ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence
To evaluate the surveillance performance of a control chart with the charting statistic of the sum of log likelihood ratios in the statistical process control (SPC), in this paper, we give the proof procedure based on Markov chains for the asymptotic estimation of the average run length (ARL) for th...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6649949 |
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| _version_ | 1849467026709413888 |
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| author | Yi Guo Lei Gao Yan Zhu |
| author_facet | Yi Guo Lei Gao Yan Zhu |
| author_sort | Yi Guo |
| collection | DOAJ |
| description | To evaluate the surveillance performance of a control chart with the charting statistic of the sum of log likelihood ratios in the statistical process control (SPC), in this paper, we give the proof procedure based on Markov chains for the asymptotic estimation of the average run length (ARL) for this kind of chart. The out-of-control ARL1 is approximately equal to 1 for any fixed in-control ARL0 with a negative control limit. By the equivalence between limit distribution of a sum and that of a suprema sum of Markov chain, we derive the estimation of ARL1 with a large enough positive control limit. Numerical experiments are conducted to confirm our results. |
| format | Article |
| id | doaj-art-ac53093a371f4e6181da1fce55d7faf9 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ac53093a371f4e6181da1fce55d7faf92025-08-20T03:39:14ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66499496649949ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov SequenceYi Guo0Lei Gao1Yan Zhu2Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, ChinaDepartment of Automation, Shanghai Jiao Tong University, Shanghai 200240, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaTo evaluate the surveillance performance of a control chart with the charting statistic of the sum of log likelihood ratios in the statistical process control (SPC), in this paper, we give the proof procedure based on Markov chains for the asymptotic estimation of the average run length (ARL) for this kind of chart. The out-of-control ARL1 is approximately equal to 1 for any fixed in-control ARL0 with a negative control limit. By the equivalence between limit distribution of a sum and that of a suprema sum of Markov chain, we derive the estimation of ARL1 with a large enough positive control limit. Numerical experiments are conducted to confirm our results.http://dx.doi.org/10.1155/2021/6649949 |
| spellingShingle | Yi Guo Lei Gao Yan Zhu ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence Journal of Mathematics |
| title | ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence |
| title_full | ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence |
| title_fullStr | ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence |
| title_full_unstemmed | ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence |
| title_short | ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence |
| title_sort | arl estimation of the control chart of log likelihood ratios sum for markov sequence |
| url | http://dx.doi.org/10.1155/2021/6649949 |
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