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Desarrollo de = una metodología para el cálculo de la confiabilidad en una de las áreas de proc= eso de la empresa ensambladora de vehículos denominada Ciauto Cía. <= /a>Ltda.

 =

Development of a methodology for calculati= ng reliability in one of the process areas of the vehicle assembly company cal= led Ciauto Cía. Ltd.

 


1

Sergio Raúl Villacrés Parra

&nb= sp;

https://orcid.org/0000-0002-9497-9795

 

&nb= sp;

Escuela Superior Politécnica de Chimborazo (ESPO= CH)

sergio.villacres@espoch.edu.e= c

2

Mayte Anabel Zavala León

&nb= sp;

https://orcid.org/0009-0000-9750-7438<= o:p>

 

&nb= sp;

Escuela Superior Politécnica de Chimborazo (ESPO= CH)

mayt= e.zavala@espoch.edu.ec  =

3

Mayra Alexandra Viscaíno Cuzco=

&nb= sp;

https://orcid.org/0000-0003-4987-7797

 

&nb= sp;

Escuela Superior Politécnica de Chimborazo (ESPO= CH)

= ma.viscaino@uta.edu.ec=

 

 <= /o:p>

 <= /span>

 

 <= /span>

Artículo de Investigación Científica y Tecnológica

Enviado: 09/04/2024

Revisado: 06/05/2024

Aceptado: 10/06/2024

Publicado:16/08/2024

DOI: https://doi.org/10.33262/cienciadigital.v8i3.3119

 =

 

Cítese:

&nb= sp;

 <= /p>

Villacrés Parra, S. R., Zavala L= eón, M. A., & Viscaíno Cuzco, M. A. (2024). Desarrollo de una metodología = para el cálculo de la confiabilidad en una de las áreas de proceso de la empre= sa ensambladora de vehículos denominada Ciauto Cía. Ltda . Ciencia Digital, 8(3), 137-160.

&nb= sp;

 

&nb= sp;

 

https://cienciadig= ital.org

www.celibro.org.ec=

 

 

&nb= sp;

https://creativeco= mmons.org/licenses/by-nc-sa/4.0/deed.es

 

Palabras claves: Sistema reparable, modelo NHPP, Crow Amsaa, Log-lineal, confiabilidad.

 

Resumen

El análisis de confiabilidad de los sistemas críticos en el sector industrial es una herramienta de gran utilidad para mejorar la toma de decisiones en el departamento de mantenimiento. Generalmente, los métodos de análisis de confiabilidad tradicionales asumen restauraciones de los equipos a su condición original, pero en la práctica esto no sucede, pues generalmente= se realizan intervenciones para corregir únicamente la falla que se presenta= en ese momento; por este motivo, la presente investigación tuvo como objetiv= o el desarrollo de una metodología para conocer la confiabilidad actual de act= ivos reparables en donde se ejecutan reparaciones mínimas, y su predicción a 5 años, con el cálculo de la intensidad de fallas y el tiempo medio entre fallas. La muestra se seleccionó a partir de los registros del historial = de falla desde enero de 2022 a mayo de 2024 de la planta de soldadura de una ensambladora de vehículos, se realizó un diagrama Jack Knife para prioriz= ar al análisis de los sistemas que más paradas productivas por reparación ha= yan generado. Se realizó un test de tendencia para determinar el sesgo que ti= enen los datos históricos y así poder ajustarlos a procesos estocásticos no-homogéneos de Poisson, se utilizó el modelo Crow Amsaa y Log-lineal pa= ra seleccionar aquel que mejor se ajuste a los datos y sea capaz de generar pronósticos = con el menor error posible. Del estudio realizado, se determinó que los siste= mas que más paradas productivas han ocasionado son las soldadoras SP-43 y SP-= 16, y el JIG MB-10. Para el sistema SP-43, el modelo que generó el menor error para un pronóstico dentro de 5 años fue Crow Amsaa con una estimación de = 48 fallas y una falla cada 233 horas de trabajo, mientras que para los siste= mas SP-16 y JIG MB-10, el modelo log-lineal presentó el mejor ajuste, pronosticando 19 fallas, una falla cada 987 horas y 22 fallas, una cada 8= 22 horas de operación respectivamente.

<= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",= serif; mso-fareast-font-family:"Times New Roman";mso-font-kerning:0pt;mso-ligatu= res: none;mso-ansi-language:ES-EC'> 

 

Keywords:

Repairable system, NHPP model, Crow Amsaa, Log-linear, reliability.<= /b>

<= /span>

 

Abstr= act

The reliability analysis of critical systems in the industrial sector is a very useful tool to improve decision making in= the maintenance department. Generally, traditional reliability analysis metho= ds assume restorations of the equipment to its original condition, but in practice this does not happen, since interventions are generally carried = out to correct only the failure that occurs at that moment; For this reason, = the objective of this research was to develop a methodology to know the curre= nt reliability of repairable assets where minimal repairs are carried out, a= nd its prediction for 5 years, with the calculation of the intensity of fail= ures and the average time between failures. The sample was selected from the failure history records from January 2022 to May 2024 of the welding plan= t of a vehicle assembler, a Jack Knife diagram was made to prioritize the anal= ysis of the systems that cause the most productive stops per repair have generated. A trend test was carried out to determine the bias that the historical data have and thus be able to adjust them to non-homogeneous Poisson stochastic processes, the Crow Amsaa and Log-linear model was use= d to select the one that best fits the data and is capable of generating forec= asts with the lowest possible error. From the study carried out, it was determ= ined that the systems that have caused the most productive stops are the SP-43= and SP-16 welding machines, and the MB-10 JIG. For the SP-43 system, the model that generated the lowest error for a forecast within 5 years was Crow Am= saa with an estimate of 48 failures and one failure every 233 work hours, whi= le for the SP-16 and JIG MB systems -10, the log-linear model presented the = best fit, predicting 19 failures, one failure every 987 hours and 22 failures,= one every 822 hours of operation respectively.

