-->PONE-D-26-04764-->-->A Bayesian Max-EWMA Chart for Joint Surveillance of Lognormal Process Location and Scale-->-->PLOS One

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Additional Editor Comments:

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Partly

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-->2. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: N/A

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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-->5. Review Comments to the Author

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Reviewer #1: Revised version:

The paper presents a novel and interesting idea by applying the MAX-EWMA method to the lognormal distribution. I find the concept valuable and acceptable. However, a few minor points should be addressed.

Minor:

To further strengthen the context and breadth of your contribution, I recommend engaging with recent advancements in related fields. Specifically, the work would benefit from a discussion with studies focusing on risk-informed decision-making for critical infrastructure maintenance, advanced metaheuristic optimization techniques applied to real-world scheduling challenges, and the latest trends in AI-driven non-destructive evaluation and quality control in manufacturing using deep learning for defect detection. Additionally, incorporating insights from recent data-driven process modeling in metallurgy and materials science could provide valuable perspectives on generalizing your current findings or contrasting your methodology with established industrial prediction approaches. You can cite the following works:

• Zhou, N., Luo, L., Sheng, G., & Jiang, X. (2025). Scheduling the Imperfect Maintenance and Replacement of Power Substation Equipment: A Risk-Based Optimization Model. IEEE Transactions on Power Delivery, 40(4), 2154-2166. doi: 10.1109/TPWRD.2025.3572076

• Long, X., Cai, W., Yang, L., & Huang, H. (2024). Improved particle swarm optimization with reverse learning and neighbor adjustment for space surveillance network task scheduling. Swarm and Evolutionary Computation, 85, 101482. doi: https://doi.org/10.1016/j.swevo.2024.101482

• Xu, H., Han, F., Zhou, W., Liu, Y., Ding, F.,... Zhu, J. (2024). ESMNet: An enhanced YOLOv7-based approach to detect surface defects in precision metal workpieces. Measurement, 235, 114970. doi:https://doi.org/10.1016/j.measurement.2024.114970

• Xia, Y., Song, Q., Yi, B., Lyu, T., Sun, Z.,... Li, Y. (2025). Improving out-of-distribution generalization for online weld expulsion inspection using physics-informed neural networks. Welding in the World, 69(5),1309-1322. doi: 10.1007/s40194-025-01950-6

• Wang, G., Yang, Y., Zhou, S., Li, B., Wei, Y.,... Wang, H. (2024). Data Analysis and Prediction Model for Copper Matte Smelting Process. Metallurgical and Materials Transactions B, 55(4), 2552-2567. doi:10.1007/s11663-024-03115-0

I suggest to change the fonts of the figures including xticks and yticks and labels to time new roman.

A literature review table can be added.

Major:

The simulation section is well designed and implemented; no major revisions are required. My only suggestion is to highlight (e.g., bold) the best-performing method in each comparison table to enhance readability and understanding.

The case study section, however, requires further development. The dataset should be made available, and a step-by-step procedure should be provided for reproducibility. For example, a Kolmogorov–Smirnov (K–S) test can be used to demonstrate that the data follow a lognormal distribution. Additionally, including a flowchart to illustrate the practical problem-solving process would strengthen this section. Some exploratory data analysis (EDA)—such as a time-series plot for the illustrative example—would also improve clarity and insight.

Finally, the R or Python code used for simulations and data generation should be included in the supplementary material, along with sufficient explanations and comments to help readers understand and replicate the results.

Reviewer #2: Revised Reviewer Comments:

The paper presents an interesting idea; however, several clarifications and improvements are required.

1. Comparison with existing work:

The following paper also proposes a MAX-EWMA approach:

“Joint monitoring of mean and variance using Max-EWMA for Weibull process” by Muhammad Noor-ul-Amin, Irfan Aslam, and Navid Feroze.

Please clarify how your work differs from this study. In that paper, two statistics are defined, whereas in your paper such distinction is not clearly presented. Elaborate on this difference to better position your contribution.

2. Choice of distribution:

The paper employs the lognormal distribution. However, the Weibull model is frequently used in reliability surveillance studies, while others sometimes adopt the lognormal model. Please justify your selection of the lognormal distribution and consider conducting a goodness-of-fit test—such as the Kolmogorov–Smirnov (K–S) test—to validate this choice.

3. Simulation type:

Your study currently reports zero-state ARL results. It is also necessary to include a steady-state simulation to provide a more comprehensive performance assessment. Please add this analysis to the paper.

