Optimal step stress accelerated life tests for the exponential distribution under periodic inspection and type I censoring

  • Published : 2009.11.30


In this paper, the inferences of data obtained from periodic inspection and type I censoring for the step-stress accelerated life test are studied. The exponential distribution with a failure rate function that a log-linear function of stress and the tampered failure rate model are considered. The maximum likelihood estimators of the model parameters are estimated and also the optimal stress change time which minimize the asymptotic variance of maximum likelihood estimators of parameters is determined. A numerical example will be given to illustrate the proposed inferential procedures and the sensitivity of the asymptotic variance of the estimated mean by the guessed parameters is investigated.


  1. Ahmad, N., Islam, A. and Salam, A. (2006). Analysis of optimal accelerated life test plans for periodic inspection. International Journal of Quality & Reliability Management, 23, 1019-1046. https://doi.org/10.1108/02656710610688194
  2. Bai, D. S., Kim, M. S. and Lee, S. H. (1989). Optimum simple step-stress accelerated life tests under periodic observation. Journal of the Korean Statistical Society, 18, 125-134.
  3. Bhattacharyya, G. K. and Soejoeti, Z. (1989). A tampered failure rate model for step-stress accelerated life test. Communications in Statistics, Theory and Methods, A 18, 1627-1643.
  4. DeGroot, M. H. and Goel, P. K. (1979). Bayesian estimation and optimal designs in partially accelerated life testing. Naval Research Logistics Quarterly, 26, 223-235. https://doi.org/10.1002/nav.3800260204
  5. Islam, A. and Ahmad, N. (1994). Optimal design of accelerated life tests for the weibull distribution under periodic inspection and type I censoring. Microelectronics and Reliability, 34, 1459-1468. https://doi.org/10.1016/0026-2714(94)90453-7
  6. Miller, R. W. and Nelson, W. (1983). Optimum simple step-stress plans for accelerated life testing. IEEE Transactions on Reliability, 32, 59-65.
  7. Moon, G. A. and Kim, I. H. (2006). Parameter estimation of the two-parameter exponential distribution under three step-stress accelerated life test. Journal of Korean Data & Information Science Society, 17, 1375-1386.
  8. Moon, G. A. (2008). Step-stress accelerated life test for grouped and censored data. Journal of Korean Data & Information Science Society, 19, 697-708.
  9. Nelson, W. (1980). Accelerated life testing step-stress models and data analysis. IEEE Transactions on Reliability, 29, 103-108. https://doi.org/10.1109/TR.1980.5220742
  10. Seo, S. K. and Yum, B. J. (1993). Estimation methods for the mean of the exponential distribution based on grouped and censored data. IEEE Transactions on Reliability, 42, 87-96. https://doi.org/10.1109/24.210276
  11. Xiong, C. and Ji, M. (2004). Analysis of grouped and censored data from step-stress life test. Transactions on Reliability, 53, 22-28. https://doi.org/10.1109/TR.2004.824832
  12. Yum, B. J. and Choi, S. C. (1989). Optimal design of accelerated life tests under periodic inspection. Naval Research Logistics, 36, 779-795. https://doi.org/10.1002/1520-6750(198912)36:6<779::AID-NAV3220360604>3.0.CO;2-2