 

 

=  

=  

Introducción

La evaluación de la confiabilidad desempe= ña un papel fundamental en la mejora de la disponibilidad y la productividad e= n la industria de ensamblaje automotriz, a través de la implementación de un mantenimiento planificado de la manera correcta (Soltanali et al., 2020). La importancia del desarrollo de una metodología para calcular la confiabilidad radica en que sirve para garantizar y mejorar el desempeño de= los sistemas, permite evaluar y predecir la probabilidad de que este funcione correctamente durante un período de tiempo dado, proporciona información út= il para la toma de decisiones en la gestión y planificación de mantenimiento y= es útil al momento de implementar estrategias efectivas que servirán como sopo= rte para futuros planes de mantenimiento de acuerdo a las condiciones actuales = de los equipos, optimizando el proceso productivo, aumentando la rentabilidad = y la seguridad de la planta. Por este motivo, la presente investigación no solo estudia el incremento esperado de fallas en sistemas reparables con reparaciones mínimas, sino que también busca resaltar la importancia de proponer estrategias de mantenimiento más efectivas y proactivas para mejor= ar la situación futura.

El análisis de confiabilidad es usado ampliamente en aplicaciones industriales (Hu et al., 2021) debido a que esta metodología permite determinar y conocer el comportamiento de falla y la posible estimación de un pronóstico del número= de eventos de falla, lo que conlleva a identificar cuáles son los equipos en l= os que se pueden presentar nuevos eventos de falla, así como su comportamiento operativo a largo plazo. El momento exacto en el que un equipo fallará no se puede determinar con certeza, no obstante, se puede usar el comportamiento = del histórico de fallas y la ayuda de la estadística para estimar la probabilid= ad de ocurrencia del evento (Gasca et al., 2017)<= /span>. La validez de los resultados obtenidos depende de la precisión y exactitud de los datos, aunque en varias ocasiones no existen suficientes d= atos de fallas y no se pueden obtener los intervalos de confianza para los índic= es de confiabilidad (Carlos R Batista-Rodríguez, 2017)<= /span>.

La confiabilidad, disponibilidad y mantenibilidad en la industria automotriz son un factor crucial, pues las empresas buscan que exista una producción eficiente y continuidad operativa para cumplir con las demandas del mercado, reducir los costos de operación y mantenimiento, y aumentar la competitividad de su organización (Echeverr, 2018), adoptando una cultura de mejora continua (Dias et al., 2019).

Los sistemas se dividen en no reparables y reparables. En donde, si un sistema es no reparable presenta una única fall= a a lo largo de su vida (Brown et al., 2023)<= /span>, mientras que en un sistema reparable existen varios modos de falla. Los modelos más destacado para el análisis de la confiabilidad de sistemas reparables sujetos a reparaciones mínimas, son los procesos no-homogéneos de Poisson (Slimacek & Lindqvist, 2017) y para dichos sistemas, el cálculo de la confiabilidad involucra el= análisis de los tiempos de operación y las tasas de fallas en ciclos de falla-reparación. 

El interés por controlar la confiabilidad, mantenibilidad y disponibilidad en las diferentes industrias surge debido a= la necesidad de garantizar operaciones eficientes y con el menor tiempo de inactividad. La confiabilidad es la probabilidad de que un elemento pueda desempeñar su función requerida durante un intervalo de tiempo establecido y bajo condiciones definidas; si no hay fallas, el equipo es totalmente confi= able; si la frecuencia de fallas es muy baja, la confiabilidad del equipo es aún aceptable; pero si la frecuencia de fallas es muy alta, el equipo es poco confiable, este análisis es de vital importancia cuando se requiere mantene= r la productividad. La mantenibilidad juega un papel fundamental ya que permite reparaciones rápidas y efectivas. Mientras que, la disponibilidad se refier= e a la capacidad de los equipos para estar en condiciones operativas en un determinado tiempo.

El enfoque de la presente investigación e= s el desarrollo de una metodología eficiente que sea capaz de mejorar la gestión= del mantenimiento y maximizar la confiabilidad de sus equipos, contribuyendo a = una mayor eficiencia operativa. En este estudio, se aplicó dos modelos no-homog= éneos de Poisson con distinta función de intensidad, el modelo Crow Amsaa y el mo= delo log-lineal para realizar la estimación o predicción del número de fallas en= un periodo de tiempo de 5 años, con el fin de que el área de mantenimiento de = la empresa tome decisiones en función de los resultados obtenidos respecto a la tasa de falla de los sistemas y a la reducción del tiempo medio entre falla= s; para el cálculo se analizarán las fallas de todos los sistemas de la planta= de soldadura de una ensambladora de vehículos según los datos obtenidos desde enero de 2= 022 a mayo de 2024.

Estado del arte:

En el ámbito de la industria automotriz, un tema de interés creciente es la me= jora de la productividad, debido a la necesidad de garantizar la eficiencia y reducir los costos de mantenimiento, por lo que se han adoptado metodologías para optimizar la confiabilidad, disponibilidad y mantenibilidad (Soltanali et al., 2019).

La confiabilidad operacional constituye la capacidad de un sistema para cumpli= r la función requerida, dentro de un cierto contexto operacional, durante un per= iodo específico de tiempo (Echeverr, 2018); en términos matemát= icos corresponde a la función inversa de la probabilidad de falla = (Cruz et al., 2017), y permite mejorar la disponibilidad de los equipos, lo que conlleva un incremento de beneficios económicos en la organización (Montalvo et al., 2022).

La investigación de Orrantia y otros, aborda el desarrollo de una metodología = para medir la confiabilidad en líneas de ensamble, dicha metodología consta de c= inco etapas que incluyen la identificación del área de estudio, la recolección de información relevante como la hora de inicio y fin de una parada, el motivo= y el problema ocurrido; la aplicación del modelo matemático donde las variables = calculadas: capacidad de entrega, índice de eficiencia, calidad y disponibilidad, son analizadas mediante distribuciones probabilísticas y es seleccionada la distribución de mejor ajuste, la cual posee el valor más pequeño del estadístico Anderson-Darling; el análisis de resultados, etapa en la que se considera los índices críticos que afectan la confiabilidad; y por último, = la propuesta de mejoras (Orrantia Daniel et al., 2022).

