On Estimation of Reliability Functions for the Extended Rayleigh Distribution under Progressive First-Failure Censoring Model

Round 1

Reviewer 1 Report

The paper investigated statistical inference on progressive first failure censoring model with extended Rayleigh distribution (ERD).

The statistical inference includes asymptotics of the MLE and Bayesian estimation by MCMC. In particular confidence interval for the MLE and Bayesian credible interval are derived. They have shown simulation study and real data application to show performance of the proposed method.

The work is not particularly innovative, but based on the paper, this work is not done before. It may be interest of applied work in reliability.

Author Response

We would like to thank the referee for his\her effective comments. We read very carefully the referee's report and we follow his request about revising the manuscript.  Please find below the attached file of responses.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors developed asymptotic confidence intervals and credible intervals for the ERD parameters, as well as reliability and hazard functions. Simulation studies and real-world applications are analyzed and compared to the performance of the proposed method for various sample sizes and review scenarios. Although the article is generally interesting, there are some problems in literature review, formula expression, and innovation. I agree that this paper was published after the authors revised it according to my comments. Here are some specific suggestions:

1. The position of the List of Abbreviations should be at the beginning of the article, not the second chapter

2. It is recommended that the authors summarize the contribution of the method proposed in this article in the introduction part of the article to highlight the research advantages of this article

3. In the introduction part of the article, on the part of system reliability, the article analyzes some old work, and it is suggested that the authors analyze more recent work, for example, lifetime extension approach based on levenberg-marquardt neural network and power routing of dc- dc converters, an integrated multi-head dual sparse self-attention network for remaining useful life prediction

4. There are some formulas in the article, such as formula (1.1-1.3), the explanation of many parameters is not explained clearly

5. Regarding the third part, Maximum Likelihood Estimation, the article lacks relevant supporting literature. It is recommended to analyze some related work, such as remaining useful life prediction of lithium-ion battery with adaptive noise estimation and capacity regeneration detection, an adaptive remaining useful life prediction approach for single battery with unlabeled small sample data and parameter uncertainty

6. Please strengthen the experimental verification of real data. At present, it is difficult to see that the actual data set can reflect the advantages of this method. Why the rigorous and complex formula derivation can clearly discuss the results of the actual data in only 2 pages.

7. The article should strengthen innovative discussions to highlight the research advantages of this article

Extensive editing of English language required

Author Response

We would like to thank the referee for his\her effective comments. We read very carefully the referee's report and we follow his request about revising the manuscript. English language have been revised, Please find below the attached file of responses.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Thanks to the authors' revision. I think it can be accepted.