This document discusses concepts related to risk analysis and simulation modeling. It defines key terms like risk, models, and Monte Carlo simulation. It explains that Monte Carlo simulation randomly samples input variable distributions thousands of times to model outcomes. The benefits of simulation include analyzing risk and optimizing decisions. Graphs and Excel tools can analyze simulation results to explore outcomes and sensitivities.

1. !" #
$ $
$ $ % &
# ! " # $
& $ ' # % &
' $ # ' ( ) % *
+*(, + ! + !
&! - ( ! (+! (! +. !
+ ( + , ' ! /!
& - +! ! +(
0 - 1!
' 1
+ *( , 2334
(

2. ! /-
,
&5 ,
- ( ( + / ! + ( ,( 0
! $$ ( ') !
!" # #
6 7
+ "
: 6
# , , " ,
! , 7
8 ": %
8 ; -
( ) 9 8 ( )
" : ; * ;
+ ; :!
& ,;
( < % ,
( < , " :,
# " ! # ( =#
" !$7 / : !$7
" - "
( ;8 ) = =
1
= :; = 7 = >= ) =
# ? 7 > = 7
+ ! ; 1

3. +*(, + ! + !
&! - ( ! (+! (! +. !
+ ( + , ' ! /!
& - +! ! +(
0 - 1!
' 1
+ *( , 2334
(

4. 1. TABLA DE CONTENIDO
@1 - ( ! + (+
- 4
21 +,
- !! + A
B1 ,( (+ C
41 - ! C
, -
D1 " *
(- E
D1@1 " * 0 (,
(- (+ E
D121 " *
(- ( % &!
(! E
F1 " - &! ! .+ @3
A1 !+ (
! ( % 9 (-( @3
C1 ! + (%
! - ' ! @@
C1@1G #
9 H @@
C121G #
9 H @@
C1B1G #
9 7 ! H @2
C141G #
9 7H @2
C1D1 ; 7 ! ; H @B
C1F1G 7
! 7H @B
C1A1G #
9 ; H @4
C1A1@1 0 ; @4
C1A121 ; = 7 @4
C1A1B1 0 @D
C1C1G! ;
! 2333H @D
C1E1G #
9 = 7 H @D
C1@31 G9 = 7 = H @F
E1 *(, + @F
(

5. @31 ,(9 (, (+- ( , 5 , @C
(
@@1 ,(9 (, (+- ( & 5 , @C
- (
@21 ! ,! / -
, @C
@21@1 G I
9 ! ! /-
( , H @C
@2121 G7
! ; = H @E
@21B1 G7
! ! 8 (6 H 23
@2141 G #
9 = H 2B
@2141@1 G 7
! = H 2B
@21D1 G7
! = 7 H 2A
@21F1 G7
! 7H 2C
@21A1 G! 8 =
= 7 H B@
@21C1 G7
! ; H BB
@21E1 G7
! = H B4
@21@31 BF
@21@31@1 ; & BF
@21@3121 ! = BA
@21@31B1 % ! BA
@21@3141 !: BC
@21@31D1 - !: BE
@21@31F1 ! - BE
@21@31A1 (6 = BE
@21@@1 (" %
( ( % ! !.+ ( ( 43
@21@@1@1 %, (, (" % 1 J
( & = K 43
@21@@121 (0 + (" % 1 J
( * , :K 44
@B1 ! /-
, - FC
@B1@1 8 FE

6. @B1@1@1 :& FE
@B1@121 7 FE
@B1@1B1 - !: FE
@B121 A3
@B121@1 = A3
@B12121 ( 7 A3
@B121B1 A3
@B12141 7 A3
@41 +' ( (,, (+- A@
@41@1 8L =- M A@
@41@1@1 :& A@
@41@121 7 AD
@41@1B1 ! - !: AE
@4121 C4
@4121@1 = C4
@412121 ( # 7 CD
@41B1 (8 = CF
@41B1@1 - ; = E3
@41B121 ED
@41B1B1 7 ; @33
@D1 0 & /5( 0 & @3A
, N , N

7. 2. INTRODUCCION
! = )
)
> :
) = =
7 ) ; > )
= = ;; # > ;
6
= = 1
( = ) : ) :
> = !
( 7 ) = )
1
% 7 = (6 O>
= 8 7 >
P ! > : ;
= 7
& ! ( 7 > ) =
= : 6 7 = 7 >
= 7 7 ) )
= = 1

8. 3. RESUMEN
# = :
7 ) ; : ; 7
Q = : # ) :
= = = 7 = =
71
(6 : : =
= > 7 = !
= : : > = 7
= ;
Q) =
: ; = ) =
= 1
% > : 7>
= ; : 8
; > = = ; 7
8 ; Q
7 > > >
4. ABSTRACT
-: : : : : = = P : :
: : : : : : P Q
= : : ) : : = :
= R = = :
1
(6 : ; :
: > P: : ! ; =
: > P : :
< Q:
: P < : == ;
: == = < 1
5 : : : = ; S
= S
P: P : : ;
: < > :
= P : P: : :
; = 1

9. 5. OBJETIVOS
5.1. OBJETIVO GENERAL
! 8 : ) P !
O > ) = =
) = ; ! ( 7
; ) = =
= 7 ! ; & (1
!
5.2. OBJETIVOS ESPECIFICOS
• ! 8 : ! ) =
; 7 =
) ) 1
• $ = 7 ; ;
P ! 1
• ! ) = : ! O
7 = ; = ! ( 7 1

10. 6. JUSTIFICACIÓN
= 7 = = = =
= = ; 7
1 = = 7
; P Q ;
=T; = 7 # = =
! 1
! P ) = 7
= = 7 = >
=
= >: = 71
( = = 7 > )
= 6 >
7Q
; 1
% # > ! $ = 7
) 7 8
8 7 = >= 7 : ;
= = 7 1
7. ALCANCE DEL PAQUETE
( = = = 7 >
= = ) : ) = =
= 7 > = ; ) = =
7 1
( = ; ) = )
: ; > ) = 7
= ) # = ) ;
= = > = 8
= ;; ; 1
! = 7 = 7 > = =
=
1 + = )
= ; > = = =
= 7 T 1

11. 8. CONCEPTOS BÁSICOS
8.1. ¿Qué es riesgo?
! 7 = 6= ; >
) = =# # >
6 =
; 71
= ) =
) ; 1
> = ; )
= = ; > =
= >
) = 1
8.2. ¿Qué es un modelo?
= = ; > 7
> = 7 )
: 8 = = ! 1
% = = ; =
>
= ) #>
; 1
! ) = ;
= > 7 = >
= )
= 7 ; = )
8 7= = = 7> ;
7 = 7 1

12. Ilustración 1. Ejemplo de Cristal Ball en MS Excel
! : 7
; : = =
= ) = =
= > ) ) ; ; >
: = > 6 1
8.3. ¿Qué es la simulación Monte Carlo?
7 ) # ;8
= = 7
1 ( = =
= 1
8.4. ¿Qué sucede durante una simulación?
7 T =
= 8 = ;
= ;; = ;
1 ! 2333 =
L M ) 1
> ! 2333
= ; L ; 7M
= ; = # : 8 ; 81
; = ; = 1
( = ; 7 ; )
; 1 = ; 7

13. 8.5. De donde obtiene la Simulación Monte Carlo su
nombre?
7 ! ; ! > 7 >
= = 8 Q
> > ) 1
( = 7
! ; > =
1 % 8 = > ; )
T ; @> 2> B> 4> D F = ; =
= 1 (
= = =
L=1 1 = #> = > >
7 = > 1M
8.6. ¿Cómo analizar los resultados de una simulación?
% : 8
= > ; > > )
1 ! 2333 =
= 7 @1 = = 7
>! = 7
= 1
7 = ; : >
@ = 7 7 )
1

14. = ;; > = = 7 1
7> = = 7
; : ; 7 1 = #
= ;
) 1
Ilustración 2. Cuadro de diálogo - Define Forecast
8.7. ¿Qué es la certeza o certidumbre?
! ; = 8 )
= 7 = 1 %
> =
= > ;# = ; = ;;
1 ( ! 6 =
= 1(
8.7.1. Grafica de sensibilidad:
% ; 7 = L ; M
= 7> ) = 1 %
= = G #
9 ;
H ( ; =
; 1
8.7.2. La gráfica de sobreposición:
( = T = = 8> )
# : 8 1 (
8 1 ( : = ;
G! = ; L
M
H1

15. 8.7.3. Gráfica de tendencia:
% = 7 ) = 6
; 1 G7
! ;
= H
8.8. ¿Cuales son los beneficios de realizar un análisis de
riesgos con Crystal Ball 2000?
! 8 ! : ; >
=
) = = = 1
! = >
= = 7 : 1
+ 6 : 8 (6
7 ! = T =
: 8 ; >
: ! 1
! ; ! )
1
! ! 7
= > ) : )
= 1
8.9. ¿Qué es Optimización?
= 7 = ) 8 7=
7 = 1 + : 8
= 7Q ; # =
; ) =
L% 1 0
1(8 M ) 6 )
= ; 1
% 8 = > = 7 = =
; ; 7 = = ;
; ; 1
! : 8 > =
= = = (6 1
; = =
1 ! =9 > = ! > =
=
: ; = (6 > = ;8

16. ; 1 > =9 =
; 7 = ;
; = 1
8.10. ¿Que son los pronósticos de series de tiempo?
= 7 = # = 7 )
8 : 7 = = 1 (
: 7 J = K
1
9. VERSIONES
( = ) 7 = !
= > ) =
= 5 ; 2> = = ; !
! 1
!
• ( 7 ! L ! M
• ( 7 % ! L ! > !
% =9 M
• ( 7 % ! L ! > ! %
=9 > ! - ;M
• ( 7 # + =
P = # = = =
$ = 1 ( =
> = =
) =
2 : = ?PPP1
? 1

17. : ; : 8
!
( 7 # !
• * 7 ( 7 ;# J 7
6 K =
> ) ;
1( 7 : ; @43 = #
71
• * 7 # ( 7 # =
: ; $ = #
: = 1 % ) 7 ;
= 1
- ;# 7 = ; = ; 5 ; 1
7 7 > ) : ; = A
= # 71 %
= 5 ; 7 ; 7
= = : > ;
$1
% = P >
>= U: P )
; $1
= ) = =
) = > ) ; $1
: = = =
=
• ! % = = 7 = L
% % =
= 1M
• =9 > = ; 7 L
% % M
• ! - ;> = = = ; ) =
L 7 % M
• ! - > = 8 7
!
• ! L 7 M
7 = : 1= >
7 = 7 = 1

18. 10. REQUERIMIENTOS DE HARDWARE
• % % ) 433 M
• F4 ,
• B3 = ;
• ! U, L( 7 ! ! M
• - 8 C336F33 = 6
7
11. REQUERIMIENTOS DE SOFTWARE
% 8 ! > ;
P ) = 1
• = 5 P EC> 5 P
( L M5 > P + 413 5
- < % <F
= > 5 P 2333 % > 5 P V% ( >
5 P V %%
• (6 EA> 2333> 2332 LV M
%> 233B1
• (6= D13 = 1L M
• ; ; , 413 = L = =
7 = = M
12. COMO USAR CRYSTAL BALL
12.1. ¿QUÉ HACE CRYSTAL BALL?
! 6 = = ; : 8
(6 = 7 = )
P = 8
1! (6 >
• = ; = 1 ! >
6= >
= ) : = ;
1
• ( J
5: U K = =

19. 7 ) = ;; T
= 1
! =
• % ; = ; =
; : 8 1 > )
= ) 6=
= 1
• = ' &!" $ &> !
8 = 7 )
= ; = ;;
) 1
8 = ;8 ; 8 =
! 1
12.2. ¿Cómo abrir el programa?
! P =
> : = > ;8 ;
: 8 = (6 O1 ( =
; ; (6 ! >
;8 1
% = ! :
; = 8 7 > ;8 ; 8 =
! % : 1% ; 8 =
! > = : T 1 T
= ; = 7 !
: ; = 1
= # ; = 7> ! =
; ; 7 ! ; ; Q
; >= ;; : = 7 =
(6 L= ) :
7 P M
1
Ilustración 3 Barra de tareas ejecutando Crystal Ball
; ! T
+! 1

20. Ilustración 4 Ubicación de Crystal Ball en el menú Inicio
! % : 16 > )
8 = ! 1 ( ; 7 =
; = =
# 1
% = ; ) >
: ) = 7 L M ; ; 81
) L M !
> =
> 8 1
12.3. ¿Cómo Crystal Ball mejora Excel?
: 8 (6 6 : =
> = = 7 : 1
7 (6 ) > =
= Q ) = ;
; 1
! 8 (6 = ;

21. = >
; 1% ! T
; : (6 1
Ilustración 5 Barra de Herramientas de CB
! = ; ; : = =
= ) : 1 =
; = 8 6
= ! 1 7
T ; ; = Q
1
T !( L M ("
> (! - , L M
! (,, (+- L M
1
Ilustración 6 Barra de Menús de Excel con CB
( T!( L M= ! 1
Ilustración 7 Menú Cell
( T ("(! - , L M =
>
1

22. Ilustración 8 Menú Run
( T ! (,, (+- L M
: 7 > : = =
( 7 % ! 1
Ilustración 9 Menú CBTools

23. 12.4. ¿Qué es un supuesto?
( ) : 8 6
; ) = 1 ; (6
= > =
= ; 1
( > ! ;
= ;; J = K) = = ;;
= ; = ; 1 ( ;
= ;; = 7 = ;
; 1 ! ; 7
= = = 1
( 8 = = L! %: M
> ;8
; > L ;#
! = 0 M
1
( 7 = =
; 1
12.4.1. ¿Cómo definir un supuesto?
( = = = =
; > > ; ) ;
1
% 8 = ! %: > = 8
; = ) = ;
1

24. Ilustración 10 Hoja de Calculo del ejemplo CellPhone
% = = ; 7> L @@M
: ; ; 7 J = KL = M 1
; 7 1 =
! > ) ;
= ) L! @@M1

25. Ilustración 11 Cuadro de dialogo Distribution Gallery
Ilustración 12 Distribución Triangular para la celda B11
1 = )
; T ) = ;8 = =
1

26. = = > > 6 >
= ;; 1 ( = ;
) T >
8 = ! %: 1 U = : ;
1% = : ; 7 J = K
L = M
1
Ilustración 13 Celda supuesto % Long Distance (B11)
;
L @3M
1 : ; ; 7
J = KL = M :
1 ; 7
1
; ) = = : ; 43 >
) = B43 4F31 =
7> ; 7 231
Ilustración 14 Distribución Normal para la celda B10
: ; = L M 1 ( !
= = ) 1

27. Ilustración 15 Celda supuesto Actual Minutes (B10)
( = = 7 !
1
12.5. ¿Cómo definir un pronóstico?
: ; ! 1 (
= 7 > ) 7 )
= U = 1 = 7 ;
#> ) Q 0 + > *
= + >!= % , 1
= = 7 ) 1 ! !
7>
= 7 1 = =
) 8 1
( ) = ; 7 & E>
= = > = #
; > = : ; (6 1
L! M =
= 7 L @4M
1 : ; ; 7
J % 7 KL & M 1
% L! @4 & M ;
= =
= LWM
Ilustración 16 Cuadro de dialogo Define Forecast
! : L! M : ;

28. > ) ) = 7 = ! 1
Ilustración 17 Celda pronostico B14
: = 71
12.6. ¿Cómo correr una simulación?
B
! 7 ! =
: 8
1 ( ) J
5: U K
= > = ; 1
% = > ;) ;
U= 7 : ; 7 J
% % K
L =M ; 1
= = L =M !
= = 1 :
BE3 ! " BBX1
3
http://www.decisioneering.com/models/beginner.html

29. Ilustración 18 Nuevos valores para el modelo al correr la simulación
(6 : 8
= 7 W21DB1 ( ! :
W41F@1
: ; 7 J
% = KL =M ;
: 8 =
= 7 ; 1
= ; ) U= 7
= = = # 1
% ; 7 L
X M)
> 433 B3X = =
>: ; 7 J
, K ; 1
% = > ) 8 = >
7 J
(8 7K L,
% M = 8 7
> ) ; T )
1

30. Ilustración 19 Cuadro de dialogo Run Preferences
#( T 6 @3333
: ; 7 J
(8 K L, M
L ;
= = =
(8 7M
1
; = 7 Y:
= U 1

31. Ilustración 20 Gráfica de pronósticos para la celda Cost Savings (B14)
12.7. ¿Como analizar los resultados arrojados por el cuadro
de pronósticos?
7 = = 7
8 >= 1
#% ; =
1
( = 7 = ) =
; = = =
> = = ;
; = = 7 1
; T*(, = 7 L M
= ; 8 = 7
) >
6 ) ; = =
= # > = ! %: 1

32. Ilustración 21 Cuadro de estadísticas para la celda B14
( = 7 = ; :
= 8 1 % 8 =
= ; ) C3X :
W @1A31
Ilustración 22 Cuadro de Percentiles para la celda B14
( : ) W 41F@ ) : ; = :
; ) = ;
: = 1
: = = ; 7 ! 8 ;
! ; L !: M
1

33. 12.8. ¿Cómo usar el cuadro de sensibilidad?
= ; = ; =
; > = )
= 1
% 6 = ; = 7 =
: # $ ! 1 %
> : ; 7 J
! ; KL
!: M 1
Ilustración 23 Cuadro de Sensibilidad medida por el rango de correlación
=
= 71 : ; ; 7 %
&
L! % M> =
% L% ; M: ;
> = 7 $
' > ; ) = L
M ; A41B X ! : 1

34. Ilustración 24 Cuadro de Sensibilidad medida por la Contribución a ala varianza
; )
7 > ) ) ) :
: ; > : ) 1% !
" 7 = > ) = 8
> 8
(
+ ! = T
= > ;
: T ) = = 1
8 ) = ) :
= > = ; =
= 1% = 8 = > ; )
7 =
> = =
= Q > 1
12.9. ¿Cómo generar un reporte?
% = 7 ! 1
% : ; ; 7 J
! = KL! ,= M
: ! 1

35. Ilustración 25 – Cuadro de diálogo Create Report
=
) ) ) = = ) $ LZM>
= = ; LZM >
7 ; = LZM
>
; = 7 (6 LZM
Q
? = ; ;8 ; )
;8 LZM
1
( = ) ! > 7 )
: L 7 2DM1
8 7 ; T = = >
= 8 = $ > =
= ) : : : ;
) 8 1
#( ; = ;
71 ! : = )
6= > = =
= 1

36. 12.10. Otros recursos
12.10.1. Distribution Fitting
: 7 ) = = >
= = 7 ; & = ; ; 7 J K
&
J ; 0 K
1
Ilustración 26 Galería de Distribuciones
Ilustración 27 Cuadro de dialogo Fit Distribution

37. 12.10.2. Correlated Assumptions
: ; = > 7 >
7 ) =
71 ( : : :
: 8 ;8 (6 1
( ; 7 % ) = )
= 1
Ilustración 28 Cuadro de dialogo Correlación
12.10.3. Precision Control
( ! % 7 ! = )
) T 8
= = = 1 ( = 7 ; 7
% ! 1

38. Ilustración 29 Cuadro PrecisionControl
12.10.4. Overlay Chart
) = = 7 > J : K
= T = = 7 ; 7
1( : = ; ; T (
Ilustración 30 Cuadro de dialogo Overlay Chart

39. 12.10.5. Trend Chart
* + T = = 7 > =
; ; = ;
1 ( : = ; ;
T (
Ilustración 31 Cuadro de Tendencias
12.10.6. CB Tools
= = = ) 8 7
! = : 1
12.10.7. Example Models
! : 8 = ) =
;8 = = : = 7
= # T 1

40. 12.11. EJEMPLOS DE APLICACIÓN DE MODELOS
12.11.1. PRIMER EJEMPLO. “Futura Apartments”
( 8 = > = = 8
& = 1 7 ) = 7
B3 ; ;8 =
71
Ilustración 32 Hoja de Calculo “Futura Apartments”
! ;8 : =
• WD33 = =
• ( T )
B3 43
• = 7 = W@D1333
= = = 8 >= =
= > ) ; ) ;
= 8 = ;
= 71 ( = : : 8
: ; L ! M
> ) =
= = )
(6 1
> ; : 8
: ; : = ;8 #
J
5: U J> ) =

41. 1 / ) ;
)
71 ! ! ; 1
Correr la simulación
% 7 ; =
• ,
• 8 7 ! 7
= 7 6= 8 = * +
* " ! + = # : ;
8 6 = LD33 = M>
; 1
( = 7 = # T 6
> = 1
Ilustración 33 Pronósticos de Ganancia/Perdida para FA
• =
• % 8 7 = 7 > ;
: > , [ =1
+ 1 = 7 =
(6 7> = >
= [- ;1

42. ( = 7 = =#
= : = 7 & = 1 ! ;
= = ; = ;;
1 ( =
= ;; > = W2D3
W 4AD3 = 1 ! ;# = = > )
= = W2333 8
) WA3331
Determinar el beneficio
: = ! = = ;;
; >
= ;; 1 % = ;; > ;
= ; ; = 7 8
• % $ = )
) = 7
• ( ; 3L M =
• %
Ilustración 34 Probabilidad de Ganancia para FA
( = ; L! M ; = 8
= ;; = W =
3
: = > ) : : 1 !
7> 8 = 7 =

43. 7 & = 1 -
7 B> =
; L0 W3M = 6 EBX1
+ ;# ) = W2333>
; > : 1
Como usa Crystal Ball la simulación de Montecarlo
( = ; ; )
: = 8 ) 1 (6
: ; = = ;
1 7 # )
) T ; T
T = 1
( = ) T :
)
• 7 6
• ( 7
( = 7 8 ; ;
U = ; 1, ) 7
! = = 6 7 1
! = = : 8
> ; 6 = ;
= : )
= 6 = ; 1
! ;# = ) ;
= 7 8 1
% = 8 =
• , [,
• = =
; 1
•
• 7 ; = 7
= 1
• ! : 8 8 =

44. 12.11.2. SEGUNDO EJEMPLO. “Vision Research”
( 8 = 7 : ) =
6 : !
: = = 1
( 8 = ) * , :4 7
; 1 = * , : :
= > ! U
* P> ) = 1 ( = =
= = ; = > =
= 7 6 $ & = ; = 1 )
;8 ; = = > #6
) & = ; = 1
* , : = ! )
; =
> = ; 1 ( = ! * P
= 1 ! =
= = 7> $ =
1
% ; ;8 ! 7 =
• ; : 8 ' =
8 = ! > T ! [% [
! [ (6 =
: 8 = * , := = !
* P = > 7 2B1
4
http://www.crystalball.com/models/pharma.html

45. Ilustración 35 Hoja de calculo ejemplo Vision Research
( : 8 = ; ) * , :
1
Definir supuestos
( ! > = = = U
; 7 = ;; ) ;
; ) 1 % >
; : @A = ; 7 )
0 ; > 0 ;
; : ! >
; = 7 = L 7 DM
1
G7
! ; ) = ; 7 H1 ( =
= = ; 7 ;
= ) = ;1 ( 8 = >
U = : 8 * , :
8 ; = ;; ) 6 ;
; = ! * P1

46. ( 8 = > 6= = ; 7
= = = 1
Definir Testing Costs. La Distribución Uniforme
: > * , : : W @313331333
! * P = WB13331333 W
D13331333 = = ; > ; = ;
1% ; > J- K*
> , : )
) WB13331333 W D13331333
= ;; 1
! > * , : 7 ; 7
= ; J
- ! K = ;1 ; 7
; 7
6 6 = ;;
) > ; 7 ) 8 ;
8 = 7 = $ = ! % ;
= 1
= ; 7> =
U = 1 % = = -
!
• !D
• ( T > : ; = 7
= : ; :
! 1( J $ ) , - =
+

47. Ilustración 36 Cuadro de dialogo “Distribution Gallery”
• ; ; 7 ( '
• ,
( J ; 7 K =
Ilustración 37 Cuadro de dialogo “Distribución Uniforme”
) !D ; ; : 8
> ; = = J = + K
; = 1 ; = ; >
; 1 > ) ! =
; 71
; 7 = >
6 1 * , : = = ;
WB13331333 6 W D133313331
) = = = = =
; 7 ! >
• ( ; B = L ) T : 8
= 7 M
1
( = WB13331333> ) *
, : = = ; L- ! M
1
• % + 8 =

48. • ( ; D =
( = WD13331333> 6 =
= ; L- ! M1
•
; 7 ; = 8 ; ) : : :
> 7 2F
Ilustración 38 Distribución Uniforme para la celda C5
= >
; 7 ; = 7 2F1
> = = 1 = #>
7> ! = ! )
D
B D 7 1
• ! = : 8
Definir Costos de marketing: La Distribución Triangular
* , : = ; <
! * P> = ; = & 1 ( =
= =
= $ = ; = =T;
= 1
= ; > * , : = W@213331333
W @C13331333> W@F13331333 = ;; 1

49. * , : 7 ; 7 = ;
! < > ) ; 7 ; 7
= 6 > = ;;
1
% U = = ! < L <
! M
• !F
• ; = 7
= : ; : ! 1 (
J $ ) , - =
+ 1
• ; J ; 7 - K
•
( J ; 7 - K =
Ilustración 39 Cuadro de dialogo “Distribución Triangular”
: = ) = = ; 7 1 !
= ; 7 2A> = =
; 7 = =
; 7 1

50. • ( ; @2 =
( = W@213331333> ) *
, : = ! <
• % = = ". / # $$ 0
(
@F> ; 1
( = W@F13331333> = ;; =
! <
• % ; @C =
( = W@C13331333> 6 =
! <
•
; 7 ; = 8 1
Ilustración 40 Distribución Triangular para la celda C6
7> ! )
@F @2 @C1
• = : 8
Definir pacientes curados: La Distribución Binomial

51. ) & = ; ! * P> * , : ;
= ; ; @33 =
$1 * , : = ) & = ; =
! * P = = 23 = >
) ) T 1 ( = ; > 23X
= ; 7
= # ! * P= $1 * , :
> = # = ; = )
= 8 #6 2DX1
% ; > J
= K*
> , :
= ; = >) #6 2DX1
G* , : = = & H1 !
> * , : 7 ; 7 ; = ;
; ) = 7Q ) ; 7
; ; T 6 L2DM T
= L@33M
1
% U = = J
% K
> =
• !@3
• ; = 7 ( '*
; =
• ; 7
•
• ( * $ ) + = 1 L&8
) = = = = ;; 31D
D3XM
1
•

52. Ilustración 41 Cuadro de dialogo “Distribución Binomial”
• ; 7 ; = % ;;
L $1M L 0( ; ) * , :
= 8 6 2DX = ; = )
> 312D = =
= ;; = = ; )
6 1
• 1 = 6= = ;;
3 @> 313B> T
= 8> BX1
•
• ; ) & = ) * , :
= ; @33 = > @33 = 6=
; 7 ; 1%
=
•
• ( ; 312D =
• ( = 2DX = ;;
=

53. • = @33> = $
• ( ; @33 =
• ( = @33 = )
= & 1
• :
• ; 7 ; = 8
•
Ilustración 42 Distribución Binomial para la celda C10
7> ! T 3
@33> = ) =
& 1
• = : 8
Tasa de crecimiento: La Distribución Personalizada
* , : : ) = = 6
4313331333 = ( = 8
3X DX = 7
$ ) ! * P = ; 1
; > = < : )
6 = ; 2DX ) = =

54. = 1 ( = =
! * P DX @DX1
( ; J
- = K = =
; 7 =;; 1 % )
; ) T > *
, : ; 7 = ! =
1 % > ; 7
= = ; ) =
; 7 = 1
( # = = = ; 7
= = ; >
; = 1
> : 0 = ; >
= = = B1
; 7 = =
7 = ! * P1 % U
= = =
• !@D
• ; = 7
• ; 7 L% M
•
( ; 7 % = 1 +7
) 7 B@ ) =
; > ) 8
8 1

55. Ilustración 43 Cuadro de dialogo “Distribución Personalizada”
% =
• ( ; 3X =
( = 3X =
• %
• ( ; DX =
( = DX =
• %
• ( ; ADX =
( = = ;; ) = *
, : = 7 = = 7
* , :1
•
; 7 3X DX = 1

56. Ilustración 44 Distribución Personalizada para C15
%
• ( ; U@DX =
( = @DX 7 =
• %
• ( ; UDX =
( = DX 7 =
• %
• ( ; 2DX =
( = 2DX = ; ) = *
, : = 7 = = 7
DX @DX
•
; 7 = @DX UDX = 1
; = : *
$ +
1

57. Ilustración 453 Distribución personalizada para C15 (2 Supuesto)
% ; 7 = T
= : 8 ;
= 1 (
7 ! )
= = 1
• = : 8
Definir penetración en el mercado: La distribución normal
( = < ) = 7
= = 7 = * , :
; CX
7 2X1 J+ ; K )
* , : = ; =
FCX = ; = = 7
7 = ;8
7 = >
FX @3X1
( > CX> )
>
= ; = 1 = <

58. DX> = #
= = 1
* , : 7 ; 7 = ; ;
J < % K %
1 U = =
= 7
• !@E
• = 7
• ; 7 +
•
( J
+ ; K =
Ilustración 34 Cuadro de dialogo “Distribución Normal”
: = ) = = ; 7
7
• = C133X> ; CX
= ( = = CX =
= 7 1
• %
• ( ; 2X = !

59. ( = 2X = 7 1
•
• ; 7 = 8 >
) ; 7 ; > ;
= = ; 1
• %
• ( ; DX = = ) = 7
=
• ( = DX ) =
= 1
•
• ; 7 ; = 8 1
Ilustración 35 Distribución Normal para la celda C19
7> ! )
; 7 ) CX
= ;8 DX ) 1
= : 8 1
Definir pronósticos

60. = # U = > =
U= 7 1( )
U = 1
= * , : = ;;
; = > = ;;
; > = 1 (
= 7 = ; L!2@M ;
L!2BM= = ! * P1
Calcular el beneficio total
! = = 7
71 ( > = = ;
; U= 1 %
= ; 1
• !2@
( = ; =
= : 8 1 !@F @E 231 !
! !
= ; =
= = = # $ L!@FM =
= 7 L!@EM ; = L! 1
23M
= # = ;
> = U= = ;
1%
• ( T : ; = 7 "
( J % + = 1( =
; = = 7 1 ; > )
= 7 ; : 8 >
; = = 1 % ;
; ; 1

61. Ilustración 36 “Definir Pronostico” para C21
• %
• ( ; J K = # > =
) 8
• = : 8
Calcular el beneficio neto
U= = ; >
; = ;
• !2B
• ( = ; = =
: 8 1( ] L! !
@@Q 2@U! U! DM
AQ 4U!
& = ; L!@@ * M
>
; L!AM ;
L! 1
2@M ; > & = ; L!@@
& M
> ; +
L!4M ! ( L! )
DM : : 1
% U= = ;
• ( T : ; = 7 "

62. Ilustración 46 “Definir Pronostico “ para C23
+ ; = ) = =
= ) 7 = #
1
• %
• ( ; J K = #
• = : 8
> : = = 7 =
* , :> ; : 8 )
; = Q
71
Correr la simulación
! 7 ! >
; 7 ) 1
1 = T -% 8 = >
7 =
= = T 1 7>
1
= 7> = ) T
> ) 7 8
= 7 1
% = T
• = 7 $% &[ ' T
• ( J
, % - K = 1
• ( = .' ' '/ ( &L 6 M
>
; D33

63. • (L M
• = 7 J ' 0 ! ( $'
'/ 1L T M
• ( = ) ; EEE
•
Ver los cuadros de pronósticos
; ) = 7 =
; = 1 ; > 6
= 7 1 (
: = 7
; 1
= ( ( ** $
( ; L0 % M = >
7 BC
Ilustración 47 Cuadro de Pronostico para “Net Profit”
= 7 2" * + ,& T
" = %
> 1
7 > ; 7
= = 7 = = 8 ;

64. U= 1 ; 7 =
;
; 7 T
= 1 ( 7 BC>
; 7 = 7
+ @F = = )
1 ( ) @F
= 1
, ) = 7
= ; 1 =
) 7 = > ! T
; 7 = U= )
8 6 1
Interpretar los resultados
Entender el cuadro de pronóstico
! = = =
* , :1 ; > = 7
T 6= > ) =
8 ) 6 6 = 1
( 7 BC>
W @41A : W B414> = 7
+ 1
( = 7 ;# ; =
= 7 1 % > ;
: = 1
! = T ;
T > =
; 1 ( 8 = : ;
@33X> ) ;
= ; 1 , ) ; = 6 7>
) : 8 = = 6
1
( ) = ) >! T
) 8 = = 7 1 ( =
= : > = 1
; ) 6 = > T

65. 6 = )
71
Determinar el nivel de certidumbre
: = * , : ) ; )
= ; = ;
= 1 % ;
=
• ( = 7 + % >= -;
• ( ; 3 =
• % (
! ; ; =
) > = = W313
; 1
= J
+ % K
> = ; )
;
; AE1C3X1 ( ) * , :
AE1C3X = ; ; 1
= = ) 6 = ; 2312X
= L@33X AE1C3XM
1
: = * , : ) ;
; W 2133313331 ! !
= = = 1

66. Ilustración 48 Pronostico para “Net Profit” con valores positivos
• ( ; 2 =
• %
! 7 BE> !
; W213 ; 1
Ilustración 49 Pronostico para “Net Profit”
* , : = ; AB1F3X =
; W2133313331
* , : ; =
= 7 1 : = ; )
= ; ; W4133313331
! ) * , : =
; W413331333 ; > =
= = = 7 = 1
>! = = = 1
• ( ; 4 =
• %
! ; W413
;

67. Ilustración 50Pronostico para “Net Profit” (2)
( = 7 J
- & 7 4@
; FFX1 ! ; =
; W4133313331 * , : ;
= ! * P =
= 1

68. 13. CRYSTAL BALL TOOLS
: ! = * )
= 1 % 7
:
= = 7 >
7> ) = 7
; )
= 1
( : ) ! = 7
D
:&
! 7
( - !:
=
-; =
(
7
7 ;
> 8>
= ; > 8
5
http://www.crystalball.com/crystal_ball/cbtools.html

69. 13.1. Herramientas de Montaje del modelo
7
13.1.1. Batch Fit
: & : = ;
F
= 1
! (6 ; :
! > T! - = = >
: &1
13.1.2. Matriz de correlación
( : ) = 6
= = Q : =
) ;8 = > >
;
7> = :
= ) 6
1 = >= 8 = 1
13.1.3. Tornado Chart
( = = ) ;
; ;8 > 8 6
; > = = 1
6
http://www.crystalball.com/spotlight/spotlight10.html

70. 13.2. Herramientas de análisis
13.2.1. Bootstrap
( # = = 7 ? ;
= = = 7
= 1 > : )
; >
= = = 7 >
7> 1
13.2.2. Escenario de decisión
( = =
6 ; 7 = >
7Q
71
13.2.3. Análisis de escenarios
) = ; =
> ) = ; =
= ) = = 1
( = 7
= > = = 7>
7> = > 1
13.2.4. Simulación Bidimensional:
= ; )
= = 7 >
7 =
1
( ; ) ; =
= 7>
7 ; = L )
= $ ; 6= M
>
) L: M
>
7 ; 67 >
= >

71. ; T
=
; L 7
T = M
14. ANÁLISIS DE LAS HERRAMIENTAS
: = = ; =
8 = )
1 7 8 = =
: L 8 M =
>
= ; =
7 1
14.1. Herramientas de Montaje (Setup Tools)
% : 8 =
; * *
! 7 ; 1
14.1.1. Batch Fit o Herramientas de serie
Ilustración 51 Asistente de Batch Fit
( # = ; = ;; T =
> = ; = ;;
L > > > 1M = ) T
= = 7 ) ; 1
# = : =

72. 7 > 7 = >
; 7 = ;; ; = )
8 1
( : = > =
> = ; ; 8 > ! U
: > Q
7 = = ; = ; 7 )
8 = = 7 7
1
( : = : )
= = ; > =
= ; ) 8 Q
> = (6 > = >
8 ) 1
Ejemplo
( = ; = 8
; ! ; >
Q= 8 ; ;
= > = = @EEC 233B> =
= : ;
= 7 ; 1
% 8 :&
( = = ; : (6 >
; ! > T !- : 1
= : &> = @ B
; 1
( = 2 B = >
=
= =
1
> = 7
> = ; : 8 1
! ; =
: 1
= 7 7 >
; 7 = ;; = 1