Según Zuo y Xiao, en el área de confiabilidad, las investigaciones pasadas suponí= an que el sistema analizado regresaba a su condición como cuando estaba nuevo, pero estas situaciones no son reales en la práctica, pues cuando el sistema= se encuentra en operación, todos los componentes son afectados por el efecto d= el envejecimiento (Zuo & Xiao, 2022). <= /span>

Para el análisis de confiabilidad, se identifican los sistemas no reparables y r= eparables, en donde se pueden realizar reparaciones mínimas, es decir actividades de m= antenimiento para reparar únicamente el componente defectuoso, y reparaciones perfectas,= en donde el sistema opera de manera tan efectiva como cuando estaba nuevo (Wu et al., 2024).

Mientras que, Mun y Kvam proponen el uso de modelos no homogéneos de Poisson (NHPP) = para la modelación de datos de fallas monótonas por reparaciones mínimas en un sistema reparable, en donde se restaura el rendimiento de este precisamente= a la misma condición en la que se encontraba antes de fallar, es decir aquel = que puede ser recuperado a su condición operativa sin reemplazar necesariamente todos los componentes del sistema después de la reparación. Estos modelos s= on usados extensamente por ser manejables y flexibles matemáticamente debido a= su capacidad para modelar una gran variedad de procesos de reparación reales <= /span>(Mun et al., 2021). El modelo NHPP se caracteriza por su función de intensidad. EL ROCOF o tasa de ocurrencia de fallas del NHPP es equivalente a la función de riesgo y las formas monótonas para calcularlo son el modelo log-lineal analizado por Cox y Lewis y el mod= elo de ley de potencia estudiado por Crow (Krivtsov, 2007)

Los modelos de intensidad proporcional basados en NHPP, son log-lineal y Crow A= msaa que es una extensión del modelo de ley de potencia, que se caracterizan por= ser capaces para modelar el comportamiento de un sistema en su etapa de vida út= il (Bacha & Bellaouar, 2023). <= /span>

En situaciones en las que se requiere obtener los valores más probables de una distribución se usa el método de máxima verosimilitud para estimar los parámetros de los modelos utilizando métodos numéricos como Newton-Raphson. Este enfoque permite justificar la selección del modelo que mejor se ajusta= a los datos (Chávez-Cadena et al., 2020), (Bacha & Bellaouar, 2023). <= /span>

Respecto al análisis del rendimiento de modelos NHPP, investigaciones con objetivos similares han usado el error cuadrático medio MSE, error absoluto medio MAE, error porcentual absoluto medio MAPE (Kim & Kim, 2016),(Chik et al., 2018)= , (Alsultan & Sulaiman, 2024)y el cálculo del coeficiente de correlación R= 2 (N. K. Srivastava & Mondal, 2014) para determinar el modelo de mejor ajuste a los datos.

Estos estudios establecen un precedente para futuras investigaciones y resaltan la importancia del cálculo de confiabilidad en la industria automotriz para bu= scar soluciones óptimas, obtener la máxima producción y lograr el éxito empresar= ial (Paez Advincula, 2022).

Existen metodologías de simulación que permiten predecir y conocer el comportamiento operativo de los equipos, lo que hace posible la estimación de un pronóstic= o de eventos de falla. En ocasiones se utilizan estimadores no paramétricos para= el cálculo de la confiabilidad, que son útiles cuando se tienen datos censurad= os, tamaños de muestra pequeños o distribuciones desconocidas ADDIN CSL_CITATION {"citationItems":[{"id":"ITEM-1"= ,"itemData":{"DOI":"10.18359/rcin.5682","= ;ISSN":"0124-8170","abstract":"Para la fiabilidad de sistemas uno de los objetivos principales es estimar la función de confiabilidad usando los estimadores de Kaplan-Meier y Nelson-Aa= len, bajo el enfoque no paramétrico. Cuando se recurren a técnicas computacional= es, la estrategia de Jackknife delete-I brinda ventajas por sus propiedades de consistencia para la estimación de la varianza. Sin embargo, se tiene incertidumbre sobre la posibilidad de mejorar las estimaciones cuando se aumenta el número (d) de observaciones que son suprimidas en el procedimien= to secuencial de Jackknife delete-d. Por otra parte, por sus propiedades asintóticas de estabilización de la varianza, las trans- formaciones log y log(-log) son usadas para encontrar intervalos de confianza (ic) para la función de confiabilidad. En este trabajo, se propone combinar simultáneame= nte las dos estrategias para encontrar los ic para la función de confiabilidad, proponiendo un nuevo procedimiento que no requiere de ajuste paramétrico en= el tiempo de ocurrencia del evento de interés. Además de mejorar la estimación= de la función de confiabilidad cuando los porcentajes de censura son altos y l= os tamaños de muestra pequeños. En la investigación se realiza una comparación= vía simulación con tamaños de muestras (10,25,50) y porcentajes de datos censur= ados (0%,15%,50%) para calcular las tasas de error (T.E) e índices de calidad (I= ), mejorando las estimaciones con porcentajes de censura altos (50%). Los resultados de este trabajo muestran que se puede mejorar la estimación por intervalo en escenarios complejos de censuras y tamaños de muestra a la literatura del análisis de datos en confiabilidad.","author":[{"dropping-particle":&qu= ot;","family":"Ramírez Montoya","given":"Javier","non-dropping-parti= cle":"","parse-names":false,"suffix":&qu= ot;"},{"dropping-particle":"","family":&= quot;Ramos Ramírez","given":"Edgar","non-dropping-partic= le":"","parse-names":false,"suffix":&quo= t;"},{"dropping-particle":"","family":&q= uot;Martínez Salazar","given":"José Luis","non-dropping-particle":"","parse-names= ":false,"suffix":""}],"container-title":= "Ciencia e Ingeniería Neogranadina","id":"ITEM-1","iss= ue":"1","issued":{"date-parts":[["2= 022"]]},"page":"71-82","title":"Est= imación de la función de confiabilidad usando remuestreo Jackknife y transformaciones","type":"article-journal","v= olume":"32"},"uris":["http://www.mendeley.com= /documents/?uuid=3Dc9859af7-68fb-4f2d-8a7d-bfe92ec8262b","http://= www.mendeley.com/documents/?uuid=3D4647ff5c-43d9-49c0-8122-70bbaa73e0d1&quo= t;]}],"mendeley":{"formattedCitation":"(Ramírez Montoya et al., 2022)","plainTextFormattedCitation":"(Ramírez Montoya et al., 2022)","previouslyFormattedCitation":"[24]"},= "properties":{"noteIndex":0},"schema":"h= ttps://github.com/citation-style-language/schema/raw/master/csl-citation.js= on"}(Ramírez Montoya et al., 2022).

