# This example is used in a journal version of the IP paper.

# The general idea is to model the machining and inspection processes
# for a titanium aircraft engine bulkhead.  Naturally it is a major
# simplification.

values: reward
discount: 1.0

######################################################################
# STATES
#
# The states consist of a number of components.  First of all there is
# a distinguishing absorbing state.  The remaining 9 states are
# comprised of two attributes, each of which takes on 3 possible
# values. The two attributes, their values and the short-hand used to
# give the states their mnemonic names are:
#
# Machined State
#   o Slab (SLAB)
#   o Rough Machined (ROUGH)
#   o Final Machined (FINAL)
#
# Material Quality
#   o Grade A (A)
#   o Grade B (B)
#   o Grade C (C)
#
# The material quality refers to both the presence/absence of defects
# and the tolerances of the machined surfaces.
#
states:
	SLAB-A SLAB-B SLAB-C 
	ROUGH-A ROUGH-B ROUGH-C 
	FINAL-A FINAL-B FINAL-C 
	DONE

######################################################################
# ACTIONS
#
# The actions consist of predominantly two classes.  At each step
# either a processing and an inspection technique is chosen.  
#
# Inspection
#   o Ultrasonic for subsurface defects (UT)
#   o Liquid penetrant for surface defects (LP)
#   o Visual (VISUAL)
#
# Processes
#   o Machine the part (MACHINE)
#   o Paint/Anodize the part and ship it out for assembly (SHIP)
#   o Decide that the part is not salvagable or useable (SCRAP)

actions:
	UT LP VISUAL 
	MACHINE SHIP SCRAP
	
######################################################################
# OBSERVATIONS
#
# The observational information can either come from the processing
# actions or the inspection actions.  For the processing actions,
# often one gets some information about whether some spurious event
# might have caused the part to come under abnormal stresses (e.g.,
# broken cutter, dropped part).  We break these down into three
# possible outcomes:
#
#   o NORMAL - nothing out of the ordinary happened during processing
#   o QUESTIONABLE - nothing particularly significant happened, but
#                    things did not go exactly smoothly
#   o PROBLEM - there was a definite problem that occured during 
#               processing the part.
#
# For the inspection outcomes there is an outcome for each 
# possible material quality: GRADE-A, GRADE-B and GRADE-C.
# Grade A being nearly completely free of defects of any kind
# while Grade B has minor defects and Grade C has fairly
# major defects.
#
observations:
	NORMAL QUESTIONABLE PROBLEM 
	GRADE-A GRADE-B GRADE-C

######################################################################
# TRANSITIONS
#

#########################
# Inspection Actions
#
# Inspection does not affect the state of the part (these are all
# non-destructive tests).
T: UT
identity

T: LP
identity

T: VISUAL
identity

#########################
# MACHINE Action
#
# The machining process can introduce defects, either through the 
# machining itself or from handling the part. Thus the part quality 
# can degrade as a result of machinining.
# There is also a chance that the machining process could remove
# a defect, but we ignore this case.
# Note that machining a finished machined part is a bit odd, but
# we assume that should it be chosen it can introduce defects
# from the material handling phase.

T: MACHINE 
#	SA	SB	SC	RA	RB	RC	FA	FB	FC	DONE
#------------------------------------------------------
#SA	
	0.0	0.0	0.0	0.97	0.02	0.01	0.0	0.0	0.0	0.0
#SB	
	0.0	0.0	0.0	0.0	0.99	0.01	0.0	0.0	0.0	0.0
#SC	
	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0
#RA	
	0.0	0.0	0.0	0.0	0.0	0.0	0.96	0.02	0.02	0.0
#RB	
	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.98	0.02	0.0
#RC	
	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0
#FA	
	0.0	0.0	0.0	0.0	0.0	0.0	0.95	0.01	0.04	0.0
#FB	
	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.96	0.04	0.0
#FC	
	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0
#DONE
	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0

#########################
# SHIP Action
# 
# Shipping means the game is over and we proceed to the absorbing 
# state.
T: SHIP : * : DONE 1.0

#########################
# SCRAP Action
#
# Shipping means the game is over and we proceed to the absorbing 
# state.
T: SCRAP : * : DONE 1.0

