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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.13672 |
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| _version_ | 1866908659680804864 |
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| author | Wu, Tung-Lung |
| author_facet | Wu, Tung-Lung |
| contents | Phase I distribution-free runs- and patterns-type control charts are proposed for monitoring the unknown target value (or location parameter) for both continuous and discrete individual observations. Our approach maintains the nominal in-control signal probability at a prescribed level by employing the finite Markov chain imbedding technique combined with random permutation and conditioning arguments. To elucidate the methodology, we examine two popular runs- and patterns-type statistics: the number of success runs and the scan statistic. Numerical results indicate that the performance of our proposed control charts is comparable to that of existing Phase I nonparametric control charts for individual observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase I Distribution-Free Control Charts for Individual Observations Using Runs and Patterns Wu, Tung-Lung Applications Phase I distribution-free runs- and patterns-type control charts are proposed for monitoring the unknown target value (or location parameter) for both continuous and discrete individual observations. Our approach maintains the nominal in-control signal probability at a prescribed level by employing the finite Markov chain imbedding technique combined with random permutation and conditioning arguments. To elucidate the methodology, we examine two popular runs- and patterns-type statistics: the number of success runs and the scan statistic. Numerical results indicate that the performance of our proposed control charts is comparable to that of existing Phase I nonparametric control charts for individual observations. |
| title | Phase I Distribution-Free Control Charts for Individual Observations Using Runs and Patterns |
| topic | Applications |
| url | https://arxiv.org/abs/2511.13672 |