Materiales y métodos:=

El desarrollo = de esta metodología consta de cinco etapas, y previo a su desarrollo, se obtuv= o los registros de fallas de una ensambladora de vehículos cuyas áreas productivas son: soldadura, pintura y ensamblaje; después de un análisis de la frecuenc= ia de fallas y tiempos de reparación, se seleccionó la planta de soldadura por= ser el área más crítica. La información recopilada, comprende los tiempos de reparación de enero de 2022 a mayo de 2024 de todos los sistemas de la plan= ta cuyo tiempo de operación son 2880h anuales y se evaluó los sistemas que oca= sionaron la mayor parte de paros de línea.

La etapa 1 consistió en la depuración de la base de datos de historial de mantenimiento de la planta de soldadura, en donde se eliminó registros duplicados, información inconsistente, modos de falla irrelevantes y errore= s de registro con el fin de garantizar la utilidad de los datos a analizar, este= fue un paso crucial pues la cantidad y calidad de información es de gran importancia para minimizar los errores. En esta etapa se realizó una revisi= ón y corrección minuciosa de errores en los registros de manera manual, los cual= es se analizaron individualmente.

En la etapa 2 se identificó el área de estudio, en donde se realizó un diagrama Jack Knife para priorizar el análisis de los sistemas agudo-críticos de la planta, priorizando a los que posean el mayor tiempo medio de reparación (MTTR), que se calculó desde la base del histórico de fallas.

La información fue organizada a nivel de sistema como se muestra en la Tabla 1= . en donde se capturó la fecha de inicio y fin de cada evento, el modo de falla,= el tiempo de reparación (TTR) en horas. Además, se calculó el tiempo hasta la falla (TTF) que proporciona información valiosa para realizar pronósticos a futuro en un cierto intervalo de tiempo dado.

En la etapa 3,= se realizó un estudio estadístico direccionado hacia equipos reparables, debido a que = su estado operativo puede ser restaurado con una reparación después de la ocurrencia de una falla, puede presentar más de un modo de falla durante su vida útil y la tasa de fallas varía a través del tiempo. Se realizó un anál= isis gráfico y analítico de la tendencia de los datos del sistema con el fin de detectar si los sistemas poseen una tendencia significativa de disminución = del tiempo entre fallas y pueden ser modelados con el proceso No-Homogéneo de Poisson, que es uno de los procesos estocásticos usados en ingeniería de confiabilidad por su capacidad para predecir el número de eventos que ocurr= en aleatoriamente en un tiempo t con tasa de eventos variable ADDIN CSL_CITATION {"citationItems":[{"id":"ITEM-1","itemDa= ta":{"DOI":"10.21833/ijaas.2023.05.002","ISSN= ":"23133724","abstract":"This study aims to compare the stochastic process model designed as a nonhomogen= eous Poisson process and α-series process, to obtain a better process for u= sing monotonous trend data. The α-series process is a stochastic process wi= th a monotone trend, while the NHPP is a general process of the ordinary Poisson process and it is used as a model for a series of events that occur randomly over a variable period of time. Data on the daily fault time of machines in Bahrri Thermal Station in Sudan was analyzed during the interval from first January 2021, to July 31, 2021, to acquire the best stochastic process model used to analyze monotone trend data. The results revealed that the NHPP mod= el could be the most suitable process model for the description of the daily f= ault time of machines in Bahrri Thermal Station according to lowest MSE, RMSE, B= ias, MPE, and highest. The current study concluded that through the NHPP, the fa= ult time of machines and repair rate occur in an inconsistent way. The further value of this study is that it compared NHPP and α-series to obtain a better process for using monotone trend data and prediction. Meanwhile, the other studies in this field focused on comparing methods of estimation parameters of the NHPP and the α-series process. The distinctive scientific addition of this study stems from displaying the precision of the NHPP better than the α-series process in the case of monotone trend data.","author":[{"dropping-particle":""= ,"family":"Alghamdi","given":"Safar M.A.","non-dropping-particle":"","parse-names= ":false,"suffix":""},{"dropping-particle"= ;:"","family":"Qurashi","given":&qu= ot;Mohammedelameen E.","non-dropping-particle":"","parse-names&q= uot;:false,"suffix":""}],"container-title":&q= uot;International Journal of Advanced and Applied Sciences","id":"ITEM-1","issue":"5&= quot;,"issued":{"date-parts":[["2023"]]},&quo= t;page":"12-19","title":"A comparison between the nonhomogeneous Poisson and α-series processes f= or estimating the machines’ fault time of thermal electricity","type":"article-journal","volume= ":"10"},"uris":["http://www.mendeley.com/docu= ments/?uuid=3De413a5ab-45b9-4238-a750-0c3133389a90","http://www.m= endeley.com/documents/?uuid=3D08fa74f6-ce3b-491c-a0ba-1653a987e962"]}]= ,"mendeley":{"formattedCitation":"(Alghamdi & Qurashi, 2023)","plainTextFormattedCitation":"(Alghamdi & Qurashi, 2023)","previouslyFormattedCitation":"[25]"},"= ;properties":{"noteIndex":0},"schema":"https:= //github.com/citation-style-language/schema/raw/master/csl-citation.json&qu= ot;}(Alghamdi & Qurashi, 2023). <= /span>

La etapa 4, co= nsta de la aplicación del modelo Crow Amsaa y Log-lineal, para el pronóstico del número acumulado de fallas en un tiempo acumulado de operación, así como el MTBF estimado para por próximos cinco años de operación del sistema.

En la etapa fi= nal, se evaluó la precisión de los modelos utilizados mediante el cálculo de err= ores de pronóstico, con el fin de elegir aquel que garantice predicciones confiables.