4. Model robustness:

The robustness analysis presented in Table 7 should also be evaluated under a Weibull distribution to verify the model’s stability and general applicability.

5. More discussions:

I think the authors can provide some other directions for this work as it can be applied in other fields. Based on my knowledge, I suggest to provide the following topics and cite the suggested works:

- Application of MAXXEWMA in quantile based moder: Hao, R., & Yang, X. (2024). Multiple-output quantile regression neural network. Statistics and Computing,34(2), 89.doi: 10.1007/s11222-024-10408-6 and Li, L., Xia, Y., Ren, S., & Yang, X. (2025). Homogeneity Pursuit in the Functional-Coefficient Quantile Regression Model for Panel Data with Censored Data, 29(3), 323-348. doi:10.1515/snde-2023-0024

- Fault detection with the proposed method: Wang, H., Li, Y., Men, T., & Li, L. (2024). Physically Interpretable Wavelet-Guided Networks With DynamicFrequency Decomposition for Machine Intelligence Fault Prediction. IEEE Transactions on Systems, Man and Cybernetics: Systems, 54(8), 4863-4875. doi: 10.1109/TSMC.2024.3389068 and Wan, A., Zhang, F., Al-Bukhaiti, K., Cheng, X., Ji, X., Wang, J.,... Shan, T. (2025). A Novel GA-PSO-SVM Model for Compound Fault Diagnosis in Gearboxes With Limited Data. IEEE Sensors Journal, 25(16),30443-30431.doi: 10.1109/JSEN.2025.3576761 and Lu, Y., Wang, S., Zhang, C., Chen, R., Dui, H., Mazurkiewicz, D.,... Zhang, Y. (2025). A dynamic imperfect inspection-based maintenance optimization considering dependent competing failure. Measurement, 253,117470. doi: https://doi.org/10.1016/j.measurement.2025.117470

Generally, I appreciate the authors and suggest the paper for publication after the revision round.

Reviewer #3: The paper proposes a Bayesian Max-EWMA framework for real-time monitoring of lognormal process mean and variance, accounting for measurement error and variable batch sizes, and demonstrates early detection of deviations and robustness in industrial applications. The topic is relevant and potentially valuable to the fields of statistical process control (SPC) and reliability monitoring.

However, in its current form, the manuscript suffers from significant scientific, methodological, validation, mathematical transparency, and presentation deficiencies. Several claims are made without formal justification or adequate comparative evaluation, and parts of the proposed methodology lack sufficient rigor or clear explanation.

Major comments:

The authors propose a Bayesian Max-EWMA framework for lognormal processes. However, Max-EWMA charts have been previously introduced, Bayesian EWMA charts are extensively studied, and the conjugate NIG model for normal mean–variance monitoring is standard. The manuscript should provide direct comparisons with state-of-the-art methods and include a table summarizing theoretical and practical contributions relative to existing studies. It should also clarify the role of key components, such as measurement-error correction, the Max statistic, and Linex loss integration.

The manuscript does not provide a clear and precise definition of the Baseline Health State model.

Please pay careful attention to the structure and writing of the manuscript. Several obvious writing errors are observed, and the paper requires a thorough revision.

Examples include:

Page 3, line 76: “1.3 Joint monitoring and Max-type statistics Joint monitoring” – it is unclear what “1.3” refers to.

Page 17, line 365: “the per-Inspection Batch estimators at time under the Baseline Health State model.” – there is no space between “ ” and “under”. Similar errors appear elsewhere in the manuscript.

Page 21, line 458: “The objective is to monitor for shifts in the underlying process parameters ( , 2)” – the notation for the parameters is incorrect.

These are just a few examples of writing issues. Careful attention is required to correct such errors throughout the manuscript.

The study assumes that the observations X_it are independent and identically distributed (i.i.d.) following a normal distribution with constant mean and variance. However, in reliability and degradation monitoring, data are often autocorrelated, time-dependent, and non-stationary. This assumption is highly restrictive and limits the applicability of the proposed method. The authors should justify it by examining the effect of autocorrelation, performing a robustness analysis, or explicitly acknowledging it as a limitation.

The Linex loss is essentially used in an ad hoc manner. The authors themselves acknowledge that for the student-t distribution, the exponential moment may not exist, and for σ^2, the integrals diverge. Moreover, the Linex loss has no role in error control or ARL: it only affects point estimation, with no theoretical analysis of how a impacts ARL, no guidance on choosing a, and no robustness check against model misspecification. As a result, the Linex loss appears mostly decorative rather than effective, and its removal would likely have minimal impact on the results. The authors should clarify and justify why the Linex loss is included at all.

