Optimized asset maintenance and replacement schedule
View Patent ↗There are provided a system, a method and a computer program product for generating an optimal preventive maintenance/replacement schedule for a set of assets. The method includes receiving data regarding an asset, said data including a failure rate function of said asset, a cost of preventative maintenance (PM) of said asset, a cost of an asset failure, and a cost of replacing an asset. An optimal number K of preventative maintenance time intervals t k and an indication of a possible replacement is computed and stored for each asset by minimizing a mean cost-rate value function with respect to an electrical age of the asset. A first PM schedule is formed without consideration of labor and budget resource constraints. The method further generates a second maintenance schedule for a system of assets by minimizing a deviation from the optimal PM time intervals subject to the labor and budget resource constraints.
1. A system for generating an optimal preventive maintenance/replacement schedule for a set of assets comprising:
a memory storage device for storing data;
a programmed processor device coupled to the memory storage device and configured to:
receive data regarding an asset, said data including a failure rate function capturing a condition of said asset up to a point in time, a cost of preventative maintenance (PM) of said asset, a cost of an asset failure, and a cost of replacing an asset;
receive a further input specifying a time horizon;
determine whether there is a need to replace said asset, and when a replacement of said asset is needed:
compute a mean cost-rate optimization problem formulated as an objective function of a total cost of the asset over said specified time horizon, said total cost being a function of a cost of preventative maintenance (PM) of said asset for K−1 PMs, and an expected cost of repairs for an asset failure computed as a function of said failure rate function, and the cost of replacing an asset;
compute an optimal number of preventative maintenance actions K and time intervals t k for each asset independently by minimizing said first objective function with respect to an age of the electrical asset y k , where k represents a k th PM, wherein said schedule is formed without considering a labor and budget resource constraint;
store data representing said optimal number of preventative maintenance time intervals for each asset in the memory storage device; and
generate a final maintenance schedule of said optimal number of time intervals from said stored data.
2. The system of claim 1 , wherein said processor device is further configured to:
determine a final maintenance schedule for the system of assets by minimizing a deviation from the optimal PM time intervals subject to the labor and budget resource constraints.
3. The system of claim 1 , wherein said optimal number of preventative maintenance time intervals includes a number K of PM intervals and an indication of a possible replacement; and a time interval t k for the k th PM.
4. The system of claim 3 , wherein said processor device is further configured to:
receive an input specifying a time horizon;
determine whether there is a need to replace said asset, and with no replacement needed,
determine the optimal scheduled intervals t k by minimizing a first mean cost-rate optimization problem formulated as a first objective function of a total cost of the asset over said specified time horizon, said total cost being a function of a cost of preventative maintenance (PM) of said asset for K−1 PMs, and an expected cost of repairs for an asset failure computed as a function of a failure rate function.
5. The system of claim 4 , wherein the first objective function of a total cost of the asset to be minimized is represented as ƒ 1 (y,K) such that:
min
y
,
K
f
1
(
y
,
K
)
=
c
p
(
K
-
1
)
+
c
m
∑
k
=
1
K
∫
b
k
-
1
y
k
-
1
y
k
h
k
(
t
)
dt
subject to at least one constraint, wherein c p is a cost of a preventive maintenance (PM) for said asset, K is the number of PMs and a possible replacement for said asset, c m is the cost of an asset failure, h k (t) is a failure rate function of said asset at the k th PM, y k is the electrical age of said asset just before the k th PM, and b k is an adjustment factor in electrical age due to the k th PM.
