V. Conclusions and Future Research
5.2 Future Research
This analysis used only data from 2018 due to limitations in the availability of the HQ EXPRESS data. Further analysis should be conducted as more data becomes available. Further, while this study looked at a subset of ten stock numbers, a more
large-scale modeling procedure would be required to increase confidence in conclusions about any causation between EXPRESS data and MICAPs. This study attempted to relate the EXPRESS data to MICAPs, but many models exhibited poor fit. There may be a different dependent variable of interest that is better impacted by the EXPRESS data. However, there is the possibility that regression-based time series models such as ARDL are simply ill-suited for maintenance data due to noise and volatility. In this case, some of the newer nonlinear time series approaches might be considered. Time series modeling using advanced computing software is a growing field and new models will be developed in the future, some of which may be more appropriate for this data. Additionally, there seems to be randomness involved in this data. Sometimes, even past MICAP values are not an accurate predictor of future MICAPs. With randomness and probabilities involved, stochastic methods or simulation might be more appropriate for future modeling efforts with EXPRESS or MICAP data. Future research might involve examining other assumptions and logic in the Air Force supply chain process instead of the Supportability Module.
Appendix A
Additional ALC Summary Graphs
Figure 24. Summary of Capacity and Funds ALC Data
NIIN 14429628 21 Day ARDL Model Q-Q Plot
Figure 25. Q-Q Plot of Residuals for First ARDL Model
NIIN 14429628 21 Day ARDL Model Residual Plot
Figure 26. Residual Plot for First ARDL Model
NIIN 14696512 7 Day ARDL Model Residual Plot
Figure 27. Residual Plot for First ARDL Model
Additional Model Statistics
Table 13. Additional Statistics for Supplemental Models
NIIN Aircraft Lag Model Res. Std. Error F-statistic
13134227 F-15E 21 1 1.798(df = 213) 1.645***(df = 66;213)
2 1.795(df = 235) 1.994***(df = 44;235)
145395245 C-135 7 1 1.76(df = 269) 4.558***(df = 24;269)
2 1.744(df = 277) 6.764***(df = 16;277)
11428094 C-135 7 1 1.311(df = 269) 2.533***(df = 24;269)
2 1.343(df = 277) 2.315***(df = 16; 277)
12043672 F-16 28 1 0.8256(df = 185) 1.463**(df = 87 ;185)
2 0.8763(df = 214) 1.088(df = 58;214)
12902065 C-135 28 1 1.14(df = 185) 2.032***(df = 87;185)
2 1.131(df = 214) 2.643***(df = 58;214)
11402105 C-135 7 1 1.323(df = 269) 1.408*(df = 24;269)
2 1.32(df = 277) 1.702**(df = 16;277)
792295 B-52
C-135 14 1 0.5086(df = 214) 1.518**(df = 45;241)
2 0.5012(df = 256) 2.08***(df=30;256)
12511153 F-15E 28 1 1.331(df = 185) 1.387**(df = 87;185)
2 1.347(df = 214) 1.458**(df = 58;214)
***p<0.01; **p<0.05; *p<0.1
Appendix B
Packages Used in Analysis l i b r a r y ( d a t a . t a b l e ) l i b r a r y ( zoo )
l i b r a r y ( d p l y r ) l i b r a r y ( i m p u t e T S ) l i b r a r y ( t s e r i e s ) l i b r a r y ( d y n a m a c ) l i b r a r y ( car )
l i b r a r y ( l u b r i d a t e ) l i b r a r y ( c o r r p l o t ) l i b r a r y ( x t a b l e )
MICAP Data Cleaning and Preparation
# I m p o r t d a t a f r o m csv f i l e
M I C A P s ← r e a d . csv ( " M I C A P D a t a v2 . csv " , h e a d e r = T R U E )
# R e m o v e l e a d i n g z e r o e s in N I I N for to m a t c h f o r m a t f r o m E X P R E S S t a b l e s
M I C A P s $ n i i n ← g s u b ( " (? < ! [0 -9]) 0+ " , " " , M I C A P s $ NIIN , p e r l = T R U E )
# R e p l a c e any N U L L v a l u e s w i t h NA for e a s e of use
M I C A P s ← a p p l y ( MICAPs ,2 , f u n c t i o n ( x ) s u p p r e s s W a r n i n g s ( l e v e l s ( x )←sub ( " N U L L " , NA , x ) ) )
M I C A P s ← d a t a . t a b l e ( M I C A P s )
# F o r m a t d a t e c o l u m n s as d a t e s
M I C A P s $ S t a r t D a t e ← as . D a t e ( M I C A P s $ M I C A P . S t a r t . D a t e ) M I C A P s $ S t o p D a t e ← as . D a t e ( M I C A P s $ M I C A P . S t o p . D a t e )
# S u b s e t t i n g to the top 10 N I I N s w i t h m i s s i n g v a l u e s for p a r t s t h a t had at l e a s t 100 M I C A P s in 2 0 1 8
M I C A P _ S u b s e t ← s u b s e t ( MICAPs , n i i n = = 1 3 1 3 4 2 2 7 | n i i n = = 1 4 5 3 9 5 2 4 5 | n i i n = = 1 1 4 2 8 0 9 4 | n i i n = = 1 2 0 4 3 6 7 2 | n i i n = = 1 4 4 2 9 6 2 8 | n i i n
= = 1 4 6 9 6 5 1 2 | n i i n = = 1 2 9 0 2 0 6 5 | n i i n = = 1 1 4 0 2 1 0 5 | n i i n = = 7 9 2 2 9 5 | n i i n = = 1 2 5 1 1 1 5 3 )
# D r o p any o b s e r v a t i o n s t h a t s t a r t e d a f t e r 10 / 31 / 2 0 1 8 M I C A P _ S u b s e t ← M I C A P _ S u b s e t [ M I C A P _ S u b s e t $ S t a r t D a t e <= "
2018 -10 -31 " ]
# F i n d i n g the d u r a t i o n of e a c h u n i q u e M I C A P d o c u m e n t M I C A P _ D u r a t i o n s ← M I C A P _ S u b s e t % >%
g r o u p _ by ( niin , M I C A P . D o c u m e n t . N u m b e r ) % >%
s u m m a r i z e ( S t a r t = min ( S t a r t D a t e ) , End = max ( S t o p D a t e , na . rm = T R U E ) )
# If no m a x i m u m s t o p d a t e was found , t h e n t h e r e w e r e no end d a t e s for t h a t M I C A P on r e c o r d - f i l l in w i t h 10 / 31 / 2 0 1 8 M I C A P _ D u r a t i o n s $ End ← as . c h a r a c t e r ( M I C A P _ D u r a t i o n s $ End ) M I C A P _ D u r a t i o n s $ End [ is . na ( M I C A P _ D u r a t i o n s $ End ) ] ← "
2018 -10 -31 "
M I C A P _ D u r a t i o n s $ End ← as . D a t e ( M I C A P _ D u r a t i o n s $ End )
# C r e a t i n g d a t a t a b l e of e a c h N I I N w i t h e a c h d a t e
# F i r s t d a t e of d a t a is 1 / 3 / 2 0 1 8 and l a s t d a t e is 10 / 31 / 2 0 1 8 t i m e _ s e r i e s _ f u l l ← seq ( ymd ( " 2018 -01 -03 " ) , ymd ( " 2018 -10 -31 " ) ,
by = " day " ) # v e c t o r of r e l e v a n t d a t e s
# C r e a t i n g r e p e a t e d v e c t o r s of e a c h N I I N to c o m b i n e w i t h the d a t e v e c t o r
N I I N s ← c ( 1 3 1 3 4 2 2 7 , 1 4 5 3 9 5 2 4 5 , 1 1 4 2 8 0 9 4 , 1 2 0 4 3 6 7 2 , 1 4 4 2 9 6 2 8 , 1 4 6 9 6 5 1 2 , 1 2 9 0 2 0 6 5 , 1 1 4 0 2 1 0 5 , 792295 , 1 2 5 1 1 1 5 3 )
i = 1
for ( v a l u e in N I I N s ) {
n a m e ← p a s t e ( " N I I N _ " , value , sep = " " )
a s s i g n ( name , rep ( value , l e n g t h ( t i m e _ s e r i e s _ f u l l ) ) ) }
# C o m b i n i n g i n t o one d a t a f r a m e
N I I N _ V e c t o r s ← c ( N I I N _ 1 3 1 3 4 2 2 7 , N I I N _ 1 4 5 3 9 5 2 4 5 , N I I N _ 1 1 4 2 8 0 9 4 , N I I N _ 1 2 0 4 3 6 7 2 , N I I N _ 1 4 4 2 9 6 2 8 , N I I N _ 1 4 6 9 6 5 1 2 , N I I N _ 1 2 9 0 2 0 6 5 , N I I N _ 1 1 4 0 2 1 0 5 , N I I N _ 792295 , N I I N _ 1 2 5 1 1 1 5 3 )
D a t e _ V e c t o r ← rep ( t i m e _ s e r i e s _ full , 1 0 )
# M a k e a b l a n k v e c t o r for n u m b e r of M I C A P s N u m M I C A P s ← rep (0 , l e n g t h ( D a t e _ V e c t o r ) )
# C h e c k " M I C A P _ D u r a t i o n s " for e a c h p a i r of N I I N / d a t e to see if t h a t d a t e is b e t w e e n any of the s t a r t / end d a t e s in t h a t t a b l e
for ( row in 1: l e n g t h ( D a t e _ V e c t o r ) ) {
N I I N ← N I I N _ V e c t o r s [ row ] d a t e ← D a t e _ V e c t o r [ row ]
d a t a s u b s e t ← s u b s e t ( M I C A P _ D u r a t i o n s , n i i n == N I I N )
N u m M I C A P s [ row ] ← sum ( d a t a s u b s e t $ Start <= d a t e & d a t a s u b s e t $ End >= d a t e )
}
# M a k e f i n a l M I C A P d a t a t a b l e
M I C A P s B y N I I N a n d D a t e ← d a t a . t a b l e ( N I I N _ Vectors , D a t e _ Vector , N u m M I C A P s )
c o l n a m e s ( M I C A P s B y N I I N a n d D a t e ) ← c ( " n i i n _ id " , " d a t e " , "
N u m M I C A P s " )
HQ EXPRESS Data Cleaning and Preparation
# I m p o r t d a t a f r o m csv f i l e
HQ _ S u p p ← r e a d . csv ( " HQ spt r e s u l t s v2 . csv " , h e a d e r = T R U E ) HQ _ S u p p ← as . d a t a . t a b l e ( HQ _ S u p p )
# F o r m i n g a m o r e u n d e r s t a n d a b l e d a t e c o l u m n f r o m " D a t e of D a t a "
c o l n a m e s ( HQ _ S u p p ) [1] ← " D a t e O f D a t a "
HQ _ S u p p $ d a t e ← s u b s t r ( HQ _ S u p p $ D a t e O f D a t a ,0 ,10) HQ _ S u p p $ d a t e ← as . D a t e ( HQ _ S u p p $ d a t e )
# R e p l a c i n g c a r c a s s c o d e s - B , F , P are all f a i l u r e s . S is s u c c e s s . New c o l u m n w i l l be 1 if t h e r e was a f a i l u r e . HQ _ S u p p $ C a r c a s s [ ! HQ _ S u p p $ c a r c _ a v a i l == " S " ] ← 1
HQ _ S u p p $ C a r c a s s [ HQ _ S u p p $ c a r c _ a v a i l == " S " ] ← 0
# R e p l a c i n g p a r t s c o d e s - F is a f a i l u r e . B and S are s u c c e s s . New c o l u m n w i l l be 1 if t h e r e was a f a i l u r e . HQ _ S u p p $ P a r t s [ HQ _ S u p p $ p a r t s _ a v a i l == " F " ] ← 1
HQ _ S u p p $ P a r t s [ ! HQ _ S u p p $ p a r t s _ a v a i l == " F " ] ← 0
# C o u n t i n g n u m b e r of f a i l u r e s per N I I N per day for c a r c a s s C a r c a s s _ F a i l u r e s ← HQ _ S u p p % >%
g r o u p _ by ( n i i n _ id , d a t e ) % >%
s u m m a r i z e ( N u m b e r _ F a i l u r e s = sum ( C a r c a s s ) )
# C o u n t i n g n u m b e r of f a i l u r e s per N I I N per day for p a r t s P a r t s _ F a i l u r e s ← HQ _ S u p p % >%
g r o u p _ by ( n i i n _ id , d a t e ) % >%
s u m m a r i z e ( N u m b e r _ F a i l u r e s = sum ( P a r t s ) )
# A d d i n g a c o l u m n to c h e c k if a N I I N f a i l e d for c a r c a s s and p a r t s
HQ _ S u p p $ P a r t s M i s s i n g [ HQ _ S u p p $ C a r c a s s == 1 & HQ _ S u p p $ P a r t s ==
1] ← 1
HQ _ S u p p $ P a r t s M i s s i n g [ is . na ( HQ _ S u p p $ P a r t s M i s s i n g ) ] ← 0
# C o u n t i n g n u m b e r of t i m e s per N I I N per day t h a t t h e r e was a C a r c a s s and P a r t s f a i l u r e
P a r t s _ M i s s i n g ← HQ _ S u p p % >%
g r o u p _ by ( n i i n _ id , d a t e ) % >%
s u m m a r i z e ( N u m b e r _ M i s s i n g = sum ( P a r t s M i s s i n g ) )
# C h a n g e f o r m a t of d a t a t a b l e s so i n f o r m a t i o n can be j o i n e d e a s i l y
C a r c a s s _ F a i l u r e s ← as . d a t a . t a b l e ( C a r c a s s _ F a i l u r e s ) P a r t s _ F a i l u r e s ← as . d a t a . t a b l e ( P a r t s _ F a i l u r e s ) P a r t s _ M i s s i n g ← as . d a t a . t a b l e ( P a r t s _ M i s s i n g )
# J o i n d a t a t a b l e s
HQ _ T a b l e ← c b i n d ( C a r c a s s _ F a i l u r e s , P a r t s _ F a i l u r e s [ ,3] , P a r t s _ M i s s i n g [ ,3])
c o l n a m e s ( HQ _ T a b l e ) [ 3 : 5 ] ← c ( " C a r c a s s _ F a i l u r e s " , " P a r t s _ F a i l u r e s " , " P a r t s _ M i s s i n g " )
# F i n d i n g N I I N s w i t h the m o s t f a i l u r e s o v e r the y e a r HQ _ Y e a r ← HQ _ S u p p % >%
g r o u p _ by ( n i i n _ id ) % >%
s u m m a r i z e ( C a r c _ F a i l u r e s = sum ( C a r c a s s ) , P a r t _ F a i l u r e s = sum ( P a r t s ) , P a r t _ M i s s i n g = sum ( P a r t s M i s s i n g ) )
# V i e w i n g the c o r r e l a t i o n of the v a r i a b l e s
M ← cor ( HQ _ Y e a r [ , c ( " C a r c _ F a i l u r e s " , " P a r t _ F a i l u r e s " , " P a r t _ M i s s i n g " ) ])
c o r r p l o t ( M , m e t h o d = " s q u a r e " )
# C a l c u l a t i n g s u m m a r y p e r c e n t a g e s
t a b l e ( HQ _ Y e a r $ C a r c _ F a i l u r e s ) [1] / dim ( HQ _ Y e a r ) [1] # p e r c e n t of N I I N s w i t h NO c a r c a s s f a i l u r e s in y e a r 2 0 1 8
t a b l e ( HQ _ Y e a r $ P a r t _ F a i l u r e s ) [1] / dim ( HQ _ Y e a r ) [1] # p e r c e n t of N I I N s w i t h NO p a r t s f a i l u r e s in y e a r 2 0 1 8
t a b l e ( HQ _ Y e a r $ P a r t _ M i s s i n g ) [1] / dim ( HQ _ Y e a r ) [1] # p e r c e n t of N I I N s w i t h NO p a r t s m i s s i n g in y e a r 2 0 1 8
# F o r m i n g L a T e X t a b l e s of top o f f e n d i n g N I I N s
x t a b l e ( h e a d ( HQ _ Y e a r [ o r d e r ( HQ _ Y e a r $ C a r c _ F a i l u r e s , d e c r e a s i n g = T R U E ) ,] ,25) [ , c (1 ,2) ] , c a p t i o n = " Top N I I N s for C a r c a s s F a i l u r e s " , d i g i t s = 0)
x t a b l e ( h e a d ( HQ _ Y e a r [ o r d e r ( HQ _ Y e a r $ P a r t _ F a i l u r e s , d e c r e a s i n g = T R U E ) ,] ,25) [ , c (1 ,3) ] , c a p t i o n = " Top N I I N s for P a r t s
F a i l u r e s " , d i g i t s = 0)
x t a b l e ( h e a d ( HQ _ Y e a r [ o r d e r ( HQ _ Y e a r $ P a r t _ Missing , d e c r e a s i n g = T R U E ) ,] ,25) [ , c (1 ,4) ] , c a p t i o n = " Top N I I N s for P a r t s M i s s i n g " , d i g i t s = 0)
Merging Information from HQ and MICAP Data Tables
# S u b s e t t i n g to the top 10 N I I N s for c a r c a s s f a i l u r e s t h a t had at l e a s t 100 M I C A P s in 2 0 1 8 ( at l e a s t 100 u n i q u e M I C A P d o c u m e n t n u m b e r s )
HQ _ S u b s e t ← s u b s e t ( HQ _ Table , n i i n _ id = = 1 3 1 3 4 2 2 7 | n i i n _ id
= = 1 4 5 3 9 5 2 4 5 | n i i n _ id = = 1 1 4 2 8 0 9 4 | n i i n _ id = = 1 2 0 4 3 6 7 2 | n i i n _ id
= = 1 4 4 2 9 6 2 8 | n i i n _ id = = 1 4 6 9 6 5 1 2 | n i i n _ id = = 1 2 9 0 2 0 6 5 | n i i n _ id
= = 1 1 4 0 2 1 0 5 | n i i n _ id = = 7 9 2 2 9 5 | n i i n _ id = = 1 2 5 1 1 1 5 3 )
HQ _ S u b s e t ← HQ _ S u b s e t [ HQ _ S u b s e t $ d a t e <= " 2018 -10 -31 " ]
# M e r g e w i t h M I C A P d a i l y a g g r e g a t e d d a t a
F u l l D a t a ← m e r g e ( HQ _ Subset , M I C A P s B y N I I N a n d D a t e , by = c ( " n i i n _ id
" , " d a t e " ) , all = T R U E )
Preparing Data For Time Series Analysis
# E x t r a c t d a t a for N I I N of i n t e r e s t f r o m the 10 in the t a b l e N I I N _ S u b s e t ← s u b s e t ( F u l l D a t a , n i i n _ id == 1 4 4 2 9 6 2 8 , s e l e c t = c ( " n i i n _ id " , " d a t e " , " C a r c a s s _ F a i l u r e s " , " P a r t s _ F a i l u r e s " , "
P a r t s _ M i s s i n g " , " N u m M I C A P s " ) )
# F o r m u n i v a r i a t e t i m e s e r i e s d a t a s e t s c a r c a s s ← N I I N _ S u b s e t [ ,3]
p a r t s ← N I I N _ S u b s e t [ ,4]
p a r t s _ m i s s i n g ← N I I N _ S u b s e t [ ,5]
num _ m i c a p s ← N I I N _ S u b s e t [ ,6]
c a r c a s s _ f a i l u r e s _ zoo ← zoo ( carcass , N I I N _ S u b s e t $ d a t e ) p a r t s _ f a i l u r e s _ zoo ← zoo ( parts , N I I N _ S u b s e t $ d a t e )
p a r t s _ m i s s i n g _ zoo ← zoo ( p a r t s _ missing , N I I N _ S u b s e t $ d a t e ) num _ m i c a p s _ zoo ← zoo ( num _ micaps , N I I N _ S u b s e t $ d a t e )
# P e r f o r m L O C F m i s s i n g d a t a i m p u t a t i o n
c a r c a s s _ f a i l u r e s _ s m o o t h ← na . l o c f ( c a r c a s s _ f a i l u r e s _ zoo ) p a r t s _ f a i l u r e s _ s m o o t h ← na . l o c f ( p a r t s _ f a i l u r e s _ zoo ) p a r t s _ m i s s i n g _ s m o o t h ← na . l o c f ( p a r t s _ m i s s i n g _ zoo )
ts _ df ← c b i n d ( num _ m i c a p s _ zoo , c a r c a s s _ f a i l u r e s _ smooth , p a r t s _ f a i l u r e s _ smooth , p a r t s _ m i s s i n g _ s m o o t h )
# P l o t s s h o w i n g the i n t e r p o l a t i o n for c a r c a s s f a i l u r e s , can be r e p e a t e d for o t h e r v a r i a b l e s - i m p u t e d v a l u e s are s h o w n in red
par ( mar = c (5 , 5 , 5 , 5) )
p l o t ( c a r c a s s _ f a i l u r e s _ smooth , t y p e = " l " , col = " red " , y l a b
= " N u m b e r of C a r c a s s F a i l u r e s " , x l a b = " D a t e " , m a i n = "
C a r c a s s F a i l u r e s " ) par ( new = T R U E )
p l o t ( c a r c a s s _ f a i l u r e s _ zoo , t y p e = " l " , col = " b l a c k " , x a x t =
" n " , y a x t = " n " , y l a b = " " , x l a b = " " ) # P a r t s
l e g e n d ( " t o p l e f t " , l e g e n d = c ( " O r i g i n a l " , " I m p u t e d " ) , col = c ( "
