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Propuesta= de modelo matemático del rendimiento de mano de obra en porcelanato en pisos. = Caso de estudio: ciudad de Cuenca<= /span>

&nbs= p;

Proposal for a mathematical model of labor perform= ance in porcelain floors. Study case: Cuenca city

= 1=

Jorge Fabián Lucero Bonilla

https://orcid.org/0009-0001-6891-8606

 

 <= /span>

Maestría en Construcción con mención en Administración de la construcción, Univers= idad Católica de Cuenca, Cuenca, Ecuador.

jorge.lucero.01@est.ucacue.edu= .ec=

= 2=

Carlos Julio Calle Castro

https://orcid.org/0000-0002-6891-0030  

 

 <= /span>

 Maestría en Construcción con Mención en Administración de la Construcción Sustentable, Universidad Católica de Cuenca, Cuenca, Ecuador.

cjcallec@ucacue.edu.ec=

= 3=

Nayra Mendoza Enríquez

https:= //orcid.org/0000-0002-6673-2306 

 <= /span>

Cotutor de la maestría en Construcción con Mención en Administración de la Construcción Sustentable, Universidad Católica de Cuenca, Cuenca, Ecuador= .

nayra.= mendoza@ug.edu.ec=

 

 

 

 =

 

 

Artículo de Investigación Científica y Tecnológica

Enviado: 15/01/2024=

Revisado: 18/02/2024

Aceptado: 04/03/2024

Publicado:05/04/2024

DOI: https:/= /doi.org/10.33262/concienciadigital.v7i2.2969  =           =  

 

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Cítese= : <= /b>

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Lucero Bonilla, J. F., Calle Castro, C. J., & Mendoza Enríquez , N. (2024). Propuesta de modelo matemático del rendimiento de mano de obra en porcelanato en pisos. Caso = de estudio: ciudad de Cuenca. ConcienciaDigital, 7(2), 6-27. https://doi.org/10.33262/concienciadigital.v7i2.2969

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CONCIENCIA DIGITAL, es una revista multidisciplinar= , trimestral, que se publicará en soporte electrónico tiene como misión contribu= ir a la   formación de profesionales competentes con visión humaníst= ica y crítica que sean capaces de exponer sus resultados investigativos y científicos en la misma medida que se promueva mediante su intervención cambios positivos en la sociedad. https://concienc= iadigital.org  

La revista es editada por la Editorial Ciencia Digital (Editorial de prestigio registrada en la Cámara Ecuatoriana de Libro con = No de Afiliación 663) www.celibro.org.ec

 

 

<= /p>

 

Esta revista está protegida ba= jo una licencia Creative Commons AttributionNonCommercialNoDerivatives 4.0 International. Copia de la licencia: http://creativecommons.org/licenses/by-n= c-nd/4.0/

 

Palabr= as claves: Rendimiento, Mano de obra, Modelo matemático, Regresión lineal, Porcelanato

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Resumen

Introducción.  = El rendimiento de mano de obra en la actividad de colocación de porcelanato = en piso es clave para una eficiente planificación de proyectos constructivos. Sin embargo, aún hoy, la planificación de este rendimiento no se realiza = de manera técnica y se asume la linealidad en los resultados, sin considerar= la variabilidad de este rendimiento en función de factores externos e intern= os de los obreros. Objetivo.  Proponer un modelo matemático para predecir el rendimiento de la mano de obra en la instalación de porcelanato en pisos en la ciudad de Cuenca, específicamen= te en la parroquia Machángara. Metodología.  Se realizó una revisión de la literatura relacionada con los factores que influyen en el rendimiento de los obreros en esta actividad.= A partir de esta información, se diseñó una ficha de observación que incluy= ó 6 variables y 35 indicadores relevantes. Se aplicó una metodología descript= iva de tipo correlacional con enfoque cuantitativo, recolectando datos de una muestra de 5 edificaciones en fase de colocación de porcelanato. Resul= tados. Los resultados, analizados estadísticamente, revelaron una eficacia del 9= 8% del modelo propuesto en relación con el rendimiento real de los trabajado= res. Además, se evidenció que, en Machángara, los rendimientos de los obreros = se sitúan por debajo del estándar teórico proporcionado por el GAD de Cuenca= . Conclusión.  Se concluye que los modelos matem= áticos basados en los factores estudiados son capaces de predecir con precisión = el rendimiento de los obreros, lo que puede mejorar las predicciones y tiemp= os de ejecución de los gestores de obra.

 

 

Keywords:

Yield, Labor, Mathematical model, Linear regression, Porcelain tile, Porcelain tiles<= /p>

 

Abstract<= /p>

Introduction.  The labor performance in the activity of porcela= in tile floor tile installation is key for an efficient planning of construc= tion projects. However, even today, the planning of this performance is not carried out in a technical way and linearity is assumed in the results, without considering the variability of this performance as a function of external and internal factors of the workers. Objective.  To propose a mathematical model to predict the labor performance in the installation of porcelain tile floor= s in the city of Cuenca, specifically in the Machángara parish. Methodology= .  A review of the literature relate= d to the factors that influence the performance of workers in this activity was carried out. Based on this information, an observation sheet was designed that included 6 variables and 35 relevant indicators. A descriptive methodology of a correlational type with a quantitative approach was appl= ied, collecting data from a sample of 5 buildings in the porcelain tile installation phase. Results.  The results, analyzed statistically, revealed an efficiency of 98% of the proposed model in relation to the actual performance of the workers. In addition, it was evidenced that, in Machángara, the workers' performance = is below the theoretical standard provided by the GAD of Cuenca. Conclusi= on.  It is concluded that the mathemat= ical models based on the factors studied are capable of accurately predicting = the performance of the workers, which can improve the predictions and executi= on times of the site managers.