A serious concern is the negative estimates of σ^2. The paper itself states that “if β_t/(α_t-1)<τ^2 occurs, the estimator becomes negative … enforce a floor” which constitutes a direct violation of Bayesian principles, making the resulting estimator no longer truly Bayesian. This represents a significant weak spot in the proposed methodology.

The data are not publicly accessible. PLOS ONE places strong emphasis on Data Availability, yet the authors state that the data are available only “upon reasonable request.” This is generally not acceptable for PLOS ONE and limits reproducibility.

The definition of FEWMA is not clearly specified.

These issues should be addressed consistently throughout the paper.

Some subsection headings appear without numbering and are presented only in boldface, which disrupts the structural consistency of the manuscript. For example, “Notation and Assumptions”, “Bayes Estimators under SELF” and “Variance of the Dispersion Estimator” are not numbered like other sections. Please ensure that all sections and subsections are consistently numbered throughout the manuscript.

Several phrases and subsection titles are repeated verbatim in the manuscript. For example, “Bayes Estimators under LLF: Bayes Estimators under LLF” appears consecutively in duplicate form. Such repetitions suggest insufficient proofreading and affect the overall presentation quality. A thorough and careful revision of the entire manuscript is strongly recommended to eliminate redundancies and improve clarity and consistency.

Many sentences, particularly in the Introduction and Methodology sections, are excessively long and contain multiple ideas in a single sentence, which reduces clarity. The authors are encouraged to split such sentences into shorter, more focused statements.

The manuscript frequently capitalizes common technical terms (e.g., Baseline Health State, Inspection Batch, Sensor Measurement Uncertainty) that are not proper nouns. Capitalization should be used consistently and limited to proper names or formally defined acronyms.

Several statements use strong, promotional language (e.g., “offers a principled tool,” “ensures robustness”) without sufficient empirical or theoretical support. A more neutral, evidence-based scientific tone is recommended.

Verb tense usage is inconsistent across sections, particularly between present and past tense in the Methods and Simulation sections. The authors should standardize tense usage.

Several symbols and notations are introduced without immediate definition or are redefined later in the manuscript. All symbols should be clearly defined at their first occurrence and used consistently thereafter.

Some closely related concepts are described using different terms across sections (e.g., variability, dispersion, and volatility), which may confuse readers. The authors are encouraged to standardize terminology throughout the manuscript.

The manuscript contains scattered minor grammatical and typographical errors (e.g., missing articles, inconsistent hyphenation, spacing issues). A careful language edit is recommended to improve overall polish.

Figure and table captions should provide concise and clear titles that identify the content of the figure or table, rather than descriptive explanations. All figure and table captions should be carefully reviewed and revised accordingly.

Some equations in the manuscript are numbered while others are not. All mathematical expressions presented as displayed equations within the text should be consistently numbered.

Some figure references in the manuscript are incorrect. For example, the text states “is compared in Figure 10,” whereas the correct reference should be Figure 11. Please carefully check and correct all in-text references throughout the manuscript.

The references should be presented in a uniform and correct format.

It is recommended to provide a table listing all abbreviations and their corresponding full terms. Throughout the manuscript, consistently use the abbreviations instead of repeatedly writing long expressions.

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Reviewer #1: Yes: Ali Yeganeh

Reviewer #2: No

Reviewer #3: No

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A Distributionally-Robust Bayesian Adaptive EWMA Chart for Joint Surveillance of Lognormal Process Location and Scale

PONE-D-26-04764R1

Dear Dr. Himmat,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #1: All comments have been addressed

Reviewer #3: All comments have been addressed

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-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #1: Yes

Reviewer #3: Yes

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-->3. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: Yes

Reviewer #3: Yes

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-->4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #3: Yes

**********

-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: Yes

Reviewer #3: Yes

**********

-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: (No Response)

Reviewer #3: The revised manuscript demonstrates substantial improvement in clarity, methodological soundness, and overall presentation quality. The authors have carefully and comprehensively addressed both the major and minor reviewer comments. In its current form, the paper meets the scientific standards of the journal and I consider it suitable for acceptance.

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-->7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

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Reviewer #1: Yes: Ali Yeganeh

Reviewer #3: Yes: Sara Abossedgh

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