b l a c k " , " red " ) , f i l l = c ( " b l a c k " , " red " ) , cex = 1)
# P l o t t i n g c a r c a s s f a i l u r e s , p a r t s f a i l u r e s and M I C A P s on the s a m e p l o t w i t h two y a x e s
par ( mar = c (5 , 5 , 5 , 5) )
p l o t ( ts _ df [ ,2] , t y p e = " l " , col = " b l u e " , y l a b = " N u m b e r of F a i l u r e s " , x l a b = " D a t e " ) # C a r c a s s F a i l u r e s
par ( new = T R U E )
p l o t ( ts _ df [ ,3] , t y p e = " l " , col = " d a r k g r e e n " , x a x t = " n " , y a x t = " n " , y l a b = " " , x l a b = " " ) # P a r t s F a i l u r e s
par ( new = T R U E )
p l o t ( ts _ df [ ,1] , t y p e = " l " , col = " red " , x a x t = " n " , y a x t =
" n " , y l a b = " " , x l a b = " " ) # M I C A P s a x i s ( s i d e = 4)
m t e x t ( " N u m b e r of M I C A P s " , s i d e = 4 , l i n e = 3)
l e g e n d ( " t o p l e f t " , l e g e n d = c ( " C a r c a s s F a i l u r e s " , " P a r t s
F a i l u r e s " , " N u m b e r of M I C A P s " ) , col = c ( " b l u e " , " d a r k g r e e n "
, " red " ) , f i l l = c ( " b l u e " , " d a r k g r e e n " , " red " ) , cex = 0 . 8 )
# P l o t t i n g p a r t s m i s s i n g and M I C A P s on the s a m e p l o t w i t h two y a x e s
par ( mar = c (5 , 5 , 5 , 5) )
p l o t ( ts _ df [ ,4] , t y p e = " l " , col = " p u r p l e " , y l a b = " N u m b e r
of F a i l u r e s " , x l a b = " D a t e " ) # P a r t s M i s s i n g par ( new = T R U E )
p l o t ( ts _ df [ ,1] , t y p e = " l " , col = " red " , x a x t = " n " , y a x t =
" n " , y l a b = " " , x l a b = " " ) # M I C A P s a x i s ( s i d e = 4)
m t e x t ( " N u m b e r of M I C A P s " , s i d e = 4 , l i n e = 3)
l e g e n d ( " t o p l e f t " , l e g e n d = c ( " P a r t s M i s s i n g " , " N u m b e r of
M I C A P s " ) , col = c ( " p u r p l e " , " red " ) , f i l l = c ( " p u r p l e " , " red
" ) , cex = 1)
# F o r m d a t a set for d y n a m a c package , w h i c h doesn ’ t w o r k w i t h t i m e s e r i e s o b j e c t s
df ← c b i n d ( num _ micaps , as . v e c t o r ( c a r c a s s _ f a i l u r e s _ s m o o t h ) , as . v e c t o r ( p a r t s _ f a i l u r e s _ s m o o t h ) , as . v e c t o r ( p a r t s _ m i s s i n g _ s m o o t h ) )
c o l n a m e s ( df ) [ 2 : 4 ] = c ( " C a r c a s s _ F a i l u r e s " , " P a r t s _ F a i l u r e s " , "
P a r t s _ M i s s i n g " )
Performing Time Series Analysis
# T e s t i n g for u n i t r o o t
# A u g m e n t e d Dickey - F u l l e r T e s t adf . t e s t ( c a r c a s s _ f a i l u r e s _ s m o o t h ) adf . t e s t ( p a r t s _ f a i l u r e s _ s m o o t h ) adf . t e s t ( p a r t s _ m i s s i n g _ s m o o t h ) adf . t e s t ( num _ m i c a p s _ zoo )
adf . t e s t ( d i f f ( c a r c a s s _ f a i l u r e s _ s m o o t h ) ) adf . t e s t ( d i f f ( p a r t s _ f a i l u r e s _ s m o o t h ) ) adf . t e s t ( d i f f ( p a r t s _ m i s s i n g _ s m o o t h ) )
adf . t e s t ( d i f f ( num _ m i c a p s _ zoo ) )
# P h i l l i p s - P e r r o n T e s t
pp . t e s t ( c a r c a s s _ f a i l u r e s _ s m o o t h ) pp . t e s t ( p a r t s _ f a i l u r e s _ s m o o t h ) pp . t e s t ( p a r t s _ m i s s i n g _ s m o o t h ) pp . t e s t ( num _ m i c a p s _ zoo )
