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Predicción de la fiabilidad de elementos no repara= bles dirigido a lámparas de alumbrado público

&nbs= p;

Prediction of the reliabil= ity of non-repairable elements directed to street lighting lamps of street ligh= ting

¹⁼

César Marcelo Gallegos Londońo https://orcid.org/0000-0002-86= 85-7501

Escuela Superior Politécnica de Chimborazo (ESPOCH), Facultad de Mecánica. Riobamba, Ecuador.

cesar.gallegos@espoch.ed= u.ec

²⁼

Félix Antonio García Mora = https://orcid.org/0000-0001-5814-3694

Escuela Supe= rior Politécnica de Chimborazo (ESPOCH), Facultad de Mecánica. Riobamba, Ecuad= or.

felix= .garcia@espoch.edu.ec

³⁼

Alex Giovanny Tenicota García https://orcid.org/0000-0002-0707-7698

Escuela Superior Politécnica de Chimborazo (ESPOCH), Facultad de Mecánica. Riobamba, Ecuador.

alex.tenicota= @espoch.edu.ec

	Artículo de Investigación Científica y Tecnológica Enviado: 24/12/2021 Revisado: 29/12/2021 Aceptado: 18/= 01/2022 Publicado:14/= 02/2022 DOI: https://doi.org/10.33262/ap.v4i1.179<= /a>

Cítese:		Gal= legos Londońo, C. M., García Mora, F. A., & Tenicota García, A. G. (2022). Predicción de la fiabilidad de elementos no reparables dirigido a lámpara= s de alumbrado público. AlfaPublicaciones, 4(1), 144–162. https://doi.org/10.33262/ap.v4i1.179
		CONCIENCIA DIGITAL, es una Revista Multidisciplinar, Trimestral, que se publicará en soporte electrónico tie= ne como misión contribuir a la formación de profesionales competentes con visión humanística 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. ht= tps://concienciadigital.org <= /span> La revista es editada por la Editorial Ciencia Digital (Editorial de prestigio registrada en la Cámara Ecuatoria= na de Libro con No de Afiliación 663) ww= w.celibro.org.ec
		Esta revista está protegida bajo una licencia Creative Commons Attribution Non Commercial No Derivatives 4.0 International. Copia de la licencia: http://creativecommons.org/licenses/by-nc-nd/= 4.0/
*Pal= abras claves:* fiabilidad, probabilidades, equipos no reparables, distribuciones paramétricas		Resumen <= o:p> El presente estudio tiene como propósito determinar los pasos necesarios par= a el cálculo de los indicadores de fiabilidad en equipos no reparables, el est= udio se lo realizó en una muestra de 250 lámparas de sodio de 100 watios destinadas al alumbrado público. Siendo el tiempo para la falla TTF el parámetro más importante para realizar un análisis de fiabilidad en equip= os no reparables, (tiempos desde la instalación del equipo hasta la falla), = en este caso los equipos no se pueden reparar, por consiguiente, deben ser reemplazados después del fallo, la recolección óptima de estos datos es fundamental para realizar un análisis correcto de los indicadores de fiabilidad. Se debe buscar cuál de las funciones paramétricas es la que m= ejor se ajusta a los datos recolectados, para esto es necesario hallar la Func= ión F(t) que representa a la distribución paramétrica tiempo acumulado hasta = la falla y compararla con la función no paramétrica o función empírica. Se d= eben calcular los parámetros de todas las distribuciones hipotéticas seleccion= adas con los datos recolectados en este estudio. Para cada distribución se cal= cula el valor de prueba el que es comparado con el valor crítico de la prueba = de ajuste de bondad de Kolmogorov–Smirnov, definiendo de esta manera si las hipótesis son rechazadas o no, el rechazo significa que el valor de la pr= ueba es mayor que el valor crítico de la prueba, caso contrario las hipótesis = son aceptadas y el valor más bajo decide la distribución paramétrica que mejo= r se ajusta a los datos de la muestra. Una vez seleccionada la distribución se puede estimar los indicadores de la fiabilidad como la función de probabilidad de fallas acumulada F(t), la Función de Supervivencia R(t) y= la función de la tasa de fallos conocida también como función de riesgo λ(t). El método proporcionará una herramienta muy útil para el cálcu= lo de la fiabilidad en equipos reparables y su futura evaluación que proporcionará ideas para la toma de decisiones en función de la una mejora continua.
Key= words: reliability, probabilities, unrepairable equipment, parametric distributions		Abstract The purpose of this s= tudy is to determine the necessary steps for the calculation of reliability indicators in non-repairable equipment, the study was carried out on a sa= mple of 250 100-watt sodium lamps for public lighting. Being the time to failu= re TTF the most important parameter to perform a reliability analysis on non= -repairable equipment, (time since the equipment installation until its failure), in = this case the equipment cannot be repaired, therefore, it must be replaced. Af= ter the failure, the optimal data collection is essential to carry out a corr= ect analysis of the reliability indicators. It is necessary to find which of = the parametric functions is the one that fits the best the collected data, for this it is imperative to find the Function F(t) that represents the parametric distribution accumulated time to failure and compare it with t= he non-parametric function or empirical function. Parameters of all selected hypothetical distributions must be calculated with the data collected in = this study. For each distribution, the test value is calculated, which is comp= ared with the critical value of the Kolmogorov-Smirnov kindness fit test, ther= efor defining whether the hypotheses are rejected or not. If rejected, it means that the value of the test is greater than the critical value, otherwise = the hypotheses are accepted, and the lowest value decides the parametric distribution that fits the best with the sample data. Once the distribution has been selected, reliabi= lity indicators can be estimated, such as the cumulative failure probability function F(t), the Survival Function R(t), and the failure rate function, also known as the risk function λ(t). The method will provide a very useful tool for calculating the reliability of repairable equipment and i= ts future evaluation, which will provide ideas for decision-making based on continuous improvement.

Introducción

El estudio de la fiabilidad proporciona información esencial en el desarrollo = de las técnicas o modelos productivos, su enfoque se cimenta en la predicción de procesos basado en conceptos estadísticos. El análisis de la Fiabilidad y s= us indicadores proporcionan herramientas importantes para la toma de decisiones enfocadas a eliminar o disminuir la incidencia de las fallos sus efectos y consecuencias (Escobar et al., 2003), además es útil en múltiples aplicacio= nes como: predecir la fiabilidad de un activo nuevo, mejorar la calidad de su d= iseńo, medir la fiabilidad en operación, permitiendo determinar la longevidad y la repercusión de los fallos en los sistemas o equipos industriales (Nachias, 1995). El estudio de la fiabilidad se basa en la investigación de los tiemp= os operativos hasta el fallo.

Se reconoce que los componentes de activos industriales tienen ciclos de vida finitos, en la práctica se distinguen dos tipos de componentes, los que son reparados y los que son reemplazados después de la ocurrencia del fallo. Con esta premisa se distinguen dos tiempos, el tiempo hasta el fallo utilizado desde que el dispositivo empieza a funcionar hasta el fallo donde es reemplazado comentado en Nachias (1995) y Crespo et al. (2004), el tiempo e= ntre fallos que es el tiempo operativo entre dos fallos consecutivos (Comité Eur= opeo de Normalización, 2018). De los tiempos mencionados derivan otros conceptos como MTBF (siglas en ingles de Tiempo Medio Entre Fallos) y MTTF (Tiempo Me= dio para el Fallo) (Gómez, 2002).

La fiabilidad está definida como la capacidad de un activo para cumplir óptimamente con las funciones para lo que fue adquirido, analizado en un período de tiempo y bajo condiciones operacionales definidas (Holmber et al= ., 1991; Mors, 2009).

El inicio para el estudio de la fiabilidad en equipos no reparables, los cuales son reemplazados después de la ocurrencia de un fallo está enfocado en el estudio de la variable aleatoria tiempos de funcionamiento correcto hasta el fallo, para luego analizar su contraparte la causa del estado de fallo.

El indicador más básico para el estudio de la fiabilidad en equipos no reparab= le es MTTF (Tiempo Medio Para la Falla), como se visualiza en la figura 1. “De= finido como la suma de los tiempos operativos hasta el fallo dividido para el núme= ro de fallos en un tiempo de análisis” (Ruiz, 2013).

MTTF =3D ∑TTF / Numero de fallos (1)

Figura 1<= /o:p>

Tiempo medio h= asta el fallo

En un activo no reparable el tiempo para la falla trata de determinar la probabilidad que un activo trabaje sin fallas en un tiempo igual o superior= al tiempo de análisis:

Fiabilidad (t) =3D Pr (t ≥ tiempo de análisi= s)

Las funciones de distribución más utilizadas para el estudio de la fiabilidad:”= la distribución de densidad de probabilidad f(t), función de densidad acumulada F(t) y función acumulada inversa o de Supervivencia R(t) de la variable aleatoria continua tiempo hasta la falla información compartida por (Parra = & Crespo, 2014), ver figura 2.

Figura 2<= /o:p>

Distribuciones= de probabilidad del tiempo hasta el fallo

La fiabilidad se define:

R(t) =3D Pr (t ≥ tiempo de análisis (ta)) =3D               (2)

Donde ta es el tiempo de análisis.

La ecuación anterior define a la fiabilidad R(t) como la probabilidad de que el activo no falle después del tiempo definido para el análisis (Parra & Crespo, 2016), y se calcula como la integral definida desde el tiempo de análisis hasta el infinito de la función de densidad de probabilidad.<= /o:p>

Como la probabilidad de fallo más la probabilidad de supervivencia es igual a 1 (Acuńa, 2003) se puede definir que:

R(t) =3D 1- Pr (t ≥ ta) =3D 1 - =3D 1 – F(t)                     (3)

El tiempo medio para fallar MTTF es el parámetro utilizado para el diseńo y selección de sistemas y se calcula como la media de la distribución de dens= idad acumulada del tiempo para la falla:

MTTF =3D = =3D                                     (4)

Su Representación gráfica se muestra en la Figura 3.

Figura 3<= /o:p>

Representación= del tiempo para la falla

Otra representación del tiempo para la falla en la función de la tasa de fallos, la media de la tas= a de fallos es el comportamiento del número de fallas por unidad de tiempo mient= ras que la tasa de fallos instantánea llamada también como “la función del ries= go y se describe como probabilidad de que un equipo que ha sobrevivido a un tiem= po t sobreviva en un intervalo mayor a este tiempo (t + Δt)” = (Yánez et al., 2004). Se expresa como:

λ(t) =3D                                                    (5)=

Los tiempos hasta el fal= lo son variables aleatorias continuas, estos datos se representan por medio de distribuciones, lo importante es determinar cuál de las distribuciones prop= orciona un mejor ajuste al conjunto de datos.

Entre las distribuciones= más comunes para el estudio de la fiabilidad con variables aleatorias continuas= son expresa (Yánez et al., 2004)

·&nb= sp;        Distribución de Weibull

·         Distribución Gamma

·         Distribución Normal

·         Distribución Log – Normal

·         Distribución Exponencial

Las expresiones para el cálculo de las funciones de distribución tomadas de Ebeling (= 1997) y Knezevic (1996), se describen en la tabla 1.

&nbs= p;

&nbs= p;

&nbs= p;

&nbs= p;

Tabla 1

Funciones distribuciones= continuas

FUNCIÓN=

Densidad f(t)

Distrib= ución F(t)

Supervi= vencia R(t)

Riesgo<= o:p>

Exponencial

λe-λt<= /span>

1-<= m:sSupPr>e-λt<= /span>

e-λt<= /span>

λ=

Weibull

^= 6;^= 5;t-ϒ= α<= /m:f>^= 6;-1= e-t-ϒ<= /m:r>αβ <= span lang=3DES style=3D'font-size:11.0pt;line-height:115%;font-family:"Calibri= ",sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:"Times New Roman= "; mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi; mso-ansi-language:ES;mso-fareast-language:ES;mso-bidi-language:AR-SA'>

1-e-t-ϒ<= /m:r>αβ

e-t-ϒ<= /m:r>αβ

^= 6;^= 5;t-ϒ= α<= /m:f>^= 6;-1=

Normal

1Ϭ= 2∏ e-1<= span style=3D'mso-bookmark:_Hlk79441612'>2t-<= m:r>μϬ2

-= 734;t1<= span style=3D'mso-bookmark:_Hlk79441612'>Ϭ2= e-12= t-μ= Ϭ2d(t)

tW= 34;1<= span style=3D'mso-bookmark:_Hlk79441612'>Ϭ2∏<= /m:rad>e-12= t-μ= Ϭ2d(t)

f(t)= R(t)=

Log-Normal

1Ϭ= 2∏ e-1<= span style=3D'mso-bookmark:_Hlk79441612'>2ln⁡(<= m:r>t<= m:r>)-= μϬ2

-= 734;t1<= span style=3D'mso-bookmark:_Hlk79441612'>Ϭ2∏<= /m:rad>e-12= t-μ= Ϭ2d(t)

tW= 34;1<= span style=3D'mso-bookmark:_Hlk79441612'>Ϭ2∏<= /m:rad>e-12= t-μ= Ϭ2d(t)

f(t)= R(t)=

Gamma

1βα = 27;αt^= 5;-1= e-t<= span style=3D'mso-bookmark:_Hlk79441612'>β=

1βα = 27;α0ttα-= 1e-tβ<= /m:f>d(t)

1βα = 27;αtt∞<= /span>tα-= 1e-tβ<= /m:f>d(t)

f(t)= R(t)=

Los parámetros para el cálculo de cada distribució= n de los puede apreciar en la tabla 2.

Tabla 2

Ecuaciones de parámetros

FUNCIÓN

PARÁMETROS

Exponencial

λ <= /span>

-

Weibull

α=3D <= /span>

= <= /span>

Normal

μ=3D <= /span>

<= /span>

Log - Normal

μt=3D

=3D <= /span>

Gamma

α=3D <= /span>

β=3D <= /span>

“Seleccionadas las distribuciones hipotéticas a evaluar en función de la variable aleatori= a se debe realizar una prueba de bondad ajuste” (Gasca et al., 2017), para determinar cuál de las distribuciones hace un mejor ajuste al grupo de dato= s, hay varias pruebas de bondad de ajuste de bondad:

^·&nb=
sp;Prueba Chi Cuadrado x²(Utilizada en variables aleatorias discretas)

·&nb= sp;        Prueba de Kolmogorov – Smirnov

·&nb= sp;        Prueba de Ande= rson – Darling

“La prueba de Kolmogorov – Smirnov es la más utilizada” (Yánez et al., 2004). l= os pasos a seguir son los siguientes:

Calcular la función acumulada F(t) para cada una de las distribuciones seleccionadas= y calcular la función de distribución empírica F_e(t):

F_e(t) =3D          =                                                             (5)=

Donde n es el número de orden y N el tamańo de la muestra

= 1.      Graficar las distribuciones

= 2.      Calcular el K-S valor máximo, utilizando:

K-S_VALOR =3D (|F(t) – F_e(t)|= ); (|F(t) – F_e(t-1) |)             = (6)

3.&n= bsp;     Comprar el K-S= _VALORcon valor el correspondiente de la tabla del Kolmogorov Smirnov seleccionado con el número de datos y con un valor de significancia del 5%.= Si el dato es menor que el de la tabla la hipótesis es verdadera y la distribu= ción es seleccionada, si varias distribuciones cumplen el requerimiento se selecciona la de menor K-S_VALOR, en la tabla 3 corresponde a los valores críticos de la prueba del Kolmogorov – Smirnov.
Tabla 3