73. % B B
)
= 1
( = = ; 7 7
>) = 3 @1
= = 7 ; 7
>= = = 1
: > = : 8
! = = = T 7
(6 > ; = = ; :
= 1
( T, = 7 = ; =
7 T
7 ! >=
^ = 7 ,
:& 8 = > = =
>
= = 1 % :
= 1
Ilustración 52. Vista “Statistics”. Observese que el coeficiente de variación es del 9%.
: 7 =

74. = > 8 ! % >
= = = 7 8 = 71
! : J : &K 8 >
= ; 7> 8 ; 7
= $ > )
1
( ) = )
= 7 L& M= WD1233> =
; 7 = E@>2X = 6
= ; = : ; 1
Ilustración 53 . “Frequency chart” del ejemplo

75. 14.1.2. Matriz de correlación
Ilustración 54 Matriz de Correlación
) 6 ;
= = > =
= 7 U= >
= 7 = 7
; =
= 6
= 71 = ; ; =
) 6 >
A
(6 7
7 =
( 7 $ ) ;
7
Cárdenas Héctor, Curso de Econometría, capitulo 2. Profesor de la Facultad de Ciencias Económicas de la
Universidad Nacional de Colombia

76. = L ; 6=
6= M
> = 7 = 7
= Q= 8 =
=
/] @2>B2@4CEEC _ 3>3EACDFCB V _ 3>42F4442@ V 3>4DBF4CFA V
@ 2_ B
- ; 67 6=
V@ = 7
V2 6= 7 = 7
VB 6= 7 Q
; ) : ; 6 )
= ;
= ; 7 6= > >
/ = 7 = 7 ! ;
7
7 6 ; ) ; 6=
= > ) ; 7
Q = =
) ; > = ; ;
) = = 1
7C = 6 ) ;
= 6= = 7 > 6
7 = > )
: @ = 6 ;
8 7 6 1
8
Mide el grado de asociación lineal entre la variable dependiente (endógena) y la independiente o exógena,
eliminando el efecto de las demás variables del modelo

77. ! = T = ; =
= 7 6 )
; > = 7 ; =
> >= > 1
( = 7 ; : =
T !- > = 7
= = > =
7
= = 1 > = =
: 8
> ; = : = )
71
7 = =
= >
$ 7 ; > =
: 1
Ilustración 55 – Matriz de correlación
7> ! ;
8 >= ) 1
Ejemplo
! 8 = * ;
> = ; 7 =
L > = 7 7M ;
6= > Q
7 = = 1
7 T
= 81
% 8 ! 7>
; ! (6 ; :
! = 8 LK K>
M
8 = > > =
= 7 L D33M>
LEEEM ! 1

78. , 7 = 7 J K
7 L M
1
= 7 = ;
7 DF1
Ilustración 56 Cuadro de EStadisticas
!- > 7
= 7Q
; ;# = = = :
; ; = 8 =
1
( $ >
= > = 8 7 1 (
7
2333
233@
2332
233B
! 7
2333 @>333 3>233 3>B33 3>@33
! 7

79. 233@ @>333 3>@33 3>B33
! 7
2332 @>333 3>433
! 7
233B @>333
( ; ) 8 ; ) >
= ) ) =
J K = = >
7 8 1
> 7
! 1
7 = 7
> ) =
1
14.1.3. Cuadro Tornado Chart
Ilustración 57 Asistente de Tornado Chart
( : = ;
> # 7> )
: = ; = > 7 = ) ; >
; > = = Q
; > ; = 1
= ) ; ;
= 7Q ) ; >
: # ;# ; J
= ; 7

80. = K J = # K
1
( - : = = ; 7
`- !:
` = !:
) = ! ) 2D3 ;
= : = : 1
Tornado Chart
( : = ; ;
= = > = 7
= > $ = 7= 6
= 7 = ; > >
) ; = 7
( : = ; ;
! > ;
8 ; > :
; 71
; 7 )
; = 7 Q= ; ) =
= 7 $ ; )
81
(6 = 7 = ;
> 6 7 ;
# = 1 6
= 7 = = ; > ;
7 U
= 71
Spider Chart
$ 6 6
= 7 = ) #
; = ; 1 ! =
> = > ) ;
; ; = 7Q )
: = ) $ ; = 71
Ejemplo:
% 8 = ; ;
: 8 ) # >= )

81. = = 8 1
; T !- > - !: > =
> ;8 L= @ BM1
!
; L= 2 BM
= 1!
) ; ) ;
1
! 1
( = B B ; = =
L @3X E3XM
T = L DM
> =
6 L 8 =
= 7M
( = 7 = = 7 ( #
- = = = ; 1
= 7 - !: = !:
! 1
: - !:
= !: >
8 = = : 1

82. Ilustración 58 - Tornado Chart
Ilustración 59 - Spider Chart

83. ( 8 = > 4 = = >
; >
; > = 7
; ; = ; 81
- !: = !:
; ) :
= ; ; = > =
= = ; =
71
8 = : =
6 = = ; ;8 >
6
@33X > 7 = ;
= ; : = = ;
1 ( = ; ; )
7 7 ; 1

84. 14.2. Herramientas de Análisis
14.2.1. Bootstrap
Ilustración 60 - Asistente para Bootstrap
( # ) ) 6
= 7 Q
: ) ; 7
= 6 > =
1
: # ; >=
) = ; 7 >
= = 71
! ) = ; => = 6
> = ;
; > = 7 ;
> = =
# 1
7 ; 7 =
; = ; ;
1
(6 # =
( # = ; = # 7 T

85. ( >
= ; )#
7> 1 7
; = 1
( ) = # = ; =
7 6
= 7 ; 7 ; = >
; Q # 7
= ) > ) = 8 7 7
: ) # 71
14.2.2. El método de la Multisimulación
! = >
; 7 > = =
7 = =
7 = > ; 7 7
L M%1 = 7
= = = 7 = ; =
71
( # 7 ) = ;
= # > = # : > = ;
5 6 > U5: > Q =
= ; 7 ) = :
Q ; = =
; 71
( ; = = ; >
= 6 = >
# = 8 >) ;
T = = ; =
= = 1

86. Ilustración 61 – Comparación única simulación vs. Multisimulación Fuente: Tools tutorial
14.3. Ejemplo:
% = 8 = > )
= = ; > 7 ; 1
( ) : ; )
= : ! Q =
; (6 ; : = 8 = = >
= : ) = ; ! =
8 ) = 7 1

87. Ilustración 62 – Vision general Modelo “Planta energia nuclear”
!- > = 7 =
; = ;8 )
1
6 =#
= = 7> 7
= = 2 B ; )
# T 7 = ; = #
) = # 1 ! 1
( = = B B = )
= T > = =
D33 > $ 7 = 7 1! 1
T, = >
= 1
= = 6
@X EEX> = 1

88. % 7 ; =
= > > 7 > >
> < 7Q
= = =
6 > : 1
=; = = = 7
= = ) = ) >
) ; = 1
Ilustración 63 – Frecuency chart para la variable “Mean”
! 7 L M
7 > = ;
; = ) ) 1
( 6 7 )
Q = ;
7 >
7 > ; 7
; 71
% = 8 > 6=
; = > $ 7

