Stochastic Analysis of an Industrial System with Preparation Time Repair under Warranty Policy

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors study the reliability and sensitivity of a system with a single-unit with a repair preparation time under product warranty policy conditions. They use the state transition rate diagram and the Laplace transform for the probability of each state. The results of numerical examples make the investigation of the research appear promising. The reviewer believes that the paper needs improvement in the following issues:

- The description of some variables seems to be missing. All variables are should be described in the manuscript, e.g., on page 2, x, nu, S_0, …etc.

- Could the authors explain the diagram in Figure 1? More detailed descriptions of the states and transitions would be needed to help readers.

- What is the difference between R(s) and R(t) in Eqs. (8) and (9)?

- How did you choose three system parameters in line 218? And the {.} might be needed in line 218.

- Is the reliability sensitivity in Eq. (49) derived from the partial derivative? Is the sigma vector? If it is derived from on the numerical equation of Eq. (9), the explicit expression of the sensitivity for each variable would be helpful to the reader.

- What is the “relative sensitivity” in line 224? Authors may need the description and the references.

- Similarly, in Eqs. (51) and (52), the authors expressed the sensitivity and relative sensitivity for MTSF using partial derivative and integration in the time domain. Could the authors elaborate on the computational procedure or method for solving Eqs. (51) and (52)?

Some minor comments are:

On page 2, the table should be explicitly mentioned with its title, e.g., Table 1. State specification. The contents of the table should also be aligned (numbering and text).

For tables listed on lines 117~ and 119~, the authors may want to capitalize the first letter in the right text.

Lines 126, 128-9, are these inline equations? If not, the authors should add equation labels.

Line 164, “Mean” is written in a different style.

Overall, the text is not aligned, and the font, size, and mathematical notation are not consistent. For example, in lines 258-275. Specific revisions are needed here.

Author Response

The suggested comments in the attached file have been answered. Many thanks and appreciation to you.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article studied the expression of reliability indicators under the framework of the Markov process and warranty strategy, in the condition that all times follow a negative exponential distribution. The article's innovation and appropriate application scenarios have not been clarified, which makes it hard to know where the article's contribution to theory and practical applications lies. Other suggestions are as follows:

1.       In the literature review part, only relevant literature was listed without sorting and summarizing. What is the difference between your article and other literature? 2. Have existing literature also studied warranty strategies that consider preparation time? You need to mention them in the article and point out the differences between your article and them. Reference [21] is not related to the content of the article

2.       What is the basis for assuming that all time follows a negative exponential distribution?

Author Response

Please see the attachment
Thank you very much for all the suggestions provided

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors clarified all issued reported in the review. Publication is recommended.

Author Response

Thank you very much for your clear contribution with useful suggestions for us.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Add content mentioned in Answer 2 to the article to clarify the application scenarios of the model proposed in the article.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf