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3.2. The Troubleshooting Model
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mode of C at time t − 1. An effect that changes the mode of a feature variable
F := f is treated similarly and the event F t := f is generated. An operation effect
operate(τ ) generates an operation event ωt (τ ). For an observe effect obs(O),
one of |ΩO | different events is generated depending on the response from the
system. The event Ot = o means that the variable O is observed to be in the
mode o at time t, e.g. at time t the effect obs(O2 ) generates one of the events
O2t = normal and O2t = low.
The value of the feature variables will not be affected by any other event
than those of the type F := f . After the occurrence of such an event at time t, we
can trivially infer the values of the feature variables at time t given their value
at time t − 1. We indicate this by writing et ∧ Ft−1 ` Ft where et = { Fit := f i0 }
is the event that results from assigning the value f i0 to the feature Fi at time t,
Ft−1 = [ f 1 , . . . , f n ] is a sequence specifying all feature values at the preceding
time step t − 1, and Ft = [ f 1 , . . . , f i−1 , f i0 , f i+1 , . . . , f n ] is the same sequence
with a new value for the modified feature Fi .
Example 3.2 (Actions of Sample System). Below are the actions for the sample
system introduced in Section 3.1. The costs are values that reflect the time to
execute the action and the costs of resources consumed when performing the
action. When any of the actions that repair components (a1 –a4 ) or change feature modes (a9 –a12 ) are performed, a single event corresponding to the effect
is generated with certainty. When an observing action (a5 –a8 ) is performed,
one of two events may be generated. For example if the action a7 Check Visible
Leakage is performed, the generated event may either be O1 = no or O1 = yes.
Action
a0
Stop
a1
Repair Pump
a2
Replace Gasket
a3
Replace Pres. Sensor
a4
Fill Oil
a5
Inspect Pump
a6
Check Oil Level
a7
Check Visible Leakage
a8
Test System
a9
Remove Casing
a10 Fit Casing
a11 Remove Pipe
a12 Fit Pipe
Precondition
F1 = fit. ∧ F2 = fit.
F1 = rem.
F2 = rem.
F2
F1
F2
F1
F1
F1
F1
F1
F2
= fit.
= rem.
= fit.
= rem. ∧ F2 = fit.
= fit.
= fit.
= rem. ∧ F2 = fit.
= rem. ∧ F2 = fit.
= rem.
Effects
{}
{repair(C1 )}
{repair(C2 )}
{repair(C3 )}
{repair(C4 )}
{obs(C1 )}
{obs(C4 )}
{obs(O1 )}
{obs(O3 )}
{ F1 := rem.}
{ F1 := fit.}
{ F2 := rem.}
{ F2 := fit.}
Cost
0
150
15
100
20
10
10
10
40
25
25
40
40