Inference on Constant Stress Accelerated Life Tests Under Exponentiated Exponential Distribution


Accelerated life tests have become increasingly important because of highercustomer expectations for better reliability, more complicated products withmore components, rapidly changing technologies advances, and the clear needfor rapid product development. Hence, accelerated life tests have been widelyused in manufacturing industries, particularly to obtain timely informationon the reliability. Maximum likelihood estimation is the starting point whenit comes to estimating the parameters of the model. In this paper, besides themethod of maximum likelihood, nine other frequentist estimation methodsare proposed to obtain the estimates of the exponentiated exponential distribution parameters under constant stress accelerated life testing. We considertwo parametric bootstrap confedence intervals based on different methods ofestimation. Furthermore, we use the different estimates to predict the shapeparameter and the reliability function of the distribution under the usualconditions. The performance of the ten proposed estimation methods isevaluated via an extensive simulation study. As an empirical illustration,the proposed estimation methods are applied to an accelerated life test dataset.

DOI Code: 10.1285/i20705948v16n2p234

Keywords: Accelerated life testing; Anderson-Darling estimation; Cramervon-Mises estimation; exponentiated exponential distribution; maximum likelihood method; least squares method


Abdel Ghaly, A. A., Aly, H. and Salah, R. (2016). Dierent estimation methods for

constant stress accelerated life test under the family of the exponentiated distributions. Quality and Reliability Engineering International, 32, 1095-1108.

Anderson, T. W., Darling, D. A. (1952). Asymptotic theory of certain "goodness-of

t criteria" based on stochastic processes. Ann Math Statist., 23, 193-212.

Bagdonavicius, V. and Nikulin, M. (2002). Accelerated Life Models: Modeling and

Statistical Analysis. Chapman & Hall/CRC Press, Boca Raton, Florida.

Bartoluccia, A. A., K. P. Singha, A. D. Bartoluccib, and Baea, S. (1999). Applying

medical survival data to estimate the three-parameter Weibull distribution by the

method of probability-weighted moments. Math. Comput. Simulation, 48, 385-392.

Bhattacharyya, G. K. and Fries, A. (1982). Inverse gaussian regression and accelerated life tests. In Survival Analysis: Proceedings of the Special Topics Meeting.

Institute of Mathematical Statistics: Hayward, California. 101-118.

Bhattacharyya, G. K. and Soejoeti, Z. (1981). Asymptotic normality and eciency

of modied least squares estimators in some accelerated life test models. The Indian

Journal of Statistics, 43, 18-39.

Cheng, R. C. H. and Amin, N. A. K. (1979). Maximum product of spacings estimation with applications to the lognormal distribution. Technical report, Department

of Mathematics, University of Wales.

Cheng, R. C. H. and Amin, N. A. K. (1983). Estimating parameters in continuous

univariate distributions with a shifted origin. J. R. Statist. Soc., B, 45, 394-403.

Cramer, H. (1928). On the composition of elementary errors. Scandinavian Actuarial

Journal, 1, 13-74. doi:10.1080/03461238.1928.10416862.

Dey, S. and Nassar, M. (2019). Classical methods of estimation on constant stress

accelerated life tests under exponentiated Lindley distribution. Journal of Applied


Fan, T. and Yu, C. (2013). Statistical inference on constant stress accelerated life

tests under generalized gamma lifetime distribution. Quality and Reliability Engineering International, 29, 631-638.

Gui, W. and Chen, M. (2016). Parameter estimation and joint condence regionsfor the parameters of the generalized Lindley distribution. Mathematical Problems

in Engineering,

Haghighi, F. (2014). Optimal design of accelerated life tests for an extension of the

exponential distribution. Reliability Engineering & System Safety.131,251-256.

Han, D. (2015). Time and cost constrained optimal designs of constant-stress and

step-stress accelerated life tests. Reliability Engineering & System Safety. 140, 1-14.

Kim, C. and Bai, D. S. (2002). Analysis of accelerated life test data under two

failure modes. International Journal of Reliability. Quality and Safety Engineering,

, 111-125.

Meeker, W. Q. and Escobar, L. K. (1998). Statistical Methods for Reliability Data.

Wiley, New York.

Nadarajah, S., Bakouch, H. S. and Tahmasbi, R. A. (2011). Generalized Lindley

distribution. Sankhya B, 73, 331-359.

Nassar, M. and Dey, S. (2018). Dierent estimation methods for exponentiated

Rayleigh distribution under constant-stress accelerated life test. Qual Reliab Engng

Int., 1-13. DOI:10.1002/qre.2349.

Nelson, W. B. (2004) Accelerated Testing: Statistical Model. Test Plan and Data

Analysis. Wiley: New York.

Oluyede, B. and Yang, T. (2014). A new class of generalized Lindley distributions

with applications. Journal of Statistical Computation and Simulation, 85, 2072-2100.

Park, J. L., Bae, S. J. (2010). Weighted rank regression with dummy variables for

analyzing ALT data. International Journal of Industrial Engineering, 17, 236-245.

Singh, S. K, Singh, U. and Sharma, V. K. (2013). Expected total test time and

Bayesian estimation for generalized Lindley distribution under progressively TypeII censored sample where removals follow the Beta-binomial probability law. Applied

Mathematics and Computation, 222, 402-419.

Singh, S. K, Singh, U. and Sharma, V. K. (2014). Bayesian estimation and prediction

for the generalized Lindley distribution under asymmetric loss function. Hacettepe

Journal of Mathematics and Statistics, 43, 661-678.

Singh, S. K, Singh, U. and Sharma, V. K. (2016). Estimation and prediction

for Type-I hybrid censored data from generalized Lindley distribution. Journal of

Statistics & Management Systems, 19, 367-396.

Singpurwalla, N. D. (1974). Estimation of the join point in a heteroscedastic regression model arising in accelerated life tests. Communications in Statistics, 3,


Torabi, H. (2008). A General Method for Estimating and Hypotheses Testing Using

Spacings. Journal of Statistical Theory and Applications, 8, 163-168.

von Mises, R. E. (1928). Wahrscheinlichkeit, Statistik und Wahrheit. Julius


Wu, S. and Huang, S. (2017). Planning two or more level constant-stress accelerated life tests with competing risks. Reliability Engineering & System Safety. 158, 1-8.

Zhang, J. P., Wang, R. T. (2009). Reliability life prediction of VFD by constant temperature stress accelerated life tests and maximum likelihood estimation. Journal

of Testing and Evaluation, 37, 316-320.

Zhu, Y., Elsayed, E. (2010). Design of equivalent accelerated life testing plans under

dierent stress applications. Quality Technology and Quantitative Management, 8,


Full Text: pdf

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.