6. The system of claim 1 , wherein the objective function of a total cost of the asset to be minimized is represented as ƒ 2 (y,K) such that:
min
y
,
K
f
2
(
y
,
K
)
=
c
p
(
K
-
1
)
+
c
r
+
c
m
∑
k
=
1
K
∫
b
k
-
1
y
k
-
1
y
k
h
k
(
t
)
dt
y
K
+
∑
k
=
1
K
-
1
(
1
-
b
k
-
1
)
y
k
-
1
subject to at least one constraint, wherein c p is a cost of a preventive maintenance (PM) for said asset, K is the number of PMs and a possible replacement for said asset, c r is the cost of replacing the asset, c m is the cost of an asset failure, h k (t) is a failure rate function of said asset at the k th PM, y k is the electrical age of said asset just before the k th PM, and b k is an adjustment factor in electrical age due to the k th PM.
7. The system of claim 1 , wherein to compute a failure rate function h 0 (t) of an asset, said processor device is further configured to:
receive parameter values comprising: Weibull parameter input values α, β, a current age t 0 of the asset, a number of simulation intervals N, a time interval Δt for simulation, an asset aging factor acc_factor, and a given time t wherein
N
0
=
[
t
Δ
t
]
;
and
compute:
h
acc
(
t
)
=
β
(
t
0
+
Δ
t
∑
i
=
1
N
0
acc_factor
″
i
``
+
acc_factor
″
N
0
+
1
``
(
t
-
N
0
Δ
t
)
)
α
wherein said failure rate function h 0 (t) is said h acc (t) when t is less than or equal to said specified time horizon.
8. The system of claim 2 , wherein to minimize a deviation from the optimal PM time intervals subject to the labor and budget resource constraints, said processor device is further configured to:
solve, using integer linear programming:
min
x
i
k
,
n
∈
{
0
,
1
}
∑
i
∈
I
,
n
∈
N
,
k
n
∈
K
n
w
n
x
i
k
n
,
n
i
-
t
k
n
,
n
,
subject constraints, wherein
w n is an impact weight of the n-th asset; t k,n is the optimal PM intervals for the n-th asset; an x i k,n binary variable indicating whether the k-th PM or a replacement is conducted for the n-th transformer during an i-th interval, and said labor and budget resource constraints comprises: a number of PMs for the n-th asset, a k th PM being performed within a lower bound and upper bound deviation of the k th PM of the n-th asset, a total budget constraint, a maximum manpower availability at the i-th interval, and a maximum budget availability at the i-th interval.
9. The system of claim 8 , wherein said processor device is further configured to:
compare said impact weight w n against a threshold; and if the impact is bigger than said threshold:
fix a maintenance schedule computed for the n-transformer; and
select values for said lower and upper bounds for PM intervals to reduce a size of parallel integer linear programming problem.
10. A computer program product for determining when to carry out a preventive maintenance/replacement for a set of assets, the computer program product comprising a computer readable storage medium readable by a machine and storing instructions run by the machine to perform a method, said method comprising:
receiving data regarding an asset, said data including a failure rate function capturing a condition of said asset up to a point in time, a cost of preventative maintenance (PM) of said asset, a cost of an asset failure, and a cost of replacing an asset;
receiving a further input specifying a time horizon;
determining whether there is a need to replace said asset, and when no replacement of said asset is needed:
computing a mean cost-rate optimization problem formulated as an objective function of a total cost of the asset over said specified time horizon, said total cost being a function of a cost of preventative maintenance (PM) of said asset for K−1 PMs, and an expected cost of repairs for an asset failure computed as a function of said failure rate function, and the cost of replacing an asset;
computing an optimal number of preventative maintenance time intervals t k for each asset independently by minimizing said first objective function with respect to an age of the asset y k where k represents a k th PM, wherein said schedule is formed without considering a labor and budget resource constraint; and
storing said optimal number of preventative maintenance time intervals for each asset in a memory storage device, the optimal number of preventative maintenance time intervals including a number K of PM intervals and an indication of a possible replacement; and a time interval t k for the k th PM;
and generating a final maintenance schedule of said optimal number of time intervals from said stored data.
11. The computer program product according to claim 10 , wherein the method further comprises:
determining a final maintenance schedule for the system of assets by minimizing a deviation from the optimal PM time intervals subject to the labor and budget resource constraints