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 =

 =

Introducción

A La industria de la construcción en Ecuador juega= un papel importante en la economía del país, pues es un sector intensivo en ma= no de obra que atrae inversión extranjera directa y tiene un impacto significa= tivo en los sectores de suministro de insumos y las instituciones financieras (Velástegui et al., 2022). En el futuro se prevé un aumento de la actividad constructora en este país, pero con un nuevo énfasis, que estará en la eficiencia, asegurando que los proyectos se ejecuten de la manera más óptima posible, esto significa maximizar la producción y minimizar el desperdicio = de recursos como tiempo, dinero, mano de obra y materiales (Díaz et al., 2022)= . En el sector de la construcción, Ecuador continúa enfrentando diversos desafío= s en organización, educación, gobierno y cultura que dificultan la implementació= n de enfoques eficientes, particularmente en términos de desempeño de la fuerza laboral, también conocido como Rendimiento de Mano de Obra o RMO (Fajardo y Quizhpe, 2021).

El RMO, se refiere al trabajo realizado por los trabajadores dentro de un período de tiempo específico, teniendo en cuenta = los recursos utilizados, incluidos el tiempo, el esfuerzo y los materiales y es= ta medida es la base para la gestión de la construcción, ya que proporciona una forma de evaluar la efectividad y productividad de las actividades laborale= s en el lugar de trabajo (Manoharan et al., 2022). Comprender el desempeño labor= al es un pilar para los gerentes de construcción y contratistas, ya que les permite planificar, asignar recursos y presupuestar de forma eficaz, al mis= mo tiempo, admite la optimización de los procesos de trabajo e identificar áre= as de mejora, pueden tomar decisiones informadas para mejorar la eficiencia y = la rentabilidad (Assaad et al., 2022).

A pesar de las ventajas anterior mencionado, la industria de la construcción en Ecuador se enfrenta constantemente a dificultades relacionadas con un bajo RMO de sus trabajadores. Este problema surge de una combinación de factores multifacéticos que incluyen el ambiente laboral, las condiciones y modalidades contractuales, consideraciones económicas, aspectos culturales, ambientales, entre otros (Santisteban y Si= lva, 2022). Estos elementos influyen en la capacidad del obrero para desempeñar = sus tareas dentro del tiempo estipulado y dado que, la eficiencia del sistema productivo en la industria de la construcción está estrechamente ligada a s= us recursos humanos, la falta de acciones o medidas relacionadas con el entorno laboral del trabajador para garantizar un rendimiento óptimo, representa un obstáculo significativo para alcanzar los objetivos del proyecto (Momade et al., 2023).

En la industria de la construcción, existe una e= strategia común que se utiliza para pronosticar el desempeño esperado de un trabajador durante un proyecto. Esta estrategia se puede considerar como un RMO teóric= o, que mide la cantidad de trabajo (m2) que se espera que realice dentro de un período de tiempo específico, generalmente por horas o por días, siguiendo = los protocolos establecidos. Este valor teórico está determinado por organizaciones, sindicatos u organismos gubernamentales de cada país que se basan en el historial de desempeño de cada actividad de construcción dispon= ible en su base de datos y en la experiencia de los profesionales en el campo (H= amza et al., 2022). Sin embargo, existen discrepancias entre la ejecución real de las obras y la información documentada en los expedientes técnicos, esto se debe a que el RMO real puede verse influenciada por varios factores específ= icos del proyecto, que pueden afectar la continuidad del rendimiento y dificulte= la estimación inicial proporcionada por los directores de la obra (Aguilar et = al., 2013; Van et al., 2021).

Una de las actividades constructivas mayormente afectadas por esta falta de continuidad en el RMO es la colocación de porcelanato, pues, si bien hay un estándar de rendimiento ecuatoriano determinado por la Industria Prefabricado de Hormigón ANDENCE que es de 30m2/día, la realidad es que, en muchas ocasiones no se logra obtener este rendimiento (Fajardo y Quizhpe, 2021). El porcelanato es un revestimiento p= ara pisos y paredes, de bajo espesor (8 a 12mm), con extraordinarias presentaci= ones técnicas y variadas posibilidades decorativas, es una masa muy compacta con excelentes propiedades mecánicas y químicas, se cataloga como la evolución = de los cerámicos esmaltados, pero más resistente, mucho más durable y con poca absorción, Se puede instalar en cualquier lugar, tanto interior como exteri= or (Herrera et al., 2023). La colocación de porcelanato implica una serie de procesos, = que van desde la preparación de la superficie hasta el sellado de las juntas, utilizando adhesivos específicos. Cada paso requiere precisión y eficiencia= , y cualquier perturbación, tanto interna como externa, puede afectar el rendimiento final. Por lo tanto, la actividad demanda una coordinación meticulosa y una gestión cuidadosa para garantizar resultados óptimos (Alve= s et al., 2023).

Una estrategia común que se emplea a menudo en el campo ecuatoriano para lograr resultados favorables en la instalación de porcelanato, es la supervisión constante brindada por la persona a cargo. E= sto asegura que se siguen minuciosamente los procedimientos de preparación y fabricación de los materiales, de acuerdo con su lugar de origen. Además, normalmente se designa a un inspector con el poder de rechazar materiales de mala calidad o detener el proyecto si se considera necesario. Sin embargo, = supervisar esta actividad es sólo un aspecto a considerar. Actualmente, existen factor= es adicionales que pueden impactar el desempeño de los trabajadores, los cuale= s no son comúnmente utilizados en el ámbito profesional y organizacional para garantizar un desempeño óptimo (Guzmán, 2012; Salgado, 2016).

Un experto del sector que profundiza en los fact= ores que impactan en el desempeño laboral es Luis Fernando Botero a través de su trabajo, "Análisis del desempeño y consumo de mano de obra en las actividades de construcción", que proporciona información valiosa en e= sta área. El autor destaca la presencia de 7 factores que conviene tener en cue= nta. El primer factor a considerar es el estado general de la economía, esto inc= luye factores como la disponibilidad de trabajadores calificados, supervisores experimentados y materiales esenciales necesarios para el proyecto de construcción. Otro factor importante a considerar son los aspectos laborale= s, que abarcan diversos elementos como condiciones laborales, horarios, descan= sos, incentivos y más. El tercero son los factores climáticos como la temperatur= a, las condiciones del suelo y la posibilidad de trabajar a cubierto, que pued= en afectar el desempeño de los trabajadores.

