A New Two Sample Type-II Progressive Censoring Scheme

TL;DR

This paper introduces a new two-sample type-II progressive censoring scheme that is more analytically tractable, providing exact inference methods, and demonstrates its effectiveness through simulations and data analysis.

Contribution

The paper proposes a novel two-sample type-II progressive censoring scheme that simplifies analysis and improves inference compared to existing methods.

Findings

The new scheme is more analytically tractable.

Bootstrap confidence intervals perform well and are easy to implement.

Simulation results show the proposed method's satisfactory performance.

Abstract

Progressive censoring scheme has received considerable attention in recent years. In this paper we introduce a new type-II progressive censoring scheme for two samples. It is observed that the proposed censoring scheme is analytically more tractable than the existing joint progressive type-II censoring scheme proposed by Rasouli and Balakrishnan \cite{RB:2010}. It has some other advantages also. We study the statistical inference of the unknown parameters based on the assumptions that the lifetime distribution of the experimental units for the two samples follow exponential distribution with different scale parameters. The maximum likelihood estimators of the unknown parameters are obtained and their exact distributions are derived. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals are also constructed. For comparison purposes we have used bootstrap confidence intervals also. It is observed that the bootstrap confidence intervals work very well and they are very easy to implement in practice. Some simulation experiments are performed to compare the performances of the proposed method with the existing one, and the performances of the proposed method are quite satisfactory. One data analysis has been performed for illustrative purposes. Finally we propose some open problems.