Valores críticos. Test de Kolmogorov- Smirnov

n

ϒ

0.20=

0.15=

0.10=

0.05=

0.01=

1

0.900

0.925

0.950

0.975

0.995

2

0.684

0.726

0.776

0.842

0.929

3

0.565

0.597

0.642

0.708

0.828

4

0.494

0.525

0.564

0.624

0.733

5

0.446

0.474

0.510

0.565

0.669

6

0.410

0.436

0.470

0.521

0.618

7

0.381

0.405

0.380

0.486

0.577

8

0.358

0.381

0.411

0.457

0.543

9

0.339

0.360

0.388

0.432

0.514

10

0.322

0.342

0.368

0.410

0.490

11

0.307

0.326

0.352

0.391

0.468

n<= /i>

ϒ

0.20=

0.15=

0.10=

0.05=

0.01=

12

0.295

0.313

0.338

0.375

0.450

13

0.284

0.302

0.325

0.361

0.433

14

0.274

0.292

0.314

0.349

0.418

15

0.266

0.283

0.304

0.338

0.404

16

0.258

0.274

0.295

0.328

0.392

17

0.250

0.266

0.286

0.318

0.381

18

0.244

0.259

0.278

0.309

0.371

19

0.237

0.252

0.272

0.301

0.363

20

0.231

0.246

0.264

0.294

0.356

25

0.210

0.220

0.240

0.270

0.320

30

0.190

0.200

0.220

0.240

0.290

35

0.180

0.190

0.210

0.230

0.270

>35

1.07/W= 30;n

1.14/W= 30;n

1.22/W= 30;n

1.36/W= 30;n

1.63/W= 30;n

Metodología

Recolectados los tiempos hasta el fallo (ti) de los elementos no reparables, se deben plantear tantas hipótesis como distribuciones de hayan seleccionado (la hipótesis está relacionada con que los datos recolectados se ajusten a la distribución analizada).

Para cada distribución calcular sus respectivos parámetros utilizando las ecuaci= ones específicas, ver tabla 2.

Para cada valor de ti (tiempo hasta el fallo) calcular la probabilidad de falla acumulada teórica F(t).

Luego debe calcularse la probabilidad de falla empírica F_e(ecuación 5) para cada valor de ti.

Graficar cada probabilidad de falla teórica Vs la empírica con todas las distribucio= nes analizadas, figura 4.

Aplicar la prueba de bondad de ajuste de Kolmogorov – Smirnov para ello calcular el= KS-VALOR de cada distribución y compáralo con el valor crítico del test de Kolmogoro= v- Smirnov (VKS). Si el KS-VALOR es inferior al valor VKS. la hipótesis no es rechazada y podría ser seleccionada para el mejor ajuste. El proceso anteri= or se repite en todas las distribuciones, de las hipótesis no rechazadas se de= be seleccionar la de menor valor y así proseguir con las estimaciones de la fiabilidad.

Figura 4

Representación F(t) vs F_e(t)

Resultados

Para el análisis se tomaron como muestra los fal= los de 250 lámparas de Na (Sodio) de alta presión de 100W, con boquilla e40, pe= rtenecientes al alumbrado público. En análisis se enfocó únicamente en las luminarias. El tiempo de recolección de las fallas se lo realizó en un período de 26 seman= as, la información fue tomada de las órdenes de mantenimiento correctivo de la empresa, en la tabla 4 representa una muestra de la recolección de datos.

Tabla 4

Muestra de datos de falla

n

Falla

Fecha y hora de la fa= lla

Horas de uso acumulad= o

1

Falla de luminaria

2020-06-16 19:00:00

13305.5

2

Falla de luminaria

2020-06-16 00:01:00

13296

3

Falla de luminaria

2020-06-13 11:00:00

13265.5

4

Falla de luminaria

2020-06-12 14:15:00

13255

5

Falla de luminaria

2020-06-12 00:30:00

13248

…

…

…

&nbs= p;

…

…

…

…

…

202<= /o:p>

Falla de luminaria

2020-01-03 08:30:00

55.5=

203<= /o:p>

Falla de luminaria

2020-01-03 08:10:00

55.5=

204<= /o:p>

Falla de luminaria

2020-01-0= 2 11:15:00

45

205<= /o:p>

Falla de luminaria

2020-01-02 12:15:00

45.5=

=

Una muestra del cálculo de la función acumulada empírica (ecuación 5) se presenta en la tabla 5.

F_e(t) =3D , donde n es el número de orden y N el t= amańo de la muestra.

Tabla 5

Muestra del cálculo de la función de probabilida= d empírica

n

Tiempo acumulado hasta el fallo (t)

Fe(t)

1

19.011537=

0.004

2

37.559079=

0.008

3

40.322394=

0.012

4

49.451985=

0.016

--

--

--

--

--

--

247<= /o:p>

321.07416= 3

0.988

248<= /o:p>

321.81291=

0.992

249<= /o:p>

323.77153= 5

0.996

250<= /o:p>

337.06206=

1

Para cada tiempo se calcula la función de probabilidad de fallo acumulada F(t) p= ara cada una de las distribuciones seleccionadas y se grafica la distribución versus la empírica. Figuras 5,6,7,8,9

Distribución Exponencial.     F(t) =3D 1 – e-λt

^{λ
=3D Tasa de fallos; t TTF =3D Tiempo hasta el fallo}=

Figura 5

F(t)Exponencia= l vs F_e(t)

Distribución de Weibull.