pp . t e s t ( d i f f ( c a r c a s s _ f a i l u r e s _ s m o o t h ) ) pp . t e s t ( d i f f ( p a r t s _ f a i l u r e s _ s m o o t h ) ) pp . t e s t ( d i f f ( p a r t s _ m i s s i n g _ s m o o t h ) ) pp . t e s t ( d i f f ( num _ m i c a p s _ zoo ) )
# R u n n i n g A R D L m o d e l s for c a r c a s s and p a r t s f a i l u r e s for l a g s of 7 , 14 , 21 and 28 d a y s
my _ m o d e l 7 ← d y n a r d l ( N u m M I C A P s ∼ C a r c a s s _ F a i l u r e s + P a r t s _ F a i l u r e s , d a t a = df , l a g s = l i s t ( " N u m M I C A P s " = 1 , "
C a r c a s s _ F a i l u r e s " = 1 , " P a r t s _ F a i l u r e s " = 1) , l a g d i f f s = l i s t ( " N u m M I C A P s " = c ( 1 : 7 ) , " C a r c a s s _ F a i l u r e s " = c ( 1 : 7 ) , "
P a r t s _ F a i l u r e s " = c ( 1 : 7 ) ) , ec = TRUE , s i m u l a t e = FALSE , t r e n d = F A L S E )
s u m m a r y ( my _ m o d e l 7 )
my _ m o d e l 1 4 ← d y n a r d l ( N u m M I C A P s ∼ C a r c a s s _ F a i l u r e s + P a r t s _ F a i l u r e s , d a t a = df , l a g s = l i s t ( " N u m M I C A P s " = 1 , "
C a r c a s s _ F a i l u r e s " = 1 , " P a r t s _ F a i l u r e s " = 1) , l a g d i f f s = l i s t ( " N u m M I C A P s " = c ( 1 : 1 4 ) , " C a r c a s s _ F a i l u r e s " = c ( 1 : 1 4 ) ,
" P a r t s _ F a i l u r e s " = c ( 1 : 1 4 ) ) , ec = TRUE , s i m u l a t e = FALSE , t r e n d = F A L S E )
s u m m a r y ( my _ m o d e l 1 4 )
my _ m o d e l 2 1 ← d y n a r d l ( N u m M I C A P s ∼ C a r c a s s _ F a i l u r e s + P a r t s _ F a i l u r e s , d a t a = df , l a g s = l i s t ( " N u m M I C A P s " = 1 , "
C a r c a s s _ F a i l u r e s " = 1 , " P a r t s _ F a i l u r e s " = 1) , l a g d i f f s = l i s t ( " N u m M I C A P s " = c ( 1 : 2 1 ) , " C a r c a s s _ F a i l u r e s " = c ( 1 : 2 1 ) ,
" P a r t s _ F a i l u r e s " = c ( 1 : 2 1 ) ) , ec = TRUE , s i m u l a t e = FALSE , t r e n d = F A L S E )
s u m m a r y ( my _ m o d e l 2 1 )
my _ m o d e l 2 8 ← d y n a r d l ( N u m M I C A P s ∼ C a r c a s s _ F a i l u r e s + P a r t s _ F a i l u r e s , d a t a = df , l a g s = l i s t ( " N u m M I C A P s " = 1 , "
C a r c a s s _ F a i l u r e s " = 1 , " P a r t s _ F a i l u r e s " = 1) , l a g d i f f s = l i s t ( " N u m M I C A P s " = c ( 1 : 2 8 ) , " C a r c a s s _ F a i l u r e s " = c ( 1 : 2 8 ) ,
" P a r t s _ F a i l u r e s " = c ( 1 : 2 8 ) ) , ec = TRUE , s i m u l a t e = FALSE , t r e n d = F A L S E )
s u m m a r y ( my _ m o d e l 2 8 )
# C h e c k m o d e l d i a g n o s t i c s for c h o s e n m o d e l
d y n a r d l . a u t o . c o r r e l a t e d ( my _ m o d e l 2 1 ) # F u n c t i o n t h a t c h e c k s for a u t o c o r r e l a t i o n and n o r m a l i t y of r e s i d u a l s
q q P l o t ( my _ m o d e l 2 1 $ m o d e l $ r e s i d u a l s , y l a b = " R e s i d u a l " , x l a b =
" N o r m Q u a n t i l e s " , m a i n = " Q - Q P l o t of R e s i d u a l s " ) # Q - Q P l o t
p l o t ( my _ m o d e l 2 1 $ m o d e l $ r e s i d u a l s , y l a b = " R e s i d u a l " , m a i n = "
