Joint reconstruction and prediction regions for unobserved exponential lifetimes under doubly Type II censoring

ABSTRACT

The doubly Type II censoring scheme, in which some of the smallest and largest lifetimes are censored, is an important and widely used censoring scheme in life-testing experiments and reliability. In this paper, the problem of simultaneous reconstruction and prediction for unobserved lifetimes in a doubly Type II censored sample from the one-parameter exponential distribution is discussed. For this purpose, the joint reconstruction and prediction (JRP) regions are obtained based on two independent pivotal quantities. First, the balanced JRP regions for the unobserved lifetimes are derived, and then a constrained optimization problem is formulated and solved to find the JRP regions with the smallest area. For illustrative and comparative purposes, a simulation study and two illustrative examples are presented.

KEYWORDS:

• Reconstruction region
• prediction region
• doubly Type II censored scheme
• exponential distribution
• pivotal quantity
• constrained optimization

Acknowledgements

We would like to thank the Associate Editor and two reviewers for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

M. Alizadeh

M. Alizadeh received the MSc degree in Statistics from Shahid Bahonar University of Kerman in Kerman, Iran. He is currently a PhD student in the Department of Statistics, University of Mazandaran, Babolsar, Iran. His research interestsinclude theory of estimation, reliability analysis and life-testing.

A. Asgharzadeh

A. Asgharzadeh is a full professor in the Department of Statistics at the University of Mazandaran, Babolsar, Iran. He received his MSC and PhD in Statistics from Shiraz University, Shiraz, Iran. His professional interests are reliability, Bayesian inference, statistical decision theory, and censored data analysis.

E. Basiri

E. Basiri is currently working as an Associate Professor in the Department of Mathematics and Applications, Faculty of Basic Sciences, Kosar University of Bojnord, Bojnord, Iran. She did her MSc and PhD in Statistics from Ferdowsi University of Mashhad, Mashhad, Iran. Her main interests are reliability analysis and censoring methodology.