#####################################################################
# OBSERVATIONS
#
#########################
# UT Action
#
# Ultrasonic tests are modelled as never detecting a part to be
# worse than it is. The predominant problem here is that the 
# orientation of the defect can often render it imperceivable.
#
O: UT
#	NORMAL	QUEST	PROBLEM	GRADE-A	GRADE-B  GRADE-C
#--------------------------------------------------------
#SA	
	0.0		0.0		0.0		1.0		0.0		0.0	
#SB	
	0.0		0.0		0.0		0.25		0.75		0.0	
#SC	
	0.0		0.0		0.0		0.10		0.15		0.75	
#RA		
	0.0		0.0		0.0		1.0		0.0		0.0	
#RB	
	0.0		0.0		0.0		0.15		0.85		0.0	
#RC	
	0.0		0.0		0.0		0.03		0.07		0.90	
#FA	
	0.0		0.0		0.0		1.0		0.0		0.0	
#FB	
	0.0		0.0		0.0		0.1		0.90		0.0	
#FC	
	0.0		0.0		0.0		0.01		0.07		0.92	
#DONE
	1.0		0.0		0.0		0.0		0.0		0.0	

#########################
# LP Action
#
# Since this liquid penetrant NDP inspection only is good for
# surface cracks, it is most effective when the part is in the final
# machine state.  In the slab or roughed out stages, only severe
# cracks could be detected, since small cracks may be removed by a
# final machining phase.
#
O: LP
#	NORMAL	QUEST	PROBLEM	GRADE-A	GRADE-B  GRADE-C
#--------------------------------------------------------
#SA	
	0.0		0.0		0.0		1.0		0.0		0.0	
#SB	
	0.0		0.0		0.0		0.99		0.01		0.0	
#SC	
	0.0		0.0		0.0		0.97		0.02		0.01	
#RA		
	0.0		0.0		0.0		1.0		0.0		0.0	
#RB	
	0.0		0.0		0.0		0.95		0.05		0.0	
#RC	
	0.0		0.0		0.0		0.90		0.05		0.05	
#FA	
	0.0		0.0		0.0		1.0		0.0		0.0	
#FB	
	0.0		0.0		0.0		0.15		0.85		0.0	
#FC	
	0.0		0.0		0.0		0.05		0.10		0.85	
#DONE
	1.0		0.0		0.0		0.0		0.0		0.0	

#########################
# VISUAL Action
#
# Like the liquid penetrant inspection, this is only good for
# surface defects and is not nerely as good.  The things you can
# detect visually are usually of such a drastic nature, that the
# detectabilktiy of the defect would make it immediately a CLASS-C
# material.  Thus, a CLASS-B material is not something observed
# visually. 
#
O: VISUAL
#	NORMAL	QUEST	PROBLEM	GRADE-A	GRADE-B  GRADE-C
#--------------------------------------------------------
#SA	
	0.0		0.0		0.0		1.0		0.0		0.0	
#SB	
	0.0		0.0		0.0		1.0		0.0		0.0	
#SC	
	0.0		0.0		0.0		0.8		0.0		0.2	
#RA		
	0.0		0.0		0.0		1.0		0.0		0.0	
#RB	
	0.0		0.0		0.0		1.0		0.0		0.0	
#RC	
	0.0		0.0		0.0		0.5		0.0		0.5	
#FA	
	0.0		0.0		0.0		1.0		0.0		0.0	
#FB	
	0.0		0.0		0.0		1.0		0.0		0.0	
#FC	
	0.0		0.0		0.0		0.25		0.0		0.75	
#DONE
	1.0		0.0		0.0		0.0		0.0		0.0	

#########################
# MACHINE Action
#
# Machining the part in the rough state
# consists of taking off a lot of material and
# handling a part which is fairly heavy.  Thus, you would imagine that
# the rough machining process should have a higher rate of something
# going wrong.  However, though this is true, the final machined part
# is much more delicate and the close tolerances makes it much more
# suspectible to damage.  Therefore there is roughly the same
# likelihood of something going wrong, though these are usually for
# slightly different reasons.  We skew the probabilities a bit, since
# something going wrong can be indicative of the part's quality
# degrading.  This model is a little too simple and it does not
# properly capture the coupling between something going wrong in the
# processing stage (a transition from good to bad) with the actual
# observation. 
#
O: MACHINE 
#	NORMAL	QUEST	PROBLEM	GRADE-A	GRADE-B  GRADE-C
#--------------------------------------------------------
#SA	
	0.98		0.01		0.01		0.0		0.0		0.0	
#SB	
	0.96		0.02		0.02		0.0		0.0		0.0	
#SC	
	0.9		0.05		0.05		0.0		0.0		0.0	
#RA		
	0.98		0.01		0.01		0.0		0.0		0.0	
#RB	
	0.96		0.02		0.02		0.0		0.0		0.0	
#RC	
	0.92		0.04		0.04		0.0		0.0		0.0	
#FA	
	0.98		0.01		0.01		0.0		0.0		0.0	
#FB	
	0.96		0.02		0.02		0.0		0.0		0.0	
#FC	
	0.92		0.04		0.04		0.0		0.0		0.0	
#DONE
	1.0		0.0		0.0		0.0		0.0		0.0	

#########################
# SHIP Action
#
# The observation we get for the ship action is not important,
# so we set it to be the same for all states.
#
O: SHIP : * : NORMAL 1.0


#########################
# SCRAP Action
#
# The observation we get for the scrap action is not important,
# so we set it to be the same for all states.
#
O: SCRAP : * : NORMAL 1.0

######################################################################
# REWARDS
#
# The absorbing state is zero cost, but not specifying gives it this cost.