El cuarto factor tiene que ver con la actividad = en sí, incluidas sus características únicas, como la complejidad, los tiempos = de ejecución, los recursos disponibles y el entorno de trabajo general. Aquí h= ay un resumen del equipo necesario para hacer bien el trabajo: las herramienta= s y el equipo adecuados, mantenerlos en buenas condiciones, mantenimiento regul= ar, garantizar un suministro oportuno y usar equipo de protección personal para priorizar la seguridad. La supervisión desempeña un papel crucial para garantizar que las actividades de construcción se lleven a cabo con la máxi= ma eficiencia y eficacia. Implica contar con supervisores experimentados que posean las habilidades necesarias para guiar y controlar el proceso. Finalmente, las condiciones del trabajador son factores cruciales que impac= tan directamente en su desempeño en el trabajo. Estas condiciones abarcan aspec= tos como la formación, la experiencia, la motivación y las condiciones laborales (Botero, 2021).

Basándonos en lo expuesto en este apartado, el objetivo de esta investigación es proponer un modelo matemático que facilit= e la predicción del rendimiento de la mano de obra en la actividad de colocación= de porcelanato en pisos en la ciudad de Cuenca, Ecuador, específicamente en la parroquia Machángara. Esta propuesta tiene como finalidad proporcionar a los gestores de obras de este sector una herramienta para planificar los tiempo= s de ejecución de sus proyectos en función del rendimiento de mano de obra esper= ado, considerando los diversos factores relacionados con la actividad de instala= ción de porcelanato.

En la primera etapa de la investigación, se identifican los factores que pueden influir en el RMO en la actividad de colocación de porcelanato, basándose en la revisión bibliográfica. Luego, se elabora una ficha de observación, la cual se aplica en diversas obras en Machángara para evaluar estos factores junto con el rendimiento real de los obreros. Posteriormente, los datos recopilados se analizan utilizando un programa estadístico para determinar la influencia de estos factores en el = rendimiento de los trabajadores y así desarrollar el modelo matemático.

En la segunda etapa, se aplica el modelo matemát= ico en un conjunto de 5 obras en Machángara para comparar el rendimiento promed= io calculado con el rendimiento real de los trabajadores. Además, se emplea el rendimiento teórico o estándar proporcionado por el Gobierno Autónomo Descentralizado (GAD) municipal de la ciudad de Cuenca para verificar posib= les variaciones en comparación con el estándar utilizado en la ciudad.<= /span>

Metodología

El enfoque metodológico de este estudio se centra = en un análisis correlacional-descriptivo. Su objetivo es examinar cómo una variedad de factores, tanto internos como externos, pueden afectar el rendimiento de los obreros durante la colocación de porcelanato, un proceso= con una secuencia definida que incluye la limpieza del área de trabajo, la aplicación de aditivos ligantes, la preparación del mortero, el asentamient= o de las piezas de porcelanato, la nivelación y el uso de separadores o crucetas= . A través de esta metodología, se buscó describir los resultados significativo= s de estas relaciones para identificar los factores más influyentes en esta actividad.

El universo de investigación comprendió las obras = de construcción de 1 y 2 pisos registradas en el GAD de Cuenca en el momento de llevar a cabo este estudio. La población objetivo se limitó a las obras en ejecución en la parroquia Machángara. Dado que la mayoría de estas obras ya habían completado la fase de colocación de porcelanato en pisos al momento = de la recopilación de datos, se optó por realizar un muestreo no probabilístic= o, específicamente un muestreo por conveniencia. Esto implicó seleccionar 5 edificaciones que estaban en la etapa de colocación de porcelanato durante = el período de recolección de datos, representando así la muestra para el estud= io. A continuación, se mencionan las características de las obras y las cuadril= las que se usaron en la investigación.

 

 

Tabla 1

Variables independien= tes e indicadores

Edificación

Tipo

Cuadrilla

Obreros

Estructura ocupacional

Sueldo por día da cada maestro

E1

Dos pisos

Cuadrilla 1 (C1)

3 maestros

C2

35 dólares

2 oficiales <= /span>

E2

22 dólares

Cuadrilla 2 (C2)

3 maestros

C2

35 dólares

2 oficiales

E2

22 dólares

E2

Dos pisos

Cuadrilla 1 (C1)

3 maestros

C2

35 dólares

2 oficiales

E2

22 dólares

Cuadrilla 2 (C2)

3 maestros

C2

35 dólares

2 oficiales

E2

22 dólares

E3

Dos pisos

Cuadrilla 1 (C1)

3 maestros

C2

35 dólares

2 oficiales

E2

22 dólares

Cuadrilla 2 (C2)

3 maestros

C2

35 dólares

2 oficiales

E2

22 dólares

E4

Un piso

Cuadrilla 1 (C1)

3 maestros

C2

35 dólares

2 oficiales

E2

22 dólares

E5

Un piso

Cuadrilla 1 (C1)

2 maestros

C2

35 dólares

2 oficiales

E2

22 dólares

Para la recolección de los datos de los 39 obreros en las 5 obras mencionadas con anterioridad, se utilizó una ficha de observación que fue implementada en campo por el investigador. Esta ficha, se basó en las variables independientes e indicad= ores propuestos por Botero (2002), quien define el rendimiento como una conjunci= ón multidimensional de condiciones: climáticas, actividad, equipamiento, supervisión y condiciones propias del trabajador. Estos factores, en su conjunto, pueden potenciar o reducir el rendimiento de un obrero, dependien= do de la naturaleza de sus tareas y del entorno laboral durante la recolección= de datos. Las variables e indicadores se muestran en la tabla 2.