Diagrama Nelson Aalen:

En la Figura 1= . se observa de manera gráfica la tendencia de los datos de tiempo de falla y la degradación de la confiabilidad a lo largo del tiempo para un sistema repar= able que ha tenido intervenciones mínimas a lo largo de su vida útil.

Test de tendencia de Laplace

El test de Lap= lace, es una prueba monótona que permite verificar si los datos siguen un proceso estocástico (Alghamdi & Qurashi, 2023) y se utiliza ampliam= ente para identificar tendencias en grupos de datos, pues se considera la prueba= más apropiada para inferir si el conjunto de datos es de tipo NHPP (Hou et al., 2022).

El test de tendencia de Laplace cuando el sistema ha sido observado hasta  se representa mediante la ecuación (1).<= /span>

Donde, =  son los tiempos acumulados de falla,  es el tiempo de observación de las falla= s y n es el número de eventos ocurridos. 

Además, facilita reconocer el crecimiento o disminución de la confiabilidad, las hipótesis p= or comprobar son: Si U =3D 0 el proceso es estacionario, si U > 0 existe una tendencia creciente (sistema triste) y si U < 0 existe una tendencia decreciente (sistema feliz).

Modelo no-homogéneo de Poisson

Entre las teorías p= ara modelar la confiabilidad de sistemas reparables, se encuentra el proceso no-homogéneo de Poisson, que es robusto y dispone la ventaja de manejar dat= os discretos tales como, número o tasa de ocurrencia de fallas, por lo que, son aplicados al análisis de fallas y de vida útil de diversos sistemas de ingeniería (Hashimoto & Takizawa, 2021).

Modelo Crow-Amsaa: El modelo Crow AMSAA, también conocido como proceso de ley de potencia (PLP) es usado y estudiado para el análisis de crecimiento de la confiabilidad. (P. W. Srivastava & Jain, 2011)<= /span>

Al usar la estimación de máxima verosimilitud, los parámetros  y , se puede calcular con las ecuaciones (2) y (3)

<= /i>

Donde,  es el intervalo de tiempo acumulado para= cada falla, es el tiempo acumulado hasta la última falla y n es el total del registro de fallas.

Las hipótesis por comprobar son:

Si  deterioro de la confiabilidad=

Si  crecimiento de la confiabilidad

Si  tasa de falla es constante. <= /span>

El incremento o disminución de la confiabilidad puede ser cuantificado al observar aspectos como el MTBF o la tasa de fallo a través del tiempo (P. W. Srivastava & Jain, 2011).<= /span>

La función de inten= sidad de fallas <= !--[if gte msEquation 12]>λt=  está dada por la ecuación (4).

<= /i>

Donde,  es el parámetro de forma, que representa= la tendencia de la tasa de fallas respecto al tiempo y  es el parámetro de escala, que evidencia= la intensidad de fallas en el sistema.

Mientras que el cál= culo del tiempo medio entre fallas (MTBF), está definido por la ecuación (5)

 

 

Modelo Log-Lineal

El modelo log-lineal = es capaz de describir procesos con tendencia monótona durante el tiempo de funcionamiento


La tasa de fallas instantánea está dada por la ecuación (6).<= /b>

Donde,  es el parámetro de escala,  es el parámetro de crecimiento que deter= mina la mejora o deterioro del sistema a lo largo del tiempo y t es el tiempo de operación (Hashimoto & Takizawa, 2021).

Los parámetros  y  están dados por las ecuaciones (7) y (8)= .

El cálculo del núme= ro esperado de fallas está definido por la ecuación (9).

En cambio, el número esperado de fallas durante la vida útil se obtiene con la ecuación (10)

<= ![if !msEquation]>

El MTBF se calcula = con la ecuación (11).

<= ![if !msEquation]>

Medición del error = de los modelos

Existen criter= ios para la selección del modelo que se ajuste mejor a los datos. El criterio m= ás significativo es el criterio de determinación y criterios de calidad de aju= ste como el sesgo, error cuadrático medio (MSE), error medio absoluto (MAE), y = el error porcentual absoluto medio (MAPE), además se realizó la medida del coeficiente de determinación R2 (Alghamdi & Qurashi, 2023). A continuación, se encuentran las expresiones para medir cada error.<= /p>

Coeficiente de determinación

El valor R es capaz= de medir el ajuste exitoso del modelo, desde la varianza de los datos evaluado= s (Kim & Kim, 2016).=

<= ![if !msEquation]>

Donde,  son los valores observados de la variable dependiente,  son las predicciones del modelo y  es la media de los valores observados. <= o:p>

El modelo con el  mayor y cercano a 1, se considera el mod= elo más eficiente (Kim & Kim, 2016).=

Error cuadrático medio (MSE)

<= ![if !msEquation]>

Donde,  es el número total de datos observados, =  son los valores observados,  son los valores pronosticados por el mod= elo para cada observación y k es el número de parámetros estimados en el modelo= .

Error medio absoluto (MAE)

<= ![if !msEquation]>

Donde,  es el número total de datos observados, =  son los valores observados,  son los valores pronosticados por el mod= elo.

Error porcentual absoluto medio (MAPE)

Para realizar una comparación de los modelos y determinar cuál es el mejor, se usa también el error porcentual absoluto medio (MAPE), según la siguiente fórmula:

Donde m(t) representa el valor real,  el valor estimado y= n el número de observaciones (Alsultan & Sulaiman, 2024).<= /span>

En la etapa final, se evaluó la capacidad predictiva de cada modelo y se seleccionó el que muestr= e la menor tasa de error posible.

Resultados y discusió= n:

En el presente estudio, se analizaron modelos predictivos para analizar sistemas reparable= s en una planta de soldadura de una ensambladora de vehículos, con el objetivo de evaluar la confiabilidad mediante la predicción del número acumulado de fal= las y el tiempo medio entre fallas (MTBF).

En este aparta= do, se presentan los resultados obtenidos una vez finalizadas las cinco etapas de = la investigación.

