Analysis of simple step-stress accelerated life test data from Lindley distribution under type-I censoring
Keywords:Accelerated life testing, Bootstrap, Lindley distribution, Maximum likelihood estimation, Type-I censoring
This article introduces step-stress accelerated life time model with Lindley lifetime under type-I censoring. The corresponding likelihood function is developed and parameter estimation by maximum likelihood approach is discussed. Also, parametric bootstrap confidence intervals are constructed for the unknown parameters. Simulation study is carried out to evaluate performance of the estimators of the proposed model.
V. Bagdonavicius (1978). Testing the hypothesis of additive accumulation of damages. Probability Theory and Applications, 23, pp. 403–408.
D. S. Bai, Y. R. C. Hun (1991). Optimum simple step-stress accelerated lifetests with competing causes of failure. IEEE Transactions on Reliability, 40, pp. 622–627.
D. S. Bai, M. S. Kim, S. H. Lee (1989). Optimum simple step-stress accelerated life tests with censoring. IEEE Transactions on Reliability, 38, pp. 528–532.
R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth (1996). On the Lambert W function. Advances in Computational Mathematics, 5, pp. 329–359.
J. R. V. Dorp, T. A. Mazzuchi, G. E. Fornell, L. R. Pollock (1996). A Baye’s approach to step-stress accelerated life testing. IEEE Transactions on Reliability, 45, pp. 491–498.
B. Efron, R. Tibshirani (1993). An introduction to the Bootstrap. Chapman and Hall, Florida.
M. E. Ghitany, B. Atieh, S. Nadarajah (2008). Lindley distribution and its application. Mathematics and Computers in Simulation, 78, pp. 493–506.
D. Han, D. Kundu (2015). Inference for a step-stress model with competing risks for failure from the generalized exponential distribution under type-I censoring. IEEE Transactions on Reliability, 64, no. 1, pp. 31–43.
D. Han, H. K. Ng (2014). Asymptotic comparison between constant-stress testing and step-stress testing for type-I censored data from exponential distribution. Communications in Statistics - Theory and Methods, 43, pp. 2384–2394.
D. V. Lindley (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society. Series B (Methodological), 20, pp. 102–107.
W. Q. Meeker, L. A. Escobar (1998). Statistical methods for reliability data. Wiley, New York.
R. Miller, W. B. Nelson (1983). Optimum simple step-stress plans for accelerated life testing. IEEE Transactions on Reliability, 29, pp. 103–108.
W. B. Nelson (1980). Accelerated life testing: step-stress models and data analysis. IEEE Transactions on Reliability, 29, pp. 103–108.
W. B. Nelson (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis. John Wiley and Sons, New York.
N. M. Sedyakin (1966). On one physical principle in reliability theory. Techn. Cybernetics, 3, pp. 80–87.