Accelerated life testing design using geometric process for pareto distribution
Abstract
In this paper the geometric process is used for the analysis of accelerated life testing under constant stress for Pareto Distribution. Assuming that the lifetimes under increasing stress levels form a geometric process, estimates of the parameters are obtained by using the maximum likelihood method for complete data. In addition, asymptotic interval estimates of the parameters of the distribution using Fisher information matrix are also obtained. The statistical properties of the parameters and the confidence intervals are illustrated by a Simulation study.About this article
References
Yang, G. B., “Optimum constant-stress accelerated life-test plans, IEEE Transactions on Reliability”, vol. 43, no. 4, (1994), pp. 575-581, available online: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=370223&isnumber=8488
Pan, Z., N. Balakrishnan, and Quan Sun, “Bivariate constant-stress accelerated degradation model and inference”, Communications in Statistics-Simulation and Computation, vol. 40, no. 2, (2011), 247–257, available online: http://dx.doi.org/10.1080/03610918.2010.534227
Chen, W., Gao, L., Liu, J., Qian, P. and Pan, J., “Optimal design of multiple stress constant accelerated life test plan on non-rectangle test region”, Chinese Journal of Mechanical Engineering, vol. 25, no. 6, (2012), pp. 1231-1237, available online: http://dx.doi.org/10.3901/CJME.2012.06.1231
Watkins, A.J. and John, A.M., “On constant stress accelerated life tests terminated by Type II censoring at one of the stress levels”, Journal of Statistical Planning and Inference, vol. 138, no. 3, (2008), pp 768-786, available online: http://dx.doi.org/10.1016/j.bbr.2011.03.031
Fan, T. H. and Yu, C. H., “Statistical Inference on Constant Stress Accelerated Life Tests under Generalized Gamma Lifetime Distributions”, Quality and Reliability Engineering International, (2012), available online: http://dx.doi.org/10.1002/qre.1412
View more references (13)
Ding, C., Yang, C. and Tse, S. K., “Accelerated life test sampling plans for the Weibull distribution under type I progressive interval censoring with random removals”, Journal of Statistical Computation and Simulation, vol. 80, no. 8, (2010), pp. 903-914, available online: http://www.tandfonline.com/doi/abs/10.1080/00949650902834478
Ahmad, N. Islam, A., Kumar, R. and Tuteja, R. K., “Optimal Design of Accelerated Life Test Plans Under Periodic Inspection and Type I Censoring: The Case of Rayleigh Failure Law”, South African Statistical Journal, 28, (1994), pp. 27-35.
Islam, A. and Ahmad, N., “Optimal design of accelerated life tests for the Weibull distribution under periodic inspection and type I censoring”, Microelectronics Reliability, vol. 34, no. 9, (1994), pp. 1459-1468, available online: http://dx.doi.org/10.1016/0026-2714(94)90453-7
Ahmad, N. and Islam, A., “Optimal accelerated life test designs for Burr type XII distributions under periodic inspection and type I censoring”, Naval Research Logistics, vol. 43, (1996), pp. 1049-1077, available online: http://dx.doi.org/10.1002/(SICI)1520-6750(199612)43:8<1049::AID-NAV2>3.0.CO;2-E
Ahmad, N., Islam, A. and Salam, A., “Analysis of optimal accelerated life test plans for periodic inspection: The case of exponentiated Weibull failure model”, International Journal of Quality & Reliability Management, vol. 23, no. 8, (2006), pp. 1019-1046, available online: http://dx.doi.org/ 10.1108/02656710610688194
Ahmad, N., “Designing Accelerated Life Tests for Generalized Exponential Distribution with Log-linear Model”, International Journal of Reliability and Safety, vol. 4, no. 2/3, (2010), pp. 238-264, available online: http://dx.doi.org/10.1504/IJRS.2010.032447
Lam, Y., “Geometric process and replacement problem, Acta Mathematicae Applicatae Sinica”, vol. 4, no. 4, (1988), pp. 366-377, available online: http://dx.doi.org/10.1007/BF02007241
Lam, Y. and Zhang, Y. L., “Analysis of a two-component series system with a geometric process model”, Naval Research Logistics, vol. 43, no. 4, (1996), pp. 491-502, available online: http://dx.doi.org/10.1002/(SICI)1520-6750(199606)43:4<491::AID-NAV3>3.0.CO;2-2
Lam, Y., “A monotone process maintenance model for a multistate system”, Journal of Applied Probability, vol. 42, no. 1, (2005), pp. 1-14, available online: http://www.jstor.org/stable/30040765
Zhang, Y. L. (2008): A geometrical process repair model for a repairable system with delayed repair, Computers and Mathematics with Applications, vol. 55, no. 8, (2008), pp. 1629-1643, available online: http://dx.doi.org/10.1016/j.camwa.2007.06.020
Huang, S., “Statistical inference in accelerated life testing with geometric process model”, Master’s thesis, San Diego State University, (2011), available online: http://hdl.handle.net/10211.10/1105
Kamal, M., Zarrin, S., Saxena, S. and Islam, A., “Weibull Geometric Process Model for the Analysis of Accelerated Life Testing with Complete Data”, International Journal of Statistics and Applications, vol. 2, no. 5, (2012), pp. 60-66, available online: http://dx.doi.org/ doi:10.5923/j.statistics.20120205.03
Zhou, K., Shi, Y. M. and Sun, T. Y., “Reliability Analysis for Accelerated Life-Test with Progressive Hybrid Censored Data Using Geometric Process, Journal of Physical Sciences, vol. 16, (2012), 133-143, http://www.vidyasagar.ac.in/journal/maths/vol16/JPS-V16-14.pdf