En la Figura 1. se muestra un gráfico de dispersión logarítmica, denominado diagrama Jack Knife, usado como método de priorización el cual permite identificar los sistemas que más paros de línea han ocasionado en la planta= de soldadura, es decir los que más han afectado a la productividad de la empre= sa según los registros de 2022 a 2024.

Se logró clasificar los sistemas en diferentes categorías: agudo crítico, crít= ico, agudo, y leve. El resultado de este método de priorización determinó que los sistemas SP-01, SP-09 y SP-24, forman parte de una zona leve; DF01, JIG 02 y SP-04 son considerados agudos; JIG G01 se encuentra en la zona crítica; mientras que los sistemas SP-43, SP-16 y JIG MB-10 requieren de mayor atenc= ión por parte del departamento de mantenimiento, al ser considerados agudo-críticos= por ocasionar mayores interrupciones y ocurrir con mayor frecuencia respecto a = los demás sistemas de la planta.

Figura  <= /b>1

Diagrama Jack Knife - Método de priorización

 

Una vez identificados los sistemas agudo-críticos, se procedió al análisis de los d= atos y se calculó los tiempos hasta la falla.

Tabla = 1

Tiempos de reparación de la soldadora SP-43

SOLDADORA SP-43=

FECHA INICIO

FECHA FIN

MODO DE FALLA

TTR<= /span>

TTF<= /span>

1

04/01/2022 11:48

04/01/2022 12:02

Falla eléctrica de pistola<= /span>

0,23

2

03/08/2022 11:46

03/08/2022 12:52

Cable de balancín SP43B roto

1,10

= 5064,83

3

27/10/2022 8:35

27/10/2022 8:55

Puntas de pistola desalineadas

0,33

= 2036,05

4

09/12/2022 14:55

09/12/2022 16:47

Falla eléctrica de pistola<= /span>

1,87

= 1039,87

5

10/04/2023 8:22

10/04/2023 9:30

Falla eléctrica de pistola<= /span>

1,13

= 2920,72

6

12/05/2023 9:45

12/05/2023 10:00

Cable de balancín roto

0,25

= 768,50

7

22/06/2023 12:00

22/06/2023 13:30

Espiral de soldadora roto

1,50

= 987,50

8

04/08/2023 12:35

04/08/2023 12:45

Cable secundario roto

0,17

= 1031,25

9

07/09/2023 7:55

07/09/2023 8:07

Cable primario roto<= /p>

0,20

= 811,37

 

Tab= la 2

Tiempo= s de reparación de la soldadora SP-16

SOLDADORA SP-16<= /p>

FECHA INICIO

FECHA FIN

MODO DE FALLA

TTR

TTF

1

31/10/2022 11:45

31/10/2022 12:20

Falla eléctrica de pistola

0,58

 

2

17/01/2023 12:57

17/01/2023 13:11

Falla eléctrica de pistola

0,23

1872,85

3

27/03/2023 9:20

27/03/2023 10:00

Cable de balancín roto

0,67

1652,82

4

09/08/2023 8:27

09/08/2023 8:40

Falla eléctrica de pistola

0,22

3238,66

5

05/09/2023 10:15

05/09/2023 12:15

Falla eléctrica de pistola

2,00

651,58

6

13/10/2023 8:45

13/10/2023 9:00

Cable secundario roto

0,25

908,75

7

15/01/2024 9:55

15/01/2024 13:15

Falla eléctrica de pistola

3,33

2260,25

8

29/05/2024 11:05

29/05/2024 11:25

Cable de balancín roto

0,33

3238,17

 

Tab= la 3

Tiempo= s de reparación de equipo de sujeción MB-10

EQUIPO DE SUJECIÓN MB-10

FECHA INICIO

FECHA FIN

MODO DE FALLA

TTR

TTF

1

18/01/2022 7:50

18/01/2022 8:30

Pin roto

0,67

 

2

28/02/2022 10:35

28/02/2022 10:45

Pin roto

3,22

989,30

3

28/03/2022 8:43

28/03/2022 8:50

Pin roto

0,12

667,03

4

22/07/2022 11:25

22/07/2022 11:45

Kit de pistón roto

0,33

2786,92

5

25/07/2022 14:16

25/07/2022 14:30

Sensor doble señal desregulado

0,23

74,75

6

17/10/2022 7:45

17/10/2022 7:52

Pin roto

0,12

2009,37

7

25/01/2023 9:00

25/01/2023 9:15

Manguera de control rota

0,25

2401,38

8

14/03/2023 10:15

14/03/2023 10:47

Sensor inductivo desregulado

0,53

1153,53

 

En la Figura 2. se presenta el análisis de supervivencia denominado, diagrama Nelson-Aalen, usado como método gráfico para la visualización de la acumula= ción de tiempos hasta la falla en un intervalo de tiempo. Se observa una tendenc= ia creciente por lo que se asume que la tasa de falla aumenta con el tiempo y = que son sistemas inestables.

Figura  <= /b>2

Diagrama Nelson-Aalen

 

 

 

 

 

 

Para verificar la hipótesis de que los datos de falla satisfacen las característ= icas que posee un NHPP, y verificar si es idóneo, se realizó un test estadístico denominado test de Laplace usando la ecuación (1), con un nivel de significancia de 0,10.

Tabla 4

Test de tenden= cia

SISTEMA

ESTADÍSTICO U

SP-43

2,16

SP-16

0,37

JIG MB-10

0,24

 

Todos los valores obtenidos son U>0, por lo que se acepta la hipótesis de la existencia de una tendencia crecien= te y se asume que se trata de un sistema triste.

Se estimó los parámetros de los modelos estudiados con las ecuaciones obtenidas con el método de máxima verosimilit= ud, ecuación (2) y (3) para el modelo Crow Amsaa y (7) y (8) para los parámetros del modelo log-lineal. Para este último modelo se usó el método numérico de Newton-Raphson con la ayuda de la biblioteca scipy en Python.

