In this talk, we introduce a new adaptive Type-I progressive hybrid censoring scheme which has some advantages over the hybrid censoring schemes already discussed in the literature. We then employ Bayesian decision theory to study the variable sampling plans for the exponential distribution under four different progressive hybrid censoring schemes—Type-I and Type-II progressive hybrid censoring schemes, and adaptive Type-I and Type-II progressive hybrid censoring schemes (see Kundu and Joarder 2006; Childs et al. 2008; Ng et al. 2009; Lin and Huang 2011). The explicit expressions of the Bayes risk of a sampling plan under the selected progressive hybrid censoring schemes are established when a general quadratic loss function, which includes the sampling cost, the time-consuming cost, and the salvage, is used. Finally, numerical comparisons between the proposed optimal sampling plans are made, and the examination of the robustness is performed.

References:

Childs, A., Chandrasekar, B. and Balakrishnan, N. (2008). Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. In Statistical Models and Methods for Biomedical and Technical Systems (Eds., F. Vonta, M. Nikulin, N. Limnios and C. Huber-Carol), pp. 323–334. Birkhäuser.

Kundu, D. and Joarder, A. (2006). Analysis of Type-II progressively hybrid censored data. Computational Statistics & Data Analysis 50, 2509–2528.

Lam, Y. (1990). An optimal single variable sampling plan with censoring. The Statistician 39, 53–67.

Lam, Y. (1994). Bayesian variable sampling plans for the exponential distribution with Type I censoring. The Annals of Statistics 22, 696–711.

Lin, C. T., Huang, Y. L. and Balakrishnan, N. (2008a). Exact Bayesian variable sampling plans for exponential distribution under Type-I censoring. In Mathematical Methods for Survival Analysis, Reliability and Quality of Life (Eds., C. Huber, N. Limnios, M. Mesbah, and M. Nikulin), pp. 151–162. Hermes, London.

Lin, C. T., Huang, Y. L. and Balakrishnan, N. (2008b). Exact Bayesian variable sampling plans for the exponential distribution based on Type-I and Type-II hybrid censored samples. Communications in Statistics – Simulation and Computation 37, 1101–1116.

Lin, C. T., Huang, Y. L. and Balakrishnan, N. (2011). Exact Bayesian variable sampling plans for the exponential distribution with progressive hybrid censoring. Journal of Statistical Computation and Simulation, First published on: 07 December 2010 (iFirst).

Lin, C. T. and Huang, Y. L. (2011). On progressive hybrid censored exponential distribution. Journal of Statistical Computation and Simulation (in press).

Ng, H. K. T., Kundu, D. and Chan, P. S. (2009). Statistical analysis of adaptive Type-II progressively hybrid censored data. Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme. Naval Research Logistics 56, 687–698.

Keywords: Bayes risk; progressive hybrid censoring; simulated annealing optimization; variable sampling plan

Biography: Chien-Tai Lin is a Professor in the Department of Mathematics, Tamkang University, New Taipei City, Taiwan. She received her Ph.D. in 1993 from Florida State University, Tallahassee, U.S.A. She has been at Tamkang University since 1993. Her research interests include reliability and applications of linear combinations of spacings.