Tabla 2

Variables independien= tes e indicadores

Variable

Dimensiones<= o:p>

Indicadores = y su equivalencia numérica

1=

2=

3=

4=

5=

Clima

Tiempo<= /o:p>

Tormenta

Aguacero

Llovizna

Nublado=

Despejado

Temperatura<= o:p>

Muy Caluroso/MuyFrio

 <= /o:p>

Caluroso/Fri= o

 <= /o:p>

Fresco<= /o:p>

Suelo

Pantanero

Charcos=

Piso húmedo<= o:p>

Piso seco

Piso duro

Cubierta

Sol

 <= /o:p>

Normal<= /o:p>

 <= /o:p>

Sombra<= /o:p>

 <= /o:p>

Dificultad

Difícil=

 <= /o:p>

Normal<= /o:p>

 <= /o:p>

Fácil

Peligro=

Peligrosa

Riesgosa

Normal<= /o:p>

Moderado

Ningún pelig= ro

Interrupcion= es

≥ 1 ho= ra

15≥60 = min

5≥15 m= in

0≥5 mi= n

Ninguna=

 

Tabla 2

Variables independientes e indicadores (continuación)

Variable

Dimensiones<= o:p>

Indicadores = y su equivalencia numérica

1=

2=

3=

4=

5=

Actividad

Orden y aseo=

Difícil acce= so

Escombro

Transitable<= o:p>

Poca sucidad=

Aseo total y orden

Actividades precedentes

Repetir=

Mucho resane=

Poco resane<= o:p>

Aceptable

Perfecta

Tipicidad

De 1 a 5

De 5 a 10

De 10 a 15

De 15 a 20

Más de 20

Tajo (Espaci= o de trabajo)

Muy estrecho=

Estrecho

Normal<= /o:p>

Amplio<= /o:p>

Muy amplio

Equipamiento=

Herramienta<= o:p>

Inadecuada

 <= /o:p>

Adecuada

 <= /o:p>

Especial

Equipo<= /o:p>

Inadecuada

 <= /o:p>

Adecuada

 <= /o:p>

Especial

Mantenimient= o

Nulo

 <= /o:p>

Aceptable

 <= /o:p>

Bueno

Suministro

Nunca

 <= /o:p>

A veces=

 <= /o:p>

Siempre=

Elemento de protección

Ninguno=

 <= /o:p>

Casi todos

 <= /o:p>

Todos

Supervisión<= o:p>

Dirección (criterios de aceptación)

Ninguno=

Informales

Verbales

Verbales pre= vios

Bajo escrito=

Instrucción<= o:p>

Ninguna=

 <= /o:p>

Verbal - requerida

 <= /o:p>

Documento requerido

Seguimiento<= o:p>

Sin revisión=

 <= /o:p>

Revisión eventual

 <= /o:p>

Siempre=

Supervisor (Maestro)

Malo

 <= /o:p>

Regular=

 <= /o:p>

Bueno

Aseguraiento= de Calidad

No existe

Esfuerzos aislados

Inventoría

En proceso

Certificado = ISO

Trabajador

Situación personal

Neurótico

Triste<= /o:p>

Normal<= /o:p>

Buena

Excelente

Ritmo de tra= bajo

Lento

 <= /o:p>

Normal<= /o:p>

 <= /o:p>

Rápido<= /o:p>

Salud

Enfermo=

 <= /o:p>

Normal<= /o:p>

 <= /o:p>

Excelente

Habilidad

Inexperto

 <= /o:p>

Hábil

 <= /o:p>

Experto=

Capacitación=

Ninguna=

Aprendiz

Requerida

Experto=

Certificado<= o:p>

Laborales

Contrato

Administraci= ón

 <= /o:p>

 <= /o:p>

 <= /o:p>

Subcontratac= ión

Sindicato

Si

 <= /o:p>

 <= /o:p>

 <= /o:p>

No

Incentivos

No

 <= /o:p>

 <= /o:p>

 <= /o:p>

Si

Salario=

SMLV

=

 <= /o:p>

=

 <= /o:p>

=

 <= /o:p>

≥SMLV<= o:p>

Nota. Esta tabla fue adapt= ada de Botero (2002). <= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se= rif; mso-ansi-language:ES-EC'>Elaborado por: Autores

Como se puede observar en la tabla 2, la operacionalización de las variables propuestas por Botero es cualitativa. S= in embargo, en esta investigación, el análisis de la información es cuantitati= vo. Por lo tanto, los indicadores han sido traducidos de términos cualitativos a números. Un ejemplo de este proceso se presenta en la tabla 3, donde los indicadores de la dimensión "Tiempo" han sido reemplazados por números del 1 al 5. En esta escala, el valor 1 representa la condición menos favorable, mientras que el valor 5 representa la condición más favorable de= la dimensión.

 

 

Tabla 3

Variables independien= tes e indicadores

= Variable

= Dimensión

= Indicadores<= /o:p>

= Transposición de = términos

Clima<= /span>

Tiempo=

Tormenta

1

Aguacero

2

Llovizna

3

Nublado

4

Despejado

5

A continuación, en la tabla 4, se muestran los datos recolectados de los 39 obreros de las 5 obras analizadas, expresados sus indicadores de manera numérica en función de la tabla 2, asimismo se añade el rendimiento real obtenido al final del día.  Es te rendimiento se calculó al dividir la cantidad de m2 totales de porcelanato colocados en una jornada de 8 horas.  Un ejemplo de esto es el rendimiento del obrero 1 (O1) que es un maestro albañil que coloco un total 1.6 m2 de porcelanato al final del día, este valor se dividió para la jornada de 8 ho= ras y dio un rendimiento total de 0.2 m2/hora. Este mismo procedimie= nto se siguió para los demás obreros.