^{β =3D Parámetro de forma; α=3D Parámetro=
de
escala}

&nbs= p;

&nbs= p;

&nbs= p;

&nbs= p;

&nbs= p;

Figura 6<= o:p>

F(t)Weibu= ll vs F_e(t)

Distribución Normal.

^{μ =3D Med=
ia; Ϭ=3D
Desviación estándar}

Figura 7

F(t) Norm= al vs F_e(t)

Distribución Log-Normal.

^{μ =3D Media; Ϭ=3D Desviación estándar}

Figura 8<= /o:p>

F(t) Log-Norma= l vs F_e(t)

=

Log-Normal.

^{β =3D Parámetro de forma; α=3D Parámetro=
de
escala}

Figura = 9

F(t) Ga= mma vs F_e(t)

Gráficamente la curvas con mejor ajuste es la Distribución de Weibull, lo cual se confirmará con la prueba de Kolmogorov–= Smirnov. Se debe calcular la función de fallos acumulada para cada distribución, com= o se muestra en la tabla 6.

Tabla 6

Muestra del cálculo de las funciones<= i> de fallo para las distribuciones

Falla No "i"

t"i&= quot; (días)

F(t) EXPONENCIAL

F(t) WEIB= ULL

F(t) NORM= AL

F(t) Log-= NORMAL

GAMMA

F(t) EMPÍ= RICA

1

19

0.108

0.0008

0.002

0

0.0001

0.004

2

37.6=

0.202

0.0068

0.0021

0.00019

0.0056

0.008

Tabla 6

Muestra del cálculo de las funciones<= i> de fallo para las distribuciones (continuación)

Falla No "i"

t"i&= quot; (días)

F(t) EXPONENCIAL

F(t) WEIB= ULL

F(t) NORM= AL

F(t) Log-NORMAL

GAMMA

F(t) EMPÍ= RICA

3

40.3=

0.215

0.0085

0.0022

0.00037

0.0085

0.012

4

49.5=

0.257

0.016

0.0024

0.0021

0.0262

0.016

5

56.3=

0.287

0.0239

0.0025

0.00557

0.0502

0.02=

--

--

--

--

--

--

--

--

--

--

--

--

--

--

--

--

247<= /o:p>

321.1

0.855

0.996

0.919

0.965

1

0.988

248<= /o:p>

321.8

0.855

0.996

0.922

0.966

1

0.992

249<= /o:p>

323.8

0.857

0.996

0.924

0.967

1

0.996

250<= /o:p>

337.1

0.868

0.998

0.927

0.974

1

1

Se procede a calcular los valores absolutos de las diferencias entre valores de las probabilidades acumuladas teóricas y empíricas, para todos los datos de= la muestra, como se indica en las siguientes ecuaciones:

·      =    |F(tᵢ)-&= #7710;e(tᵢ)|             (7)

·      =    |F(tᵢ)-&= #7710;e(tᵢ-1) |          (8)

La tabla 7 es una muestra del cálculo de los parámetros para la prueba de ajus= te de bondad K-S. Una vez calculados los valores se debe identificar los valor= es más altos para cada una de las distribuciones, estos valores se deben compa= rar con los valores críticos para el test de Kolmogorov-Smirnov de la tabla 3. = Para el estudio se tomó un nivel de significancia del 5% y como la muestra es de= 250 lámparas se debe calcular con la expresión:

Valor Crítico para 5% de significancia =3D =3D 0.086

Tabla 7

Muestra del cálculo de los parámetros de la prueba de ajuste de bonda= d de

Kolmogorov - Smirnov

Falla No "i"

F(t) EXPONENCIAL

&nbs= p;

F(t) EMPÍ= RICA

|F(t˰= 2;)-Ḟ(tᵢ)|

|F(t˰= 2;)-Ḟ(tᵢ-1)|

1

0.108

&nbs= p;

0.004

0.104

0.198

2

0.202

&nbs= p;

0.008

0.194

0.207

3

0.215

&nbs= p;

0.012

0.203

0.245

--

--

&nbs= p;

--

--

--

Falla No "i"

F(t) WEIB= ULL

&nbs= p;

F(t) EMPÍ= RICA

|F(t˰= 2;)-Ḟ(tᵢ)|

|F(t˰= 2;)-Ḟ(tᵢ-1)|

1

0.0008

&nbs= p;

0.004

0.003

0.003

2

0.0068

&nbs= p;

0.008

0.001

0.001

3

0.0085

&nbs= p;

0.012

0.003

0.004

--

--

&nbs= p;

--

--

--

Tabla 7

Muestra del cálculo de los parámetros de la prueba de ajuste de bonda= d de

Kolmogorov – Smirnov (continuación)

Falla No "i"

F(t) NORM= AL

&nbs= p;