Tab= la 5

Estima= ción de parámetros de los modelos

MODELO

PARÁMETROS

SP-43

SP-16

JIG MB-10

Crow Amsaa

=

2,611

1,278<= /span>

1,110<= /span>

=

1,05 x 10-10

3,05 x 10-5<= /sup>

2,51 x 10-4<= /sup>

Log-lineal

=

-9,373

-7,842=

-7,435=

=

0,0002056

3,54 x 10-5<= /sup>

3,13 x 10-5<= /sup>

Una vez calculados los parámetros de los modelos, se los utilizó para la estima= ción o pronóstico del número de fallas esperado en un periodo de operación t para sistemas reparables, en los cuales se realiza la reparación mínima requerida para poner al equipo en operación nuevamente. El número de fallas pronostic= adas para los próximos 5 años con los dos modelos estudiados se muestra en la ta= bla 3.

Tab= la 6

Número estimado de fallas en 5 años

Número esperado de fa= llas

Tiempo acumulado de operación (h)

SP-43

SP-16

JIG MB-10<= /span>

Modelo Crow Amsaa

Modelo Log-lineal

Modelo Crow Amsaa

Modelo Log-lineal

Modelo Crow Amsaa

Modelo Log-lineal

17545,56

13<= /span>

8

9

9

9

9

20425,56

19<= /span>

13<= /span>

11<= /span>

11<= /span>

12<= /span>

12<= /span>

23305,56

27<= /span>

23<= /span>

13<= /span>

13<= /span>

14<= /span>

15<= /span>

26185,56

36<= /span>

41<= /span>

15<= /span>

16<= /span>

16<= /span>

18<= /span>

29065,56

48<= /span>

74<= /span>

17<= /span>

19<= /span>

19<= /span>

22<= /span>

 

Las Figuras 3, 4 y 5 corresponden a las gráficas del número acumulado de fallas= en un tiempo acumulado de operación de los sistemas SP-43, SP-16 y JIG MB-10 respectivamente. Los primeros puntos comprenden las fallas acumuladas conoc= idas y tomadas de la base de datos del histórico de mantenimiento, mientras que = los siguientes forman parte de una zona de pronóstico y son valores aleatorios creados a partir de la información previa recopilada. Para dichas gráficas,= se presenta los pronósticos del modelo Crow Amsaa en el lado izquierdo (a) y d= el modelo log-lineal en el lado derecho (b).

Figura  3

Número de fallas proyectadas (SP-43)

b)      Modelo Log-lineal

a)       Modelo Crow Amsaa

 

 


Figura  4

Número de fallas proyectadas (SP-16)

b)      Modelo Log-lineal

a)       Modelo Crow Amsaa

 

 

 

 

 

 

 


Figura  5

b)      Modelo Log-lineal

a)       Modelo Crow Amsaa

Número de fallas proyectadas (= JIG MB-10)

 

Para el sistema SP-43, el modelo de Cr= ow Amsaa pronosticó 13 fallas en el primer año a partir de la última observaci= ón, 19, 27, 36 y 48 para el año dos, tres, cuatro y cinco respectivamente, mientras= que el modelo log-lineal 8, 12, 22, 40 y 73 fallas. Para SP-16, el modelo Crow Amsaa estimó 9, 11, 13, 15 y 17 fallas para los próximos 5 años de operació= n; mientras que el modelo log-lineal 8, 11, 13, 16 y 19 fallas. Para el JIG MB= -10, el modelo Crow Amsaa, proyectó 9, 12, 14, 16 y 19 fallas para los siguiente= s 5 años; por otro lado, el modelo log-lineal 9, 12, 15, 18 y 21 fallas. <= /o:p>

Este incremento pronosticado refleja l= a degradación de los sistemas analizados en su conjunto debido a que únicamente se hacen reparaciones mínimas que pueden acumularse a lo largo del tiempo y generar fallas con mayor frecuencia.

Para el análisis de confiabilidad, se calculó el tiempo medio entre fallas  (MTBF), con el fin de conocer el intervalo en horas que puede transcurrir para que ocurra una falla, conocer este tiempo es significativo porque es un indicador del rendimiento esperado del equipo ADDIN CSL_CITATION {"citationItems":[{"id":"ITEM-1","itemDa= ta":{"DOI":"10.1016/B978-0-444-64241-7.50220-2",&q= uot;ISBN":"9780444642417","ISSN":"15707946&qu= ot;,"abstract":"This paper addresses the application of reliability analysis which has been wide= ly accepted as an important tool in the strategy of maintenance management of systems. Reliability analysis of two online analyzers (A1 and A2) at a petrochemical company was carried out. The purpose of this work is to apply parametric and nonparametric methods to evaluate the reliability of two repairable systems and to estimate important parameters to maintenance management, such as mean time between failures (MTBF) and failure rate. The= two sets of failure events underwent statistical tests in order to understand t= heir behaviors and then their processes were modeled. It was observed that A1 presents a non-renewal process, better represented by the non-homogenous Poisson process (NHPP), while A2 is a renovation process consistent with the homogenous Poisson process (HPP). The study of A1 was complemented by the simulation the system's age at future times of consecutive repairs, and A2’s study returned parameters such as MTBF and failure rate. It is expected that the results contribute to the adequacy of the planned maintenance, and that= the presented tools continue to be applied, benefiting the organization mainten= ance management.","author":[{"dropping-particle":"= ","family":"Abreu","given":"Monique N.G.","non-dropping-particle":"de","parse-nam= es":false,"suffix":""},{"dropping-particle&qu= ot;:"","family":"Esquerre","given":= "Karla Patricia S.O.R.","non-dropping-particle":"","= parse-names":false,"suffix":""},{"dropping-pa= rticle":"","family":"Massa","given&= quot;:"Ana Rosa C.de G.","non-dropping-particle":"","par= se-names":false,"suffix":""},{"dropping-parti= cle":"","family":"Pessoa","given&qu= ot;:"Robson W.S.","non-dropping-particle":"","parse-names= ":false,"suffix":""}],"container-title":= "Computer Aided Chemical Engineering","id":"ITEM-1","issue":"= ;2004","issued":{"date-parts":[["2018"]]= },"number-of-pages":"1351-1356","publisher":&= quot;Elsevier Masson SAS","title":"Reliability analysis associated wi= th maintenance of online analyzers","type":"book","volume":"= 44"},"uris":["http://www.mendeley.com/documents/?uuid= =3D7184030d-d63f-4468-94af-f2b1020fa76b","http://www.mendeley.com= /documents/?uuid=3Dbf95300c-8eee-4aa6-843f-b54df386ede8"]}],"mend= eley":{"formattedCitation":"(de Abreu et al., 2018)","plainTextFormattedCitation":"(de Abreu et al., 2018)","previouslyFormattedCitation":"[29]"},"= ;properties":{"noteIndex":0},"schema":"https:= //github.com/citation-style-language/schema/raw/master/csl-citation.json&qu= ot;}(de Abreu et al., 2018).

