A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes
In this work, a control chart with multiple runs rules is proposed and studied in the case of monitoring inflated processes. Usually, Shewhart-type control charts for attributes do not have a lower control limit, especially when the in-control process mean level is very low, such as in the case of p...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/22/4671 |
| _version_ | 1797458539917082624 |
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| author | Eftychia Mamzeridou Athanasios C. Rakitzis |
| author_facet | Eftychia Mamzeridou Athanasios C. Rakitzis |
| author_sort | Eftychia Mamzeridou |
| collection | DOAJ |
| description | In this work, a control chart with multiple runs rules is proposed and studied in the case of monitoring inflated processes. Usually, Shewhart-type control charts for attributes do not have a lower control limit, especially when the in-control process mean level is very low, such as in the case of processes with a low number of defects per inspected unit. Therefore, it is not possible to detect a decrease in the process mean level. A common solution to this problem is to apply a runs rule on the lower side of the chart. Motivated by this approach, we suggest a Shewhart-type chart, supplemented with two runs rules; one is used for detecting decreases in process mean level, and the other is used for improving the chart’s sensitivity in the detection of small and moderate increasing shifts in the process mean level. Using the Markov chain method, we examine the performance of various schemes in terms of the average run length and the expected average run length. Two illustrative examples for the use of the proposed schemes in practice are also discussed. The numerical results show that the considered schemes can detect efficiently various shifts in process parameters in either direction. |
| first_indexed | 2024-03-09T16:38:36Z |
| format | Article |
| id | doaj.art-d022292e06ab4167b6467cfd1cd683a8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:38:36Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d022292e06ab4167b6467cfd1cd683a82023-11-24T14:54:25ZengMDPI AGMathematics2227-73902023-11-011122467110.3390/math11224671A Combined Runs Rules Scheme for Monitoring General Inflated Poisson ProcessesEftychia Mamzeridou0Athanasios C. Rakitzis1Department of Statistics & Actuarial-Financial Mathematics, University of the Aegean, 83200 Samos, GreeceDepartment of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, GreeceIn this work, a control chart with multiple runs rules is proposed and studied in the case of monitoring inflated processes. Usually, Shewhart-type control charts for attributes do not have a lower control limit, especially when the in-control process mean level is very low, such as in the case of processes with a low number of defects per inspected unit. Therefore, it is not possible to detect a decrease in the process mean level. A common solution to this problem is to apply a runs rule on the lower side of the chart. Motivated by this approach, we suggest a Shewhart-type chart, supplemented with two runs rules; one is used for detecting decreases in process mean level, and the other is used for improving the chart’s sensitivity in the detection of small and moderate increasing shifts in the process mean level. Using the Markov chain method, we examine the performance of various schemes in terms of the average run length and the expected average run length. Two illustrative examples for the use of the proposed schemes in practice are also discussed. The numerical results show that the considered schemes can detect efficiently various shifts in process parameters in either direction.https://www.mdpi.com/2227-7390/11/22/4671attributes control chartaverage run length count dataexpected average run lengthinflated Poisson distributionstatistical process monitoring |
| spellingShingle | Eftychia Mamzeridou Athanasios C. Rakitzis A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes Mathematics attributes control chart average run length count data expected average run length inflated Poisson distribution statistical process monitoring |
| title | A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes |
| title_full | A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes |
| title_fullStr | A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes |
| title_full_unstemmed | A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes |
| title_short | A Combined Runs Rules Scheme for Monitoring General Inflated Poisson Processes |
| title_sort | combined runs rules scheme for monitoring general inflated poisson processes |
| topic | attributes control chart average run length count data expected average run length inflated Poisson distribution statistical process monitoring |
| url | https://www.mdpi.com/2227-7390/11/22/4671 |
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