F(t) EMPÍ= RICA

|F(t˰= 2;)-Ḟ(tᵢ)|

|F(t˰= 2;)-Ḟ(tᵢ-1)|

1

0.0020

&nbs= p;

0.004

0.002

0.002

2

0.0021

&nbs= p;

0.008

0.006

0.006

3

0.0022

&nbs= p;

0.012

0.010

0.010

--

--

&nbs= p;

--

--

--

Falla No "i"

F(t)Log- NORMAL

&nbs= p;

F(t) EMPÍ= RICA

|F(t˰= 2;)-Ḟ(tᵢ)|

|F(t˰= 2;)-Ḟ(tᵢ-1)|

1

0.0000001=

&nbs= p;

0.004

0.004

0.004

2

0.0001920=

&nbs= p;

0.008

0.008

0.008

3

0.0003713=

&nbs= p;

0.012

0.012

0.010

--

--

&nbs= p;

--

--

--

Falla No "i"

F(t)GAMMA=

&nbs= p;

F(t) EMPÍ= RICA

|F(t˰= 2;)-Ḟ(tᵢ)|

|F(t˰= 2;)-Ḟ(tᵢ-1)|

1

0.000063<= o:p>

&nbs= p;

0.004

0.004

0.002

2

0.005636<= o:p>

&nbs= p;

0.008

0.002

0.001

3

0.008539<= o:p>

&nbs= p;

0.012

0.003

0.014

--

--

&nbs= p;

--

--

--

Los valores máximos obtenidos para las distribuciones se muestran en= la tabla 8.

Tabla 8

Valores máximos de los parámetros de la prueba de

bondad de ajuste

Exponencial

0.350

Weibull

0.039

Normal

0.278

Log-normal

0.079

Gamma

0.460

Estos valores se comparan con el valor crítico de = la prueba K-S (0.086), como se puede apreciar dos distribuciones están bajo es= te valor Weibull y Log-Normal, el resto de las hipótesis son rechazadas, Como = el valor de la distribución de Weibull es menor que el de la distribución Log-Normal se escoge esta distribución para continuar con el análisis confirmando de esta manera los resultados obtenidos en el análisis gráfico.=

Con la distribución de Weibull se construyen Las curvas de Supervivencia R(t), = La de Probabilidad de Fallo F(t), La función de la densidad f(t) y la Función = del Riesgo λ(t) para continuar el estudio de las luminarias figura 10.

Figura 10

Funciones de la distribución de Weibull

Se realizó una corrida de datos para varios tiempo= s de ensayo en días para calcular la probabilidad de funcionamiento y fallas para las lámparas de sodio obteniendo los resultados de la tabla 9 donde se veri= fica las variaciones de las probabilidades fallo y supervivencia en el tiempo

Tabla 9

Probabilidad de fallo y supervivencia

t (días)<= o:p>

F(t) Probabilidad de fallo

R(t) Probabilidad de supervivencia

10

0%

100%=

50

2%

98%<= /o:p>

100<= /o:p>

13%<= /o:p>

87%<= /o:p>

200<= /o:p>

72%<= /o:p>

28%<= /o:p>

350<= /o:p>

100%=

0%

Un detalle de la variación de la probabilidad de fallo en el tiempo se lo representa en la figura 11

Figura 11

Variación de la Probabilidad de fallo y Supervivencia en el tiempo

Conclusiones

·         El análisis de la fiabilidad para equipos reparable se los puede enfo= car en forma diferente, puede utilizarse para fallas en equipos similares monta= dos en máquinas diferentes como las flotas o luminarias como es el caso de estu= dio, también se lo puede hacer para un solo equipo siempre que se tenga un lista= do de fallos lo suficientemente extenso para realizar los cálculos estadístico= s, se recomienda cinco datos como mínimo.

·         Si los datos no se ajustan a ninguna distribución paramétrica se pueda trabajar con la distribución no paramétrica o empírica

·         El propósito de los cálculos de la fiabilidad o supervivencia R(t) es= tán destinados a predecir la probabilidad que un equipo siga funcionando correctamente en un período d tiempo de análisis. Pero la idea será siempre mejorar estos indicadores para esto se deberán plantear estrategias para que esto ocurra

·         Estos cálculos se los puede plantear por marca para determinar la más fiable, combinando este indicador con un análisis costo beneficio será de m= ucha utilidad en la selección de equipos.

Referencias Bibliográficas

Acuńa, J. (2003). Ingen= iería de la Confiabilidad. Costa Rica: Tecnológica de Costa Rica.<= /span>

Comité Europeo de Normalización. (2018). EN-UNE-133306 Terminología de mantenimiento. Madrid: AENOR.

Crespo, A., Sánchez, A., &= amp; Moreu de León, P. (2004). Ingeniería de mantenimiento. Madrid: AENOR= .

Ebeling, C. (1997). Reliability and Maintainability Engineering. USA: McGraw Hill.

Escobar, L., Villa, E., &a= mp; Yáńez, S. (2003). Confiabilidad: Historia, estado del arte y desafíos futuros. = Dyna, 70(140), 21.

Gasca, M., Camargo, L., &a= mp; Medina, B. (2017). Sistema para Evaluar la Confiabilidad de Equipos Crítico= s en el Sector Industrial. Información. Tecnológica, 26(4), 14.

