On a Generalized Model in Accelerated Life Testing
Affiliation(s)
Department of Epidemiology and Biostatistics, University of the Philippines, Manila, Philippines. School of Statistics, University of the Philippines, Quezon City, Philippines.
Department of Epidemiology and Biostatistics, University of the Philippines, Manila, Philippines. School of Statistics, University of the Philippines, Quezon City, Philippines.
ABSTRACT
The main objective of accelerated life tests in this setting is the recovery of the distribution of the random variable representing lifetime which is difficult to observe at a certain level of a given stress factor. A general model for accelerated life test is proposed that utilizes the inverse problem approach, that is, the variable is observe at different level/s and the transfer function is used to recover the elusive random variable (life time). The problem then is reduced to finding the transfer function. We derive some properties of the proposed general model. The Lognormal distribution and the Arrhenius model for lifetime are used as examples. Its relationship with the Cox proportional hazards model is also discussed.
The main objective of accelerated life tests in this setting is the recovery of the distribution of the random variable representing lifetime which is difficult to observe at a certain level of a given stress factor. A general model for accelerated life test is proposed that utilizes the inverse problem approach, that is, the variable is observe at different level/s and the transfer function is used to recover the elusive random variable (life time). The problem then is reduced to finding the transfer function. We derive some properties of the proposed general model. The Lognormal distribution and the Arrhenius model for lifetime are used as examples. Its relationship with the Cox proportional hazards model is also discussed.
Cite this paper
E. Cruz and A. Guzman, "On a Generalized Model in Accelerated Life Testing," Open Journal of Statistics, Vol. 2 No. 2, 2012, pp. 184-187. doi: 10.4236/ojs.2012.22021.
E. Cruz and A. Guzman, "On a Generalized Model in Accelerated Life Testing," Open Journal of Statistics, Vol. 2 No. 2, 2012, pp. 184-187. doi: 10.4236/ojs.2012.22021.
References
[1] W. Nelson, “Accelerated Testing: Statistical Models, Test Plans and Analysis,” Wiley, New York, 2004. [2] O. Aalen, “Nonparametric Inference for a Family of Counting Processes,” Annals of Statistics, Vol. 6, No. 4, 1978, pp. 701-726. doi:10.1214/aos/1176344247 [3] P. K. Andersen, O. Borgan, R. D. Gill and N. Keiding, “Statistical Model Based on Counting Processes,” Springer- Verlag, New York, 1993. [4] T. Fleming and D. Harrington, “Counting Processes and Survival Analysis,” Wiley, New York, 1992. [5] D. R. Cox and D. Oakes, “The Analysis of Survival Data,” Chapman and Hall, London, 1984. [6] R. Barlow and E. Scheuer, “Estimation from Accelerated Life Tests,” Technometrics, Vol. 13, No. 1, 1971, pp. 145- 160. [7] B. Gnedenko, I. Pavlov and I. Ushakov, “Statistical Reliability Engineering,” John Wiley & Sons Ltd., New York, 1999. [8] R. Hogg and A. Craig, “Introduction to Mathematical Statistics,” John Wiley & Sons Ltd., New York, 1995. [9] W. Q. Meeker and L. A. Escobar, “Statistical Methods for Reliability Data,” John Wiley & Sons Ltd., New York, 1998.
[1] W. Nelson, “Accelerated Testing: Statistical Models, Test Plans and Analysis,” Wiley, New York, 2004. [2] O. Aalen, “Nonparametric Inference for a Family of Counting Processes,” Annals of Statistics, Vol. 6, No. 4, 1978, pp. 701-726. doi:10.1214/aos/1176344247 [3] P. K. Andersen, O. Borgan, R. D. Gill and N. Keiding, “Statistical Model Based on Counting Processes,” Springer- Verlag, New York, 1993. [4] T. Fleming and D. Harrington, “Counting Processes and Survival Analysis,” Wiley, New York, 1992. [5] D. R. Cox and D. Oakes, “The Analysis of Survival Data,” Chapman and Hall, London, 1984. [6] R. Barlow and E. Scheuer, “Estimation from Accelerated Life Tests,” Technometrics, Vol. 13, No. 1, 1971, pp. 145- 160. [7] B. Gnedenko, I. Pavlov and I. Ushakov, “Statistical Reliability Engineering,” John Wiley & Sons Ltd., New York, 1999. [8] R. Hogg and A. Craig, “Introduction to Mathematical Statistics,” John Wiley & Sons Ltd., New York, 1995. [9] W. Q. Meeker and L. A. Escobar, “Statistical Methods for Reliability Data,” John Wiley & Sons Ltd., New York, 1998.