89. (
*
^
!
<P
7
7
, 3>C2 3>C2 3>32 3>33 3>33 B>3A 3>32
!
3>AC3 U U U U
@>333 3>3EA 3>3EA 3>3@4 3>@FB 3>@2B
@>333 U U U U U
3>3EC 3>3EC 3>2EB 3>3FA 3>@@E
7 U
( @>333 @>333 3>@CF 3>@A2 3>EEE
* U
@>333 3>@CF 3>@A2 3>EEE
<P U U
@>333 3>BFD 3>@CF
^
@>333 3>@AD
!
* 7 @>333
Ilustración 64

90. 14.3.1. Tabla para la toma de decisiones
Ilustración 65 - Asistente para la Tabla de decisiones
; 7 ) = >
) ; = = >
8 ; = = 1 + ;
; > = ; )
; 7 ; = 71
( : ; = 7 ;
7 ; 7
= 71
% ) ; 7>
) = = 7
> 8; =9 ! 1
+ ; =9 >

91. ) : Q = ; J= 9 K
= J K) ; !
: 7= = 7>
; 1E
Ejemplo
! 8 ! 7 ; > )
; 8 = 7 = )
; = ; >
7 = ; 7>
= ; =
8 = 1
% ; : ; ! >
TJ K = T
7 T
> EEE1
• 7 ! > ;
; = = =
: T, 1
• ! ^1
• = 7 !- > ) = ;
7> ;8
1
• ( 8 = 71
E
!; ) : :
= ; ! % 233312> 7 = 1

92. • ! > = 7
=
• ; 71 ! 1
) = = = = ;
7 ) 1! 1
= )
= > $ ; > T =
7 L= ; ; D33M !
1 1
L3>BFCCCCCEM
L3>BAAAAAACM
L3>BCFFFFFAM
L3>BEDDDDDFM
L3>43444444M
L3>4@BBBBBBM
L3>42222222M
L3>4B@@@@@@M
L3>BFM
L3>44M
%
L@BD33M 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE @
%
L@BCBB>BBBBBM 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE 2
%
L@4@FF>FFFFAM 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE B
%
L@4D33M 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE 4
%
L@4CBB>BBBBBM 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE D
%
L@D@FF>FFFFAM 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE F
%
L@DD33M 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE A
%
L@DCBB>BBBBBM 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE C
% 3>C@ 3>C2 3>CB 3>C4 3>C4 3>CD 3>CF 3>CA 3>CC 3>CE E

93. L@F@FF>FFFFAM
%
L@FD33M 3>C@ 3>C2 3>CB 3>C4 3>CD 3>CD 3>CF 3>CA 3>CC 3>CE @3
@ 2 B 4 D F A C E @3
: 8 7 = ; 7 )
; 7> = ;
= = 71
% > = =
;# 7> )
7 7 = Q
; 6 : T = 8
7 ; ; 7>
: = > 1
% 7 = T = 7
; > $ > ) 6=
# > )
L > > 1M
= = 7 7=
J ; 7K > > ) = ;
> 7 )
= = > ) 8
= ; 1

94. = >
= > = ; = ; 7
=
= ; 7 >
G ( ; 7 >
H
= (6
= $ ; > ; > =
= ) $ = 7 ; > = a G 8
= 6=
= ;
! = ; 7
= ; U
* 1
1
G
= ; 7
;
=
; H >
G
>
* >
!= 7 =
= 7
= 7

95. ; 7 742 > = ; 7
) = ; >
) 7 8 8 = 8
= > 8 ; 7 ; @D31
% = ; 7>
7 J K
, 8 >
; % 71 ( ) =
= ; > :
1
14.3.2. Análisis de escenario
Ilustración 66 - Asistente para el análisis de escenario
( = = =
7 > ) !
= 7 ; = 7>
= = > = = L@XM
) = = EE =
; 8 L@X1M
%
= 7> ) = > ) = : )#
= ; 1
Ejemplo
J
= K
>
; : = = =
> ;8 = = > =
; > = = Q :
= )

96. = 8 7 = > =
= =
= ) 1
! = ;
! ; : :
( > 7 = 6= 7
= ) ;
( = = ; : 7 =
(6 > :
T!- > ! Q =
;8 = 7 7 1 !
1
( 7 = 7 > = )
= = 3 @33 = 1
8 7> = =
;8 = 71
% 7 ; ) @333 T
6 = > =
233B> ) 8 = ;
= 1 /
; T =
1
, 8 = ) ;8 =
= 7 : > @333 =
= 7Q ) = 3 @33> =
; @333
= 7> = : Q
; = )
! 7= 1
= ) 8
J ( K = 7
; = ) :
= 7Q ; 6 = = ;>
; =
3: @331
% > = = =
= =# 76 1 % = 7
> = ) = = = =

97. (6 EA (6 23331
( ) ) = ) ;8 !
(6 EA 2333> ; ;
= > ) = ; = 1
% 8 = =
= 7 > 1
= : = 7
: 1
( = > )
1
( ) > = = 7
; )
% > 8 = 7
= > = =
; = = >
) 7 >
) = 7
1
A1 9 = = ; 1
, <
-
-
,
=
!
$
=
7 L!
7
M
3>3@X 3>AD BBE@4EF>3DF BEEE>ED3FE DX 22X
3>32X 3>AD DEED@FE>42B BEEE>EC242A DX 22X
3>3BX 3>AD 4F2BA4F>@B@ BEEE>E23@BE DX 22X

98. 3>34X 3>AF D2C2BCB>3@E 4333>@3EAD DX 2@X
3>3DX 3>AF 444CF4D>AAA BEEE>ECFC34 DX 2@X
3>3FX 3>AF 4AA3B4F>ADD BEEE>E4D@ FX 2@X
3>3AX 3>AF DCA@@BA>C4D BEEE>EAEBCD DX 2@X
3>3CX 3>AF 4B3B@@@>AB@ 4333>@3@F2F DX 2@X
3>3EX 3>AF D4F4C2E>@CA BEEE>E3342F 4X 2@X
3>@3X 3>AF 4E3B@24>@2A 4333>@@BBCB DX 2@X
3>@@X 3>AF 4EACAB4>FA4 4333>344ED 4X 2@X
3>@2X 3>AF D@@4C24>BDC BEEE>E4B3FD DX 2@X
3>@BX 3>AF 44CFD@3>CFD BEEE>CCE242 FX 2@X
3>@4X 3>AF 4D@ABFF>E32 BEEE>CDFFE2 FX 2@X
3>@DX 3>AF D2F24@F>E4F 4333>3B2CEF FX 2@X
3>@FX 3>AF BCD2@BE>C 4333>342D4C DX 2@X
@>FDX 3>AC D4ABE@A>4EF 4333>34BEC4 DX @EX
@>FFX 3>AC DDDBECE>42A BEEE>E2DCAD DX @EX
@>FAX 3>AC DD3D32B>4D@ BEEE>EE3D4B DX @EX
@>FCX 3>AC D22EDDD>E42 4333>3D4CE@ DX @EX
@>FEX 3>AC 4CF4AEF>23B BEEE>E@4BF2 DX @EX
@>A3X 3>AC 4CE3F43>F2D BEEE>EA@E3@ DX @EX
@>A@X 3>AC 4FEE2@D>B2B BEEE>E3BFCE 4X @EX
@>A2X 3>AC D3D4AFF>EC2 4333>@AEBEE DX @EX
@>ABX 3>AC DFCBF33>AF@ 4333>2@@3FA 4X @EX
@>A4X 3>AC 4AC33A4>E4 4333>@@@CE4 DX @EX
@>ADX 3>AC 44CC3FA>2D4 BEEE>E3F4C DX @EX
@>AFX 3>AC DDE2CD3>EA4 4333>3F22@F DX @EX
@>AAX 3>AC 4@E3D4B>3EA 4333>@@@DDF DX @EX