Tabla 4

Ficha de recolección de datos

Edificación

Cuadrilla

Obrero

Tiempo

Temperatura

Suelo

Cubierta

Dificultad

Peligro

Continuidad

Orden y aseo

Base de trabajo

Tipicidad

Tajo

Herramienta

Equipo

Mantenimiento

Suministro

Elemento de protección

Dirección

Instrucción

Seguimiento

Calif. Maestro

Aserg. Calidad

Sit. Personal

Cansancio

Habilidad

Conocimiento

Capacitación

Rendimiento real (m2/hora)

E1

C1

O1

4

2

4

4

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.2<= /span>

O2

3

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.18=

O3

4

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.2<= /span>

O4

3

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.18=

O5

4

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.2<= /span>

C2

O6

3

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.18=

O7

4

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.2<= /span>

O8

3

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.18=

O9

4

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.2<= /span>

O10

3

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.18=

E2

C1

O11

4

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.2<= /span>

O12

3

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.18=

O13

4

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.2<= /span>

O14

3

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.18=

O15

4

2

4

5

3

3

3

3

5

5

5

3

3

2

3

1

3

2

2

3

2

4

3

4

3

2

0.2<= /span>

Tabla 4

Ficha de recolección de datos (continuación)

Edificación

Cuadrilla

Obrero=

Tiempo=

Temperatura

Suelo<= span lang=3DES style=3D'font-size:6.0pt;mso-bidi-font-size:10.0pt;font-family:= "Times New Roman",serif; mso-fareast-font-family:"Times New Roman";color:black;mso-fareast-languag= e: ES-EC'>

Cubierta

Dificultad

Peligro

Continuidad

Orden y aseo

Base de trabajo

Tipicidad

Tajo

Herramienta

Equipo=

Mantenimiento

Suministro

Elemento de protección

Dirección

Instrucción

Seguimiento

Calif. Maestro

Aserg. Calidad

Sit. Personal

Cansancio

Habilidad

Conocimiento

Capacitación

Rendimiento real (m2/hora)

C2

O16

4

3

3

4

3

2

4

4

4

4

4

3

3

3

4

2

3

3

3

4

3

3

3

3

3

3

0.13=

O17

3

3

3

4

3

2

4

4

4

4

4

3

3

3

4

2

3

3

3

4

3

3

3

3

3

3

0.13=

O18

4

3

3

4

3

2

4

4

4

4

4

3

3

3

4

2

3

3

3

4

3

3

3

3

3

3

0.13=

O19

3

3

3

4

3

2

4

4

4

4

4

3

3

3

4

2

3

3

3

4

3

3

3

3

3

3

0.13=

O20

4

3

3

4

3

2

4

4

4

4

4

3

3

3

4

2

3

3

3

4

3

3

3

3

3

3

0.13=

E3

C1

O21

3

3

3

4

3

2

4

4

4

4

4

3

3

3

4

2

3

3

3

4

3

3

3

3

3

3

0.13=

O22

4

3

3

4

3

2

4

4

4

4

4

3

3

3

4

2

3

3

3

4

3

3

3

3

3

3

0.13=

O23

4

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.22=

O24

3

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.21=

O25

4

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.22=

C2

O26

3

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.21=

O27

4

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.22=

O28

3

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.21=

O29

4

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.22=

O30

3

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.21=

E4

C1

O31

4

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.22=

O32

3

3

3

5

4

4

3

3

5

5

5

4

4

3

4

3

4

4

4

4

4

3

3

4

4

3

0.21=

O33

4

3

4

4

4

3

3

3

5

5

5

4

4

3

4

2

3

3

3

4

3

3

4

4

3

3

0.18=

O34

3

3

4

4

4

3

3

3

5

5

5

4

4

3

4

2

3

3

3

4

3

3

4

4

3

3

0.16=

O35

4

3

4

4

4

3

3

3

5

5

5

4

4

3

4

2

3

3

3

4

3

3

4

4

3

3

0.18=

E5

C1 

O36

3

3

4

4

4

3

3

3

5

5

5

4

4

3

4

2

3

3

3

4

3

3

4

4

3

3

0.16=

O37

4

3

4

4

4

3

3

3

5

5

5

4

4

3

4

2

3

3

3

4

3

3

4

4

3

3

0.18=

O38

3

3

4

4

4

3

3

3

5

5

5

4

4

3

4

2

3

3

3

4

3

3

4

4

3

3

0.16=

O39

4

3

4

4

4

3

3

3

5

5

5

4

4

3

4

2

3

3

3

4

3

3

4

4

3

3

0.18=

Los datos fueron sometidos a pruebas de normalidad para evaluar su distribución y determinar la técnica de tratamiento estadístico más adecuada. En este caso= , el programa estadístico utiliza una prueba llamada Shapiro-Wilk para evaluar la distribución y homogeneidad de los datos. Calcula el P-Value, que tiene un umbral estandarizado de 0,05 y un criterio definido. Cualquier número por encima de este umbral indica una distribución normal, mientras que un número inferior sugiere que los datos no cumplen con los supuestos de normalidad.<= o:p>

Se reali= zó el análisis de Kruskal-Wallis para evaluar la presencia de una asociación significativa entre conjuntos de datos categóricos. Este análisis implica el cálculo del valor de chi-cuadrado (χ²). Dentro de este contexto particular, los grados de libertad (gl) significan la cantidad de variables independientes que pueden modificarse sin afectar las restricciones predeterminadas del análisis. El nivel de significancia (p) es un umbral preestablecido que se utiliza para determinar si los hallazgos de un estudio son estadísticamente significativos o podrían atribuirse al azar.

Después = del análisis, se emplea una regresión lineal, utilizando medidas de ajuste como= el coeficiente de correlación lineal (R) y el coeficiente de determinación (R²= ). Estas medidas representan la intensidad y la fracción de variabilidad aclar= ada por el modelo, respectivamente. Además, se emplean métricas como el Criteri= o de información de Akaike (AIC), el Criterio de información bayesiano (BIC) y la raíz del error cuadrático medio (RMSE) para evaluar la calidad del modelo. Estas métricas se minimizan para determinar la idoneidad y la capacidad predictiva del modelo para los datos analizados y continuar con el cálculo = de los coeficientes del modelo.

