactions on Reliability, 24(5), p. 310-320.
McCrory, E.S. (2006). Cavity and beam excitation for the linac 7835 tube lifetimes, Technical Report Beams-Document-2326-V1, Fermi National Accelerator Laboratory, Batavia, IL.
Miller, R. and Nelson, W. (1983). Optimum simple step-stress plans for accelerated life testing, IEEE Transactions on Reliability, 32(1), p. 59-65.
Nelson, W. (1980). Accelerated life testing-step-stress models and data analyses, IEEE transactions on reliability, 29(2), p. 103-108.
Nelson, W.B. (1990). Accelerated Life Testing, Statistical Models, Test Plans and Data Analysis, New York, John Wiley & Sons.
Nelson, W. and Kielpinski, T. J. (1976). Theory for optimum censored accelerated life tests for normal and lognormal life distributions. Technometrics, 18(1), p. 105-114.
Nelson, W. and Meeker, W. Q. (1978). Theory for optimum accelerated censored life tests for Weibull and extreme value distributions, Technometrics, 20(2), p. 171-177.
Singh, N.P. (1987). Maximum likelihood estimation of Frechet distribution parameters. Journal of Statistical Studies, 7, p. 11-22.
Singh, N. P., Singh, K. P. and Singh, U. (1990). Estimation of Frechet distribution parameters by joint distribution of'm' extremes, Statistica, 50(1), p. 59-69.
Srivastava, P. W., and Shukla, R. (2008). A log-logistic step-stress model. IEEE Transactions on Reliability, 57(3), p. 431-434.
Saxena, S., Zarrin, S. and Kamal, M. (2012). Optimum Step Stress Accelerated Life Testing for Rayleigh Distribution, International journal of statistics and applications, 2(6), p. 120-125.