Gómez, A. (2002). Manual del Ingeniero de Mantenimiento. México: Facilites.

Holmber, K., Folkeson, S., Berrgman, B., & Ostvic, R. (1991). Operational reliabi= lity and systematic maintenance. New York: Elsevier Science Publishers LTD.<= o:p>

Knezevic, A. (1996). Mantenibilidad. Madrid: Isdefe.

Mors, L. (2009). Manten= imiento. Planeación, ejecución y control. México: Alfaomega.
Nachias, J. (1995). Fia= bilidad. Madrid: Isdefe.

Parra, C., & Crespo, A. (2014). Ingeniería de Mantenimiento y Fiabilidad Aplicada en la Gestión = de Activos. Sevilla: Ingeman.

Parra, C., & Crespo, A. (2016). Métodos de análisis de fiabilidad, mantenibilidad, disponibilida= d y riego. Ingecom.

Ruiz, J. (2013). Propue= sta metodológica para el cálculo y gestión de la confiabilidad del suministro e= nergético en instalaciones. Medellín: Universidad Pontificia Bolivariana.

Yánez, M., Gómez, H., & Valbuena, G. (2004). Ingeniería de la confiabilidad y análisis probabilístico del riesgo Reliability and risk management S.A.

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

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 Alfa Publicaciones.

=

&nb= sp;

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= ISSN: 2773-7330

= Vol. 4 No. 1, pp. 144 – 162 , enero – marzo 2022<= o:p>

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Globalización = Página 144 | 1

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FUNCIÓN=	Densidad f(t)	Distrib= ución F(t)	Supervi= vencia R(t)	Riesgo<= o:p>
Exponencial	λe-λt<= /span>	1-<= m:sSupPr>e-λt<= /span>	e-λt<= /span>	λ=
Weibull	^= 6;^= 5;t-ϒ= α<= /m:f>^= 6;-1= e-t-ϒ<= /m:r>αβ <= span lang=3DES style=3D'font-size:11.0pt;line-height:115%;font-family:"Calibri= ",sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:"Times New Roman= "; mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi; mso-ansi-language:ES;mso-fareast-language:ES;mso-bidi-language:AR-SA'>	1-e-t-ϒ<= /m:r>αβ	e-t-ϒ<= /m:r>αβ	^= 6;^= 5;t-ϒ= α<= /m:f>^= 6;-1=
Normal	1Ϭ= 2∏ e-1<= span style=3D'mso-bookmark:_Hlk79441612'>2t-<= m:r>μϬ2	-= 734;t1<= span style=3D'mso-bookmark:_Hlk79441612'>Ϭ2= e-12= t-μ= Ϭ2d(t)	tW= 34;1<= span style=3D'mso-bookmark:_Hlk79441612'>Ϭ2∏<= /m:rad>e-12= t-μ= Ϭ2d(t)	f(t)= R(t)=
Log-Normal	1Ϭ= 2∏ e-1<= span style=3D'mso-bookmark:_Hlk79441612'>2ln⁡(<= m:r>t<= m:r>)-= μϬ2	-= 734;t1<= span style=3D'mso-bookmark:_Hlk79441612'>Ϭ2∏<= /m:rad>e-12= t-μ= Ϭ2d(t)	tW= 34;1<= span style=3D'mso-bookmark:_Hlk79441612'>Ϭ2∏<= /m:rad>e-12= t-μ= Ϭ2d(t)	f(t)= R(t)=
Gamma	1βα = 27;αt^= 5;-1= e-t<= span style=3D'mso-bookmark:_Hlk79441612'>β=	1βα = 27;α0ttα-= 1e-tβ<= /m:f>d(t)	1βα = 27;αtt∞<= /span>tα-= 1e-tβ<= /m:f>d(t)	f(t)= R(t)=

FUNCIÓN	PARÁMETROS
Exponencial	λ <= /span>	-
Weibull	α=3D <= /span>	= <= /span>
Normal	μ=3D <= /span>	<= /span>
Log - Normal	μt=3D	=3D <= /span>
Gamma	α=3D <= /span>	β=3D <= /span>

n	ϒ
0.20=	0.15=	0.10=	0.05=	0.01=
1	0.900	0.925	0.950	0.975	0.995
2	0.684	0.726	0.776	0.842	0.929
3	0.565	0.597	0.642	0.708	0.828
4	0.494	0.525	0.564	0.624	0.733
5	0.446	0.474	0.510	0.565	0.669
6	0.410	0.436	0.470	0.521	0.618
7	0.381	0.405	0.380	0.486	0.577
8	0.358	0.381	0.411	0.457	0.543
9	0.339	0.360	0.388	0.432	0.514
10	0.322	0.342	0.368	0.410	0.490
11	0.307	0.326	0.352	0.391	0.468

