Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

The optimal scheme in type II progressive censoring with random removals for the Rayleigh distribution based on two-sample Bayesian prediction and cost function

Document Type : Original Paper

Authors
Elham Basiri 1
Sakine Beigi 2
1 Department of Mathematics and Applications, Faculty of Basic Sciences, Kosar University of Bojnord, Bojnord, Iran
2 Department of Industrial Engineering, Kosar University of Bojnord, Bijnord, Iran
10.22055/jamm.2020.29209.1705
Abstract
A type II progressive censoring scheme is one of the censoring methods that is important in life-testing studies. This method of censoring allows the experimenter to withdraw some of the tested units at different stages of testing. One question that arises when designing a type II progressive censoring is how we can decide to remove several units from the test at each step? Different answers can be made to answer this question by considering different criteria. In this paper, assuming the censoring scheme is a random variable from Binomial distribution, we intend to obtain the optimal parameter for the distribution of censoring scheme when the distribution is the Rayleigh distribution by considering two criteria, the cost of testing and the Mean squared prediction error in the two-sample prediction problem. To illustrate the effectiveness of the results, a simulation study and a real data example are presented with the help of MATLAB software.
Keywords
Two-sample Bayesian prediction
Rayleigh distribution
Mean squared prediction error
Cost function
Optimal censoring scheme
Subjects
 Aitchison, J and Dunsmore, I. R. (1975). Statistical Prediction
Analysis. Cambridge University Press, Cambridge, England.
Geisser, S. (1993). Predictive Inference: An Introduction. Chapman and
Hall, New York.
Balakrishnan, N. and Aggarwala, R. (2000). Progressive
Censoring: Theory, Methods and Applications. Birkhauser, Boston.
Balakrishnan, N. (2007). Progressive censoring methodology: an
appraisal. Test. 16, 211-259.
 Balakrishnan, N. and Cramer, E. (2014). The Art of Progressive
Censoring. Birkhauser, New York. 
Journal of Advanced Mathematical Modeling
Volume 10, Issue 1
May 2020
Pages 135-157

  • Receive Date 18 April 2019
  • Revise Date 05 November 2019
  • Accept Date 17 January 2020