#########################
# UT Action
#
# An ultrasonic test is fairly expensive. The more machining (and
# hence surfaces) the longer it takes and the more it costs.
#
R: UT : SLAB-A : * : * -50
R: UT : SLAB-B : * : * -50
R: UT : SLAB-C : * : * -50

R: UT : ROUGH-A : * : * -200
R: UT : ROUGH-B : * : * -200
R: UT : ROUGH-C : * : * -200

R: UT : FINAL-A : * : * -350
R: UT : FINAL-B : * : * -350
R: UT : FINAL-C : * : * -350

#########################
# LP Action
#
# The liquid penetrant technique is not as expensive as the ultrasonic
# technique, but still is not that cheap.  Its price too is a factor
# of how complex the geometry is, which is directly tied to the amount
# of machining that has been done on the part.  
#
R: LP : SLAB-A : * : * -20
R: LP : SLAB-B : * : * -20
R: LP : SLAB-C : * : * -20

R: LP : ROUGH-A : * : * -35
R: LP : ROUGH-B : * : * -35
R: LP : ROUGH-C : * : * -35

R: LP : FINAL-A : * : * -55
R: LP : FINAL-B : * : * -55
R: LP : FINAL-C : * : * -55

#########################
# VISUAL Action
#
R: VISUAL : SLAB-A : * : * -5
R: VISUAL : SLAB-B : * : * -5
R: VISUAL : SLAB-C : * : * -5

R: VISUAL : ROUGH-A : * : * -10
R: VISUAL : ROUGH-B : * : * -10
R: VISUAL : ROUGH-C : * : * -10

R: VISUAL : FINAL-A : * : * -15
R: VISUAL : FINAL-B : * : * -15
R: VISUAL : FINAL-C : * : * -15

#########################
# MACHINE Action
#
R: MACHINE : SLAB-A : * : * -5000
R: MACHINE : SLAB-B : * : * -5000
R: MACHINE : SLAB-C : * : * -5000

R: MACHINE : ROUGH-A : * : * -15000
R: MACHINE : ROUGH-B : * : * -15000
R: MACHINE : ROUGH-C : * : * -15000

R: MACHINE : FINAL-A : * : * -15000
R: MACHINE : FINAL-B : * : * -15000
R: MACHINE : FINAL-C : * : * -15000

#########################
# SHIP Action
#
# We assume a material cost of $10,000 is factored into the price of
# the part, so this number reflects the price minus that material
# cost. 

# A slab of any condition is immediately reckognizable as not
# acceptable, so this will cost the company the material cost.
# Although you could argue that they can still machine the slab, so
# the cost is too much, I would think that the company's credibility
# would suffer more than this loss for trying to ship unmachined
# parts. Because this is not something that we
#
R: SHIP : SLAB-A : * : * -15000
R: SHIP : SLAB-B : * : * -15000
R: SHIP : SLAB-C : * : * -15000

# A rough machined part is no better than a slab to the customer.
R: SHIP : ROUGH-A : * : * -15000
R: SHIP : ROUGH-B : * : * -15000
R: SHIP : ROUGH-C : * : * -15000

# This is the tricky part.  The buyer has no way of knowing what the
# condition of the part is without inspecting it themselves.  We
# assume that shipping a sub-standard part is very, very constly to
# the company.  Either the buyer detects this and the reputation is
# marred or worse yet, the part fails in service and results in a big
# scandal and loss of future revenues.  We assume that shipping a
# class B part is not as bad as shipping a class C part.
R: SHIP : FINAL-A : * : * 45000
R: SHIP : FINAL-B : * : * -50000
R: SHIP : FINAL-C : * : * -100000

#########################
# SCRAP Action
#
# Scapping the part causes you to lose the material costs.  Any extra
# costs from processing will have already been accounted for.
#
R: SCRAP : SLAB-A : * : * -10000
R: SCRAP : SLAB-B : * : * -10000
R: SCRAP : SLAB-C : * : * -10000

R: SCRAP : ROUGH-A : * : * -10000
R: SCRAP : ROUGH-B : * : * -10000
R: SCRAP : ROUGH-C : * : * -10000

R: SCRAP : FINAL-A : * : * -10000
R: SCRAP : FINAL-B : * : * -10000
R: SCRAP : FINAL-C : * : * -10000