*n<= /i>*	ϒ
0.20=	0.15=	0.10=	0.05=	0.01=
12	0.295	0.313	0.338	0.375	0.450
13	0.284	0.302	0.325	0.361	0.433
14	0.274	0.292	0.314	0.349	0.418
15	0.266	0.283	0.304	0.338	0.404
16	0.258	0.274	0.295	0.328	0.392
17	0.250	0.266	0.286	0.318	0.381
18	0.244	0.259	0.278	0.309	0.371
19	0.237	0.252	0.272	0.301	0.363
20	0.231	0.246	0.264	0.294	0.356
25	0.210	0.220	0.240	0.270	0.320
30	0.190	0.200	0.220	0.240	0.290
35	0.180	0.190	0.210	0.230	0.270
>35	1.07/W= 30;n	1.14/W= 30;n	1.22/W= 30;n	1.36/W= 30;n	1.63/W= 30;n

n	Falla	Fecha y hora de la fa= lla	Horas de uso acumulad= o
1	Falla de luminaria	2020-06-16 19:00:00	13305.5
2	Falla de luminaria	2020-06-16 00:01:00	13296
3	Falla de luminaria	2020-06-13 11:00:00	13265.5
4	Falla de luminaria	2020-06-12 14:15:00	13255
5	Falla de luminaria	2020-06-12 00:30:00	13248
…	…	…	&nbs= p; …
…	…	…	…
202<= /o:p>	Falla de luminaria	2020-01-03 08:30:00	55.5=
203<= /o:p>	Falla de luminaria	2020-01-03 08:10:00	55.5=
204<= /o:p>	Falla de luminaria	2020-01-0= 2 11:15:00	45
205<= /o:p>	Falla de luminaria	2020-01-02 12:15:00	45.5=

n	Tiempo acumulado hasta el fallo (t)	Fe(t)
1	19.011537=	0.004
2	37.559079=	0.008
3	40.322394=	0.012
4	49.451985=	0.016
--	--	--
--	--	--
247<= /o:p>	321.07416= 3	0.988
248<= /o:p>	321.81291=	0.992
249<= /o:p>	323.77153= 5	0.996
250<= /o:p>	337.06206=	1

Falla No "i"	t"i&= quot; (días)	F(t) EXPONENCIAL	F(t) WEIB= ULL	F(t) NORM= AL	F(t) Log-= NORMAL	GAMMA	F(t) EMPÍ= RICA
1	19	0.108	0.0008	0.002	0	0.0001	0.004
2	37.6=	0.202	0.0068	0.0021	0.00019	0.0056	0.008

Falla No "i"	F(t) EXPONENCIAL	&nbs= p;	F(t) EMPÍ= RICA	\|F(t˰= 2;)-Ḟ(tᵢ)\|	\|F(t˰= 2;)-Ḟ(tᵢ-1)\|
1	0.108	&nbs= p;	0.004	0.104	0.198
2	0.202	&nbs= p;	0.008	0.194	0.207
3	0.215	&nbs= p;	0.012	0.203	0.245
--	--	&nbs= p;	--	--	--
Falla No "i"	F(t) WEIB= ULL	&nbs= p;	F(t) EMPÍ= RICA	\|F(t˰= 2;)-Ḟ(tᵢ)\|	\|F(t˰= 2;)-Ḟ(tᵢ-1)\|
1	0.0008	&nbs= p;	0.004	0.003	0.003
2	0.0068	&nbs= p;	0.008	0.001	0.001
3	0.0085	&nbs= p;	0.012	0.003	0.004
--	--	&nbs= p;	--	--	--

Falla No "i"	F(t) NORM= AL	&nbs= p;	F(t) EMPÍ= RICA	\|F(t˰= 2;)-Ḟ(tᵢ)\|	\|F(t˰= 2;)-Ḟ(tᵢ-1)\|
1	0.0020	&nbs= p;	0.004	0.002	0.002
2	0.0021	&nbs= p;	0.008	0.006	0.006
3	0.0022	&nbs= p;	0.012	0.010	0.010
--	--	&nbs= p;	--	--	--
Falla No "i"	F(t)Log- NORMAL	&nbs= p;	F(t) EMPÍ= RICA	\|F(t˰= 2;)-Ḟ(tᵢ)\|	\|F(t˰= 2;)-Ḟ(tᵢ-1)\|
1	0.0000001=	&nbs= p;	0.004	0.004	0.004
2	0.0001920=	&nbs= p;	0.008	0.008	0.008
3	0.0003713=	&nbs= p;	0.012	0.012	0.010
--	--	&nbs= p;	--	--	--
Falla No "i"	F(t)GAMMA=	&nbs= p;	F(t) EMPÍ= RICA	\|F(t˰= 2;)-Ḟ(tᵢ)\|	\|F(t˰= 2;)-Ḟ(tᵢ-1)\|
1	0.000063<= o:p>	&nbs= p;	0.004	0.004	0.002
2	0.005636<= o:p>	&nbs= p;	0.008	0.002	0.001
3	0.008539<= o:p>	&nbs= p;	0.012	0.003	0.014
--	--	&nbs= p;	--	--	--

Exponencial	0.350
Weibull	0.039
Normal	0.278
Log-normal	0.079
Gamma	0.460

t (días)<= o:p>	F(t) Probabilidad de fallo	R(t) Probabilidad de supervivencia
10	0%	100%=
50	2%	98%<= /o:p>
100<= /o:p>	13%<= /o:p>	87%<= /o:p>
200<= /o:p>	72%<= /o:p>	28%<= /o:p>
350<= /o:p>	100%=	0%