Statistical control of the mean in presence of interval-censored data
Occasionally, during the statistical process monitoring it is not possible to make measurements with precision on the observed units; therefore, it should be necessary to work with censored observations. Consequently, a direct application of the traditional Shewhart control charts...
| Main Authors: | , |
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2018
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| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/4668 |
| _version_ | 1801706336014041088 |
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| author | Conto López, Romario González Álvarez, Nelfi |
| author_facet | Conto López, Romario González Álvarez, Nelfi |
| author_sort | Conto López, Romario |
| collection | OJS |
| description | Occasionally, during the statistical process monitoring it is not possible to make measurements with precision on the observed units; therefore, it should be necessary to work with censored observations. Consequently, a direct application of the traditional Shewhart control charts would not be appropriate. Under these circumstances, it should be implemented control charts that include both the censoring involved and a suitable distribution for the resulting data. Under an inspection scheme, where no defective units are censored and a high censoring is presented on the stable state of the process, three control charts for X ̄ are proposed, in the case of monitoring interval-censored data. Each of them has a different way to impute the censored data. In the first one, each censored observation is replaced by its conditional expected value (CEV); in the second one, the censored data is replaced by the upper limit of the interval which the censored data belongs to, and in the third one, it is replaced by a random value of a uniform distribution within the censoring interval, considering a typical distribution and censoring type I. The power for detecting deviations from the mean for the proposed charts is compared by means of simulation with the Shewhart chart that ignores censoring. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-4668 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2018 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-46682022-06-15T17:04:47Z Statistical control of the mean in presence of interval-censored data Control Estadístico de la media con datos Censurados a intervalo Conto López, Romario González Álvarez, Nelfi Cartas de Control Censura Monitoreo de Procesos. Estadística Censoring, control charts, monitoring process Occasionally, during the statistical process monitoring it is not possible to make measurements with precision on the observed units; therefore, it should be necessary to work with censored observations. Consequently, a direct application of the traditional Shewhart control charts would not be appropriate. Under these circumstances, it should be implemented control charts that include both the censoring involved and a suitable distribution for the resulting data. Under an inspection scheme, where no defective units are censored and a high censoring is presented on the stable state of the process, three control charts for X ̄ are proposed, in the case of monitoring interval-censored data. Each of them has a different way to impute the censored data. In the first one, each censored observation is replaced by its conditional expected value (CEV); in the second one, the censored data is replaced by the upper limit of the interval which the censored data belongs to, and in the third one, it is replaced by a random value of a uniform distribution within the censoring interval, considering a typical distribution and censoring type I. The power for detecting deviations from the mean for the proposed charts is compared by means of simulation with the Shewhart chart that ignores censoring. En ocasiones, durante el monitoreo de procesos no es posible realizar mediciones exactas sobre las unidades observadas, por lo que se deberá trabajar con observaciones censuradas y, debido a esto, no sería apropiada una aplicación directa de las cartas de control tipo Shewhart tradicionales. Teniendo en cuenta esta situación, se debe recurrir a cartas de control que consideren el tipo de censura presente y una distribución adecuada para los datos. Para el caso de monitoreo sobre datos con censura a intervalo, bajo un esquema de inspección donde las unidades buenas son las que quedan censuradas y por ende se presenta alta censura en estado estable del proceso, se proponen tres cartas de control para X ̄ , donde en cada una se imputa la censura de manera diferente, asumiendo distribución normal para la variable cuya media se con- trola, y censura tipo I. En la primera carta, cada observación censurada se reemplaza por el valor esperado condicional (CEV), en la segunda, se remplaza por el valor del límite superior de censura, y en la tercera, se remplaza por un valor aleatorio de una uniforme dentro del intervalo de censura. Mediante simulación se estudia la potencia en la detección de desviaciones de la media para las cartas propuestas y se compara con la carta Shewhart tradicional que ignora la censura. Universidad Pedagógica y Tecnológica de Colombia 2018-03-05 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Control Estadístico de Procesos application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/4668 10.19053/01217488.v9.n1.2018.4668 Ciencia En Desarrollo; Vol. 9 No. 1 (2018): Vol 9, Núm. 1 (2018): Enero - Junio; 89-96 Ciencia en Desarrollo; Vol. 9 Núm. 1 (2018): Vol 9, Núm. 1 (2018): Enero - Junio; 89-96 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/4668/pdf Derechos de autor 2018 CIENCIA EN DESARROLLO |
| spellingShingle | Cartas de Control Censura Monitoreo de Procesos. Estadística Censoring, control charts, monitoring process Conto López, Romario González Álvarez, Nelfi Statistical control of the mean in presence of interval-censored data |
| title | Statistical control of the mean in presence of interval-censored data |
| title_alt | Control Estadístico de la media con datos Censurados a intervalo |
| title_full | Statistical control of the mean in presence of interval-censored data |
| title_fullStr | Statistical control of the mean in presence of interval-censored data |
| title_full_unstemmed | Statistical control of the mean in presence of interval-censored data |
| title_short | Statistical control of the mean in presence of interval-censored data |
| title_sort | statistical control of the mean in presence of interval censored data |
| topic | Cartas de Control Censura Monitoreo de Procesos. Estadística Censoring, control charts, monitoring process |
| topic_facet | Cartas de Control Censura Monitoreo de Procesos. Estadística Censoring, control charts, monitoring process |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/4668 |
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