99. @>ACX 3>AC D3@@BC@>EDF 4333>3D33E FX @EX
@>AEX 3>AC DC2@42E>A4B 4333>@4DACA DX @EX
@>C3X 3>AC 4FE@D4C>4DC 4333>3DE@D2 DX @EX
@>C@X 3>AC 423@@C4>E42 4333>2B@BAA DX @EX
@>C2X 3>AC 4A4B43B>22 BEEE>E4ABE@ 4X @EX
@>CBX 3>AC D@2ABCB>EB4 4333>3DE@CD FX @EX
@>C4X 3>AC DB2DD34>BF2 4333>@2DF4E DX @EX
@>CDX 3>AC BFAFD3B>3F@ BEEE>CCE4CE DX @EX
@>CFX 3>AC 4CEA@AA>B2F 4333>3BA3A DX @EX
@>CAX 3>AC D3D2@F4>4AF BEEE>AE24DE DX @EX
@>CCX 3>AC 43AC244>2FC BEEE>EB@@@@ FX @EX
@>CEX 3>AC 4DEB3C3>B@2 BEEE>E@34F4 DX @EX
@>E3X 3>AC 42D2@DF>B3@ BEEE>E4D3FF DX @EX
@>E@X 3>AC DDBED@E>F BEEE>ACAAAF 4X @EX
@>E2X 3>AC DCC44F4>@@@ BEEE>EAAFFA DX @EX
@>EBX 3>AC D@CEBD2>E4D 4333>@4F@FA DX @EX
@>E4X 3>AC F4ADCF@>3@C 4333>3@3CDA DX @EX
@>EDX 3>AC 4FA33D@>44E 4333>3DF4@D FX @EX
@>EFX 3>AC 4DBF@BA>A@E 4333>33FAAD DX @EX
@>EAX 3>AC 44DBA33>FD@ 4333>3CB424 FX @EX
( = )
Q ) ) = 7
= > = ; ; )
) ) = 7
) 7
= = =

100. 14.3.3. Simulación bidimensional
Ilustración 67 - Asistente para la simulación bidimensional
;
7
;
= ; = = ;; )
= ) ; 7 = ;
1
( = = ) = ;
71 (
7 ; =
= 1
* ;
( ; >
> = $ ;

101. ; )
#6 ) = Q 7 =
) = 7>
) = ;
7 = ; 1
; = ; ; = ; 7
> ;
= 1
% : = > =
@3
; ; > =
7 = ; 7 = 7 =
= ;
= ; 71
( : ;8 7
> = =
= ;; Q 7
; 8 ) 7 =
1
( = 7 ;
> ) = = ;
= ; 71
Ejemplo
= : ) ) ;
) ! 8 > = ) =
: 8 = 8
: 1
10
Hoffman, F. O. and J. S. Hammonds. “Propagación de la incertidumbre en situaciones de riesgo: La
necesidad de distinguir entre incertidumbre debida a la falta de conocimiento y la incertidumbre ocasionada
por la variabilidad” Análisis de Riesgo, vol. 14, no. 5. pp 707-712, 1994.

102. ( = = =
7 ; Q=
: : 7 >
(6 ; : 7 =
> ; =
: J K
, 8 7 = =
7 T EEE>
7 !
( T! - T = 7 :
> ; = 7 7 ; >
; 8 1
! ;8 ) = $ >
= 7 1! 1
= 1
= - $ =
7Q > = =
% = 8 7 = @33 =
@>333 > = 1
: : = ; 7
= =
; 1
: = 7
= 7 ; = 71

103. , <
, <
, <
, <
, <
, <
, <
L@M
L2M
LBM
L4M
LDM
LFM
LAM
3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3
=
-
7 L! M 4AA323@>FEE 4D33B@4>@B D32CEB4>CC@ D@AAD23>FB4 DAD2A3C>C3F DAF@CAB>FE2 4C2DD32>C@2 D
, FX DX DX DX DX 4X DX F
3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3
3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3
3>32 3>32 3>32 3>32 3>32 3>32 3>32 3
* 3>33 3>33 3>33 3>33 3>33 3>33 3>33 3
<P U3>@3 3>@2 U3>3B U3>3E U3>3E U3>32 U3>@@ 3
^ 2>EA B>2A 2>A3 2>ED 2>CA B>BB 2>C2 2
! 1 * ; 3>32 3>32 3>32 3>3B 3>32 3>32 3>32 3
3>AD 3>AF 3>AD 3>A4 3>A4 3>AD 3>AF 3
6 3>CA 3>CE 3>CC 3>CE 3>CC 3>CE 3>CE 3
, 3>@2 3>@B 3>@B 3>@4 3>@4 3>@4 3>@B 3
%
DXU 3>AE 3>AC 3>AE 3>AE 3>AE 3>AE 3>AE 3

104. @3XU 3>AE 3>AE 3>AE 3>AE 3>AE 3>AE 3>AE 3
@DXU 3>C3 3>C3 3>C3 3>C3 3>C3 3>C3 3>C3 3
23XU 3>C3 3>C3 3>C3 3>C3 3>C3 3>C3 3>C3 3
2DXU 3>C3 3>C@ 3>C3 3>C3 3>C@ 3>C@ 3>C@ 3
B3XU 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3
BDXU 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3
43XU 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3>C@ 3
4DXU 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3
D3XU 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3
DDXU 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3
F3XU 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3>C2 3
FDXU 3>CB 3>CB 3>CB 3>CB 3>CB 3>CB 3>CB 3
A3XU 3>CB 3>CB 3>CB 3>CB 3>CB 3>CB 3>CB 3
ADXU 3>CB 3>CB 3>CB 3>CB 3>CB 3>CB 3>CB 3
C3XU 3>CB 3>CB 3>C4 3>C4 3>C4 3>CB 3>C4 3
CDXU 3>C4 3>C4 3>C4 3>C4 3>C4 3>C4 3>C4 3
E3XU 3>C4 3>C4 3>C4 3>C4 3>CD 3>C4 3>C4 3
EDXU 3>CD 3>CD 3>CD 3>CD 3>CD 3>CD 3>CD 3

105. %2 # - )
= ;
= 7> = ; >
L = M ; 71
Ilustración 68 - Overlay Chart
( # = 7 = =
= > ) :
:
@3D

106. %2 # - )
Ilustración 69 - Grafico de tendencias
T = ) $
= = =
> ; = ;; >
; ) ;
: 1
: = $ = =
= = ; =
; 1
( = ; = 7 = )
= 7 = 7 L @X :
EEXM
1
@3F

107. %2 # - )
Ilustración 70 - Trend Chart
= = ) 8
: 8 7>
= ) 8 # )
= : ! >= 8
> ;8 #6 7
) ; ; = ;
1
15. BIBLIOGRAFÍA Y WEBGRAFÍA
• (* + > " , 0 + QJ 4
3 K @ECCU
Q
2334> > 1Q% 1 @U234
• - J= , :1 KF :(
Q Q
( 1% Q@EEAQ% 1 @UFA
• +> ": : Q J == , < 1
K ( 1 ": 5
> 233B1 ! , 1
@3A