 

 

 

 

 

Figura 6

Tiempo medio entre fallas proyectadas para los próximos 5 años

b)      Modelo Log-lineal

a)       Modelo Crow Amsaa

 

 

Figura 7

Tiempo medio entre fallas proyectadas para los próximos 5 años

 

 

 

 

 

 

b)      Modelo Log-lineal

a)       Modelo Crow Amsaa

 

 

 

 

 

 

Figura 8

Tiempo medio entre fallas proyectadas para los próximos 5 años

 

 

 

 

 

 

b)      Modelo Log-lineal

a)       Modelo Crow Amsaa

 

Las Figuras 6, 7 y 8 muestran las gráficas del MTBF en función del tiempo de los sistemas SP-43, SP-16 y JIG MB-10 respectivamente, modelo Crow Amsaa (derec= ha) y modelo log-lineal (izquierda). En estas gráficas se observa una notable reducción de los tiempos entre fallas, por lo que se deben plantear estrate= gias de mantenimiento efectivas para optimizar el funcionamiento con el paso del tiempo.

La calidad de las estimaciones calculadas debe ser validada e incurrir en el m= enor error posible. Se realizó la medición del error para cuantificar la diferen= cia entre los valores predichos y los valores reales. =

El desempeño de los modelos NHPP implementados se evaluó a través de la medida= del coeficiente de determinación R2, error cuadrático medio (MSE), e= rror medio absoluto (MAE), y el error porcentual absoluto medio (MAPE) para garantizar la precisión del modelo que se plantea en el estudio. Los result= ados se muestran en la tabla 7.

Tab= la 7

Medici= ón de errores de los modelos

 

SP-43<= /span>

SP-16<= /span>

JIG MB-10

 

MODELO=

MODELO=

MODELO=

CRITERIOS=

Crow-AMSAA

Log-Lineal

Crow-AMSAA

Log-Lineal

Crow-AMSAA

Log-Lineal

= =

0,931<= /span>

0,080<= /span>

0,843<= /span>

0,895<= /span>

0,889<= /span>

0,918<= /span>

MSE

0,359<= /span>

4,827<= /span>

0,628<= /span>

0,304<= /span>

0,445<= /span>

0,238<= /span>

MAE

0,455<= /span>

1,099<= /span>

0,661<= /span>

0,479<= /span>

0,519<= /span>

0,458<= /span>

MAPE<= /span>

19,11 %

24,24 %

22,26 %

16,22 %

21,35 %

19,79 %

Para la selección del mejor modelo se tomó como criterio principal el valor del error obtenido; el modelo Crow-Amsaa presentó todos los errores evaluados c= on el menor valor. Además, se determinó un valor del coeficiente de determinac= ión R2 igual a 0,932, es decir que el 93,2 % de la variabilidad en la variable dependiente, es explicado por el modelo predictivo, por lo que se asume que se trata de un modelo cuyas estimaciones se ajustan adecuadamente= a los datos observados del sistema SP-43.

En el caso del sistema SP-16 y JIG MB-10 el modelo de mejor ajuste fue log-lin= eal según la observación de los errores y el coeficiente R2 de 0,895= y 0,918 respectivamente.

Conclusiones

·&nb= sp;        En este estudio, se ha explorado dos modelos fundamentales para la evaluación = de la confiabilidad de sistemas reparables: Crow-AMSAA y el modelo Log-lineal,= los cuales ofrecen herramientas poderosas para analizar y predecir la tasa de fallas, y el tiempo medio entre fallas (MTBF), parámetros esenciales para la efectiva gestión de activos y la planificación del mantenimiento.

·&nb= sp;        La evaluación comparativa realizada, ha demostrado la capacidad que tienen amb= os modelos para pronosticar de manera efectiva el número de fallas y estimar el MTBF. La precisión de estas predicciones se determinó utilizando métricas estándar como el Error Cuadrático Medio (MSE), el Error Absoluto Medio (MAE= ) y el Error Porcentual Absoluto Medio (MAPE), proporcionando una medida cuantitativa que permita observar el mejor ajuste del modelo con relación a= los datos observados, con el fin de seleccionarlo y aplicarlo correctamente. Se= gún la medición de errores se determinó que para el sistema SP-43, el modelo Cr= ow Amsaa tiene mayor capacidad de pronóstico, mientras que para los sistemas S= P-16 y JIG MB10 el modelo log-lineal presenta un mejor ajuste; dichos modelos pu= eden ser usados para monitorear y mejorar la confiabilidad, y optimizar la gesti= ón de mantenimiento de la planta.

·&nb= sp;        Según el análisis, se observa que la tasa de reparación de los sistemas aumenta c= on el tiempo, y existe una disminución de los intervalos de tiempo medio entre fallas (MTBF), lo que indica un deterioro de la confiabilidad de estos, por= lo que es necesario plantear estrategias de mantenimiento que permitan aumenta= r el tiempo medio entre fallas, reducir las paradas productivas, y tener una evaluación continua de fallas para la planificación, programación y ejecuci= ón de tareas de mantenimiento.

Conflicto de intereses

Los autor= es declaran que no existe conflicto de intereses en relación con el artículo presentado= .

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El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Ciencia Digital.

 


 

 

 

El artículo queda en propiedad de la revista y, por tanto, su publicaci= ón parcial y/o total en otro medio tiene que ser autorizado por el director de= la Revista Ciencia Digital.

 

 

 

 

 


 

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ISSN: 2602-8= 085

Vol. 8 No. 3, p= p. 137 – 160, julio – septiembre 2024

 

 

                 Ciencia & Genética                  Página 137