Adjustment of Measurement Error Effects on Dispersion Control Chart with Distribution-Free Quality Variable
Round 1
Reviewer 1 Report
In this paper, the main idea is to convert the observed distribution-free process variables into a flexible sign statistic, and then adopt a function to adjust the measurement error effects on the sign statistic, The results of this paper are interesting.
The following issues need to be addressed：
1. The description of references should give advantages and disadvantages rather than just what is done.
2. Appendix A.1 and Appendix A.2 should be placed after the references.
3. Pay attention to details such as Funding: “Please add” can be deleted.
Author Response
Thank you for reviewing our manuscript. We appreciate your careful and constructive comments about our earlier submission. In making this revision we have carefully addressed your concerns and incorporated your suggestions to improve the presentation of the manuscript.
In what follows, we reproduce your comments in boldface, and then give our responses.
1.The description of references should give advantages and disadvantages rather than just what is done.
Our Response:
In the revised manuscript, we have added more detailed discussions of (dis)advantages of references. New inputs have been marked in blue in Section 1.
- Appendix A.1 and Appendix A.2 should be placed after the references.
Our Response:
In the revised manuscript, we have moved two appendices after the references.
- Pay attention to details such as Funding: “Please add” can be deleted.
Our Response:
In the revised manuscript, we have deleted the “Please add” in the Funding at p.18.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
- line 202, it is good to more expline the (two one-sided EWMA variance charts with measurement error) not how they find them.
- Suppose table 3 need some comment. The point need to more provide.
Comparisons with existing control charts would be Good. Good Luck.
Author Response
Thank you for reviewing our manuscript. We appreciate your careful and constructive comments about our earlier submission. In making this revision we have carefully addressed your concerns and incorporated your suggestions to improve the presentation of the manuscript.
In what follows, we reproduce your comments in boldface and then give our responses.
- line 202, it is good to more explain the (two one-sided EWMA variance charts with measurement error) not how they find them.
Our Response:
Thanks for this comment. In the revised manuscript, we have directly pointed out the difference between truly control limits and error-prone control limits (say, (6) and (14) or (7) and (15)). To ease your reading, here we have provided the following description that is placed in lines 212-215 marked in blue:
Compared with (6) and (14) or (7) and (15), the key difference is the involvement of the error-prone proportion. Since p0* is different from p0 due to measurement error (8), it is expected to see that two one-sided control limits (14) and (15) can be contaminated by measurement error, yielding unreliable detection.
- Suppose table 3 needs some comments. The point needs to more provide.
Our Response:
Thanks for this comment. In the initial manuscript, we have added some interpretations of Table 3. To address your concern, in the revised manuscript, we have provided descriptions of our numerical settings and relevant points. To ease your reading, we have provided the description in lines 254-265 below:
To assess the performance of corrected control charts, we mainly examine the setting pi1=pi2 =0.95, lamda=0.05, p0=0.1(0.05)0.45, and 0.5n=1,2,3,4,5,10,15,20 with the prespecified ARL0~370.4. Numerical results, including ,UCL5**,UCL6** , L5, L6, ARL0**^, MRL0**^, and SDRL0** , are summarized in Table 3.
Table 3 shows that p0=p0**, the values of L6 do not exist when 0.5n=1, 2, and the widths of the two control charts become narrower when p0 **or the sample size n increases. Compare with Tables 1 to 3, we find that the values of the error-corrected control limits ( UCL5** and LCL6* ) in Table 3 are much closer to the real control limits ( UCL1 and LCL2) in Table 1 than the control limits with measurement error ( UCL3* and LCL4* ). It is evident that the control limits of the error-corrected EWMA variance charts are reliable for monitoring process dispersion when measurement error exists in the process.
- Comparisons with existing control charts would be Good. Good Luck.
Our Response:
Thanks for your nice comment. However, to the best of our knowledge, few methods have been available to correct measurement error effects when constructing control charts. It is indeed an interesting issue and we can keep exploring alternative approaches and then compare them with our method in the near future. To make a clear comment, in the revised manuscript, we have inserted the following paragraph in Section 6:
As commented by a referee, it is interesting to compare with other existing methods to show the advantages of our proposed method. However, to the best of our knowledge, few methods have been available to correct measurement error effects when constructing control charts. We will keep exploring alternative approaches and then compare them with our method in the near future.
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors present a new method of constructing control charts. The method is based on discretisation i.e. introducing indicator random variables and a control process EWMA based on the binomial statistics. In this approach the quality variable may have any (not necessarilty gausian) distribution with finite variance and the control process is adjusted to the measurement error effect. In the paper the tables of signal lines are provided. The results are mathematically correct and supported by the real data analysis. It seems that the paper may be very useful in the applications in control of the industrial processes. The paper is well written and may be recommended for publication in the journal „Sustainability”.
Author Response
Thank you for reviewing our manuscript. We appreciate your careful and constructive comments about our earlier submission. In making this revision we have carefully addressed your concerns and incorporated your suggestions to improve the presentation of the manuscript.
In what follows, we reproduce your comments in boldface and then give our responses.
The authors present a new method of constructing control charts. The method is based on discretisation i.e. introducing indicator random variables and a control process EWMA based on the binomial statistics. In this approach the quality variable may have any (not necessarilty gausian) distribution with finite variance and the control process is adjusted to the measurement error effect. In the paper the tables of signal lines are provided. The results are mathematically correct and supported by the real data analysis. It seems that the paper may be very useful in the applications in control of the industrial processes. The paper is well written and may be recommended for publication in the journal „Sustainability”.
Our Response:
Thank you for your positive feedback on our manuscript. We also appreciate your careful review and useful comments on the current manuscript.