Al calcu= lar los coeficientes del modelo, se disciernen elementos cruciales, incluido el valor del estimador, que indica la relación entre las variables independien= tes y dependientes. El coeficiente EE mide la precisión de esta estimación, mie= ntras que el coeficiente t evalúa si este número se desvía significativamente de cero. El coeficiente p proporciona una medida de la probabilidad de encontr= ar esta correlación si no existe una asociación verdadera entre las variables.=

Una vez obtenidos los coeficientes se procede a derivar la fórmula general del mode= lo matemático mediante regresión lineal. La fórmula del modelo de regresión li= neal se compone de la variable de interés (y) como la variable dependiente, y múltiples variables independientes (X1, X2,...,Xn). El término independiente (b0) indica el valor esperado de y cuando todas las variables independientes son cero. Los coeficientes (b1, b2,...,bn) miden el cambio en y por cada ca= mbio unitario en las respectivas variables independientes, manteniendo constantes las demás. Cada coeficiente brinda información sobre la influencia específi= ca de la variable independiente correspondiente en la variable dependiente y se presenta a continuación:

Resultados 

El análisis estadístico realizado mediante la prueba de Shapiro-Wilk arrojó resultados significativos, con un valor de p inferior a 0,001 para t= odas las variables evaluadas. Los resultados demuestran inequívocamente que los datos recopilados, relacionados con las diferentes circunstancias de trabaj= o y parámetros de rendimiento en el contexto de la colocación de porcelanato, se desvían de una distribución normal.

Debido a la distribución no normal de los datos, se realizó un análi= sis de Kruskal-Wallis. Este análisis reveló disparidades sustanciales en el rendimiento en toda la actividad de colocación de porcelana en las distintas circunstancias de trabajo probadas. La prueba revela un resultado estadísti= co altamente significativo (p < 0,001) para todas las variables examinadas. Esto implica que al menos una de las circunstancias laborales evaluadas tie= ne una influencia sustancial en el desempeño de los trabajadores.

Como se observa en la tabla 5 las condiciones laborales como Tiempo, Temperatura, Suelo, Cubierta, Dificultad, Peligro, Continuidad, Orden y Ase= o, Base de Trabajo, Tipicidad, Tajo, Herramienta, Equipo, Mantenimiento, Suministro, Elemento de Protección, Dirección, Instrucción, Seguimiento, Ca= lif. Maestro, Aserg. Calidad, Sit. Personal, Cansancio, Habilidad, Conocimiento y Capacitación, todas muestran una variación significativa en su influencia e= n el rendimiento de los obreros en la colocación de porcelanato.

Tabla 5

Variables independientes e indicadores

Variable

χ²

p

Tiempo

21.3

< .001

Temperatura

27.5

< .001

Suelo

38.0

< .001

Cubierta

23.9

< .001

Dificultad

27.9

< .001

Peligro

38.0

< .001

Continuidad

38.0

< .001

Orden y aseo

38.0

< .001

Base de trabajo

38.0

< .001

Tipicidad

38.0

< .001

Tajo

38.0

< .001

Herramienta

27.9

< .001

Equipo

27.9

< .001

Mantenimiento

27.5

< .001

Suministro

27.5

< .001

Elemento de protección

33.3

< .001

Dirección

38.0

< .001

Instrucción

33.3

< .001

Tabla 5

Variables independientes e indicadores (continuación)

Variable

χ²

p

Seguimiento

33.3

< .001

Calif. Maestro

27.5

< .001

Aserg. Calidad

33.3

< .001

Sit. Personal

27.5

< .001

Cansancio

21.2

< .001

Habilidad

38.0

< .001

Conocimiento

38.0

< .001

Capacitación

27.5

< .001

Fuente: elaboración propia

Luego del análisis Kruskal-Wallis se procedió con la construcción del modelo matemático, a través de una regresión lineal múltiple de un factor (rendimiento) en la cual, se pudo identificar, mediante las medidas de ajus= te del modelo que únicamente 5 factores que son: tiempo, temperatura, suelo, cubierta y dificultad pueden ser utilizados en el modelo, esto, debido a que las demás variables presentan un problema de singularidad o confusión en el modelo de regresión lineal. Este fenómeno sugiere una posible relación line= al o redundancia entre algunas variables predictoras, dificultando al modelo est= imar con precisión los efectos de dichas variables sobre la variable dependiente, por lo cual, se descartaron.

Luego de realizar los ajustes necesarios, se construyó el modelo matemático utilizando los 5 factores especificados. Posteriormente se reali= zó una prueba de las medidas de ajuste del modelo. Los datos presentados en la tabla 6 demuestran claramente una correlación sólida (R =3D 0,992) entre las variables, lo que sugiere un vínculo confiable y significativo. El alto coeficiente de determinación ajustado (R² =3D 0,981) sugiere que alrededor = del 98,1% de las fluctuaciones en la variable dependiente pueden explicarse por= las variables independientes, lo que indica un fuerte ajuste del modelo. Los criterios AIC y BIC exhiben valores negativos muy cercanos a cero (-310 y -= 298 respectivamente), lo que indica un ajuste robusto del modelo. Además, las predicciones del modelo demuestran una precisión significativa, como lo demuestra el bajo valor del error cuadrático medio (RMSE =3D 0,00380).=

 

 

 

Tabla 6

Medidas de ajuste del modelo<= /i>

Modelo

R

R² corregida

AIC=

BIC=

RMSE

1

0.992

0.981

-310

-298

0.00380

Después = de verificar minuciosamente la exactitud y confiabilidad de los números utilizados, se procede a calcular los coeficientes del modelo. La Tabla 7 demuestra que el tiempo, la temperatura y el suelo poseen estimadores notab= les (p <0,001), lo que sugiere un impacto sustancial en el rendimiento. Está claro que existe una correlación positiva entre el tiempo (Estimador =3D 0,= 01371) y el rendimiento, lo que indica que las condiciones climáticas del tiempo favorables dan como resultado un aumento en el rendimiento.