R e s i d u a l P l o t for A R D L M o d e l " ) # C h e c k i n g for H e t e r o s k e d a s t i c i t y
# T e s t i n g for c o i n t e g r a t i o n of v a r i a b l e s p s s b o u n d s ( my _ m o d e l 2 1 )
# R u n n i n g A R D L m o d e l for m i s s i n g p a r t s f a i l u r e s for c h o s e n lag
my _ m o d e l 2 1 ← d y n a r d l ( N u m M I C A P s ∼ P a r t s _ Missing , d a t a = df , l a g s = l i s t ( " N u m M I C A P s " = 1 , " P a r t s _ M i s s i n g " = 1) ,
l a g d i f f s = l i s t ( " N u m M I C A P s " = c ( 1 : 2 1 ) , " P a r t s _ M i s s i n g " = c ( 1 : 2 1 ) ) , ec = TRUE , s i m u l a t e = FALSE , t r e n d = F A L S E ) s u m m a r y ( my _ m o d e l 2 1 )
# C h e c k m o d e l d i a g n o s t i c s of m o d e l
d y n a r d l . a u t o . c o r r e l a t e d ( my _ m o d e l 2 1 ) # F u n c t i o n t h a t c h e c k s for a u t o c o r r e l a t i o n and n o r m a l i t y of r e s i d u a l s
q q P l o t ( my _ m o d e l 2 1 $ m o d e l $ r e s i d u a l s , y l a b = " R e s i d u a l " , x l a b =
" N o r m Q u a n t i l e s " , m a i n = " Q - Q P l o t of R e s i d u a l s " ) # Q - Q P l o t
p l o t ( my _ m o d e l 2 1 $ m o d e l $ r e s i d u a l s , y l a b = " R e s i d u a l " , m a i n = "
R e s i d u a l P l o t for A R D L M o d e l " ) # C h e c k i n g for H e t e r o s k e d a s t i c i t y
# T e s t i n g for c o i n t e g r a t i o n of v a r i a b l e s p s s b o u n d s ( my _ m o d e l 2 1 )
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21–03–2019 Master’s Thesis Sept 2017 — March 2019
Examining the EXPRESS Supportability Module: Implementing an Autoregressive Distributed Lag Approach with Air Force Maintenance
Data
EXPRESS (Execution and Prioritization of Repairs Support System) is a program integral to the Air Force reparable supply chain. Daily, EXPRESS relies on a number of data sources and modules like the Supportability Module to determine which necessary repairs can be made. The Supportability Module examines the prioritized list of repairs and checks four constraints in order to decide whether each repair can be made given current resources. A single constraint failure means that subsequent resource checks are not made before evaluating the next repair, leading to missing data in the EXPRESS table. In this study, a time series analysis via explanatory autoregressive distributed lag models was conducted using EXPRESS and MICAP (mission capability) data to examine possible connections between missing constraint values in the EXPRESS table and future MICAPs. These models suggested that up to 0.793 MICAP days are added for each additional parts failure missing in the EXPRESS table. The potential for the use of time series models with maintenance data was also explored. Model diagnostics suggest that maintenance data is too volatile and noisy for regression-based methods and that stochastic methods or simulation may prove more useful.
EXPRESS, aircraft maintenance, supply chain, autoregressive distributed lag model
U U U UU
83
Dr. Raymond R. Hill (ENS)
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.