Por el contrario, existe una correlación negativa entre la temperatura (Estimador = =3D -0,11182) y el suelo (Estimador =3D -0,04769) con el rendimiento, lo que in= dica que un aumento en la temperatura o el tipo de suelo está relacionado con una caída en la producción. Sin embargo, la variable "Cubierta" no pa= rece ejercer un impacto sustancial (p =3D 0,473) en el desempeño, como lo demues= tra su elevado valor p. Esto sugiere que no hay datos suficientes para respaldar la idea de que afecta genuinamente al desempeño. La variable "Dificultad" muestra un impacto notable y favorable (Estimador =3D 0,08912), lo que sugiere que una escalada en la dificultad está vinculada a= un aumento en el rendimiento.

Tabla 7

Coeficientes del modelo - rendimiento

Predictor

Estimador

EE

t

p

Constante<= span style=3D'font-size:12.0pt;line-height:200%;font-family:"Times New Roman",= serif; mso-fareast-font-family:Calibri;mso-font-kerning:1.0pt;mso-ligatures:stan= dardcontextual; mso-ansi-language:ES-EC;mso-fareast-language:EN-US'>

0.30477

0.04462

6.830

< .001

Tiempo

0.01371

0.00135

10.194

< .001

Temperatura

-0.11182

0.00880

-12.713

< .001

Suelo

-0.04769

0.00477

-9.999

< .001

Cubierta

-0.00314

0.00433

-0.726

0.473

Dificultad

0.08912

0.00477

18.684

< .001

Con los coeficientes calculados ya se puede estimar la formula general del modelo, usando para ello los estimadores, dando como resultado la siguiente formula= :

y =3D 0.30477+ 0.01371*= Tiempo – 0.11182*Temperatura - 0.04769*Suelo – 0.00314*Cubierta + 0.08912*dificult= ad

Para demostrar la efectividad del modelo para predecir el rendimiento dentro de = la muestra de obras, se procede a calcular los rendimientos promedios con el modelo matemático y compararlos con el rendimiento real de los obreros. Asimismo, se incluye dentro de esta comparación el rendimiento teórico proporcionado por el GAD de Cuenca para la colocación de porcelanato que es= de 0.25m2/hora.

Figura 1.

Comparación de rendimie= nto real, teórico y promedio calculado con el modelo matemático

Fuente: Elaboración pro= pia

La comparación entre el rendimiento real y el rendimiento teórico, c= omo se muestra en la figura 1, revela diferencias significativas. Durante la recolección de datos, la muestra de estudio en ningún momento alcanza los 0.25m2/hora y permanece consistentemente por debajo de este valor, con variaciones dependientes de cada obrero. Sin embargo, el modelo matemático demuestra una capacidad notable para aproximar el rendimiento real de la muestra con precisión, adaptándose eficazmente a las fluctuaciones observad= as en función de los factores analizados.

Con el propósito de verificar la aplicabilidad y precisión del modelo matemático más allá de la muestra inicial utilizada para su desarrollo, se llevó a cabo una nueva recolección de datos en 5 obras en la etapa de colocación de cerámica. Se seleccionó aleatoriamente un obrero en cada obra para ser analizado durante 5 días laborables. Como se ilustra en la figura = 2, en esta ocasión, los obreros lograron incluso superar el rendimiento teórico establecido por el GAD de Cuenca, aunque este rendimiento fluctuó a lo larg= o de los días. Por otro lado, el modelo matemático demostró una capacidad precisa para predecir el rendimiento real de los obreros en función de los factores analizados, lo que le permitió adaptarse de manera efectiva a estas variaci= ones temporales.

Figura 2.

Comparación de rendimie= nto real, teórico y promedio calculado con el modelo matemático

Fuente: Elaboración pro= pia

A continuación, en la tabla 8 se muestran los valores de tiempo, temperatura, tipo de suelo, condiciones de cubierta y nivel de dificultad experimentados por los obreros durante la recolección de datos. Además, se presentan el rendimiento estándar o teórico, el rendimiento real y el rendimiento promedio calculado mediante el modelo matemático.

Tabla 8

Comparación de rendimientos de las nuevas obras=

Denominación

Día=

Tiempo

Temperatura

Suelo

Cubierta

Dificultad

Rendimiento Estandar (m2/hora)

Rendimiento real (m2/hora)=

Rendimiento calculado= (m2<= /sup>/hora)

Maestro 1<= /span>

1

3

3

3

5

3

0,25

0,13

0,12

2

2

1

2

5

3

0,25

0,4=

0,38

3

2

1

2

5

3

0,25

0,4=

0,38

 

Tabla 8

Comparación de rendimientos de las nuevas obras (continuación)

Denominación

Día=

Tiempo=

Temperatura

Suelo<= span style=3D'mso-ascii-font-family:Calibri;mso-fareast-font-family:"Times New= Roman"; mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;color:black; mso-ansi-language:ES-EC;mso-fareast-language:ES-EC'>

Cubierta

Dificultad

Rendimiento Estandar (m2/hora)

Rendimiento real (m2/hora)

Rendimiento calculado= (m2<= /sup>/hora)

Maestro 1

4

4

2

4

4

4

0,25

0,3=

0,29

5

4

3

4

5

3

0,25

0,11

0,09

Maestro 2<= /span>

1

1

1

2

5

1

0,25

0,19

0,18

2

1

1

2

5

3

0,25

0,35

0,36

3

3

3

4

3

3

0,25

0,1=

0,08

4

4

3

4

3

3

0,25

0,1=

0,09

5

3

2

5

3

3

0,25

0,15

0,14

Maestro 3<= /span>

1

2

1

2

5

1

0,25

0,2=

0,20

2

5

3

4

3

3

0,25

0,12

0,11

3

4

2

4

3

3

0,25

0,2=

0,20

4

5

3

3

2

3

0,25

0,17

0,16

5

5

3

4

3

5

0,25

0,26

0,28

Maestro 4<= /span>

1

5

3

4

3

3

0,25

0,12

0,11

2

5

1

5

1

1

0,25

0,12

0,11

3

5

1

5

3

3

0,25

0,3=

0,28

4

5

1

5

1

1

0,25

0,12

0,11

5

5

1

5

3

3

0,25

0,3=

0,28

Maestro 5<= /span>

1

3

3

4

3

3

0,25

0,1=

0,08

2

4

3

4

3

3

0,25

0,1=

0,09

3

3

1

3

5

3

0,25

0,3=

0,34

4

5

2

4

4

3

0,25

0,22

0,21

5

5

2

5

3

3

0,25

0,18

0,17

Maestro 6<= /span>

1

3

3

3

5

3

0,25

0,12

0,12

2

2

1

2

5

3

0,25

0,3=

0,38

3

2

1

2

5

3

0,25

0,3=

0,38

4

5

3

3

3

3

0,25

0,15

0,15

5

4

3

4

5

3

0,25

0,1=

0,09

Maestro 7<= /span>

1

5

3

4

3

3

0,25

0,12

0,11

2

5

1

5

1

1

0,25

0,12

0,11

3

5

1

5

3

3

0,25

0,3=

0,28

4

5

1

5

1

1

0,25

0,12

0,11

5

5

1

5

3

3

0,25

0,3=

0,28

Discusión=

En relac= ión con los factores que inciden en el rendimiento de la mano de obra en la colocación de porcelanato en pisos, se evidenció que todos los aspectos considerados en este estudio poseen la capacidad de influir en el rendimien= to final. No obstante, no todos estos factores en conjunto son capaces de prev= er de manera precisa el rendimiento obtenido por un trabajador en esta activid= ad. Dentro del marco de esta investigación, se demostró que únicamente las variables climáticas y las relacionadas con la actividad misma tienen esta capacidad predictiva, particularmente aquellas asociadas al tiempo, la temperatura, las condiciones del suelo, la presencia de cubierta y la complejidad de la tarea.

A pesar = de que el rendimiento teórico proporcionado por el Gobierno Autónomo Descentralizado municipal de la ciudad de Cuenca sirve como punto de refere= ncia conceptual para la predicción del rendimiento de los obreros en la colocaci= ón de porcelanatos, se ha demostrado que, al menos en la parroquia Machángara,= estos rendimientos exhiben una fluctuación constante. En la mayoría de los casos,= los datos recopilados no logran alcanzar este rendimiento teórico establecido. = Esta situación puede tener un impacto significativo en las planificaciones de los gestores de obra, ya que, si se basan en el rendimiento teórico para estima= r el tiempo de finalización del proyecto, es probable que este plazo no se cumpla debido a las discrepancias entre las expectativas teóricas y la realidad observada en el terreno.

El rendimiento promedio calculado mediante el modelo matemático demostró ser eficaz en la predicción de las variaciones en el rendimiento de la mano de obra, particularmente en relación con las variables climáticas y las asocia= das con la actividad en sí. Este hallazgo subraya la considerable aplicabilidad= de la regresión lineal en el ámbito de la construcción. Los gestores de obra a= hora tienen la capacidad de anticipar el rendimiento de los obreros basándose únicamente en las previsiones climáticas y el nivel de riesgo percibido por= los trabajadores durante los meses de ejecución del proyecto. Esto les permite realizar planificaciones más precisas y evitar posibles incumplimientos de = los plazos de entrega, al menos en lo que respecta a esta actividad constructiva específica.

Conclusiones<= /b>

·         El rendimiento real de los obreros en la actividad de colocación de porcelanato para pisos, difiere del rendimiento teórico del GAD de Cuenca e= n la Parroquia Machángara pues fluctúa con los días y en muchas se mantiene por debajo del rendimiento estándar.

·         El modelo matemático basado en la aplicación de una regresión lineal logró una eficiencia del 98% para predecir el rendimiento real de los obrer= os en la colocación de porcelanato, sin embargo, esta predicción se condiciona únicamente a factores de: tiempo, temperatura, suelo, cubierta y dificultad= .

·         Una limitación importante de esta investigación radica en el hecho de que se utilizaron únicamente las construcciones ubicadas en la parroquia Machángara de la ciudad de Cuenca como muestra. Esta limitación se debió a = la indisponibilidad de datos o recursos para incluir obras de toda la ciudad de Cuenca. Como resultado, los hallazgos y conclusiones obtenidas pueden no ser completamente representativos de la situación en toda la ciudad, limitando = la generalización de los resultados a un contexto más amplio.

·         En futuras investigaciones, sería recomendable ampliar la muestra pa= ra incluir una mayor variedad de construcciones en diferentes áreas de la ciud= ad, lo que permitiría una evaluación más completa y representativa del rendimie= nto de la mano de obra en la actividad de colocación de porcelanato.=

Agradecimiento

El presente artículo es parte del trabajo de investigación y titulación del Programa de Maestrías en Construcción con Mención en Administración de la Construcción Sustentable de la Universidad Católica de Cuenca, por ello agradecemos a todos y cada uno de los instruct= ores pertenecientes a los grupos de investigación; Ciudad, Ambiente, y Tecnología(CAT), y Sistemas embebidos y visión artificial en ciencias, Arquitecturas, Agropecuarias, Ambientales y Automática (SEVA4CA), por los conocimientos e información brindados para la elaboración del trabajo.

Conflicto de intereses

No existe conflicto de intereses=

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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 Concienc= ia Digital.


 

 

 

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

 

 

 

 

 


=  

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ISSN: 2600-5= 859

Vol. 7 No. 2, p= p. = 627, abril - junio 2024

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www= .concienciadigital.org

 

 

 

 

 

                                      Estado del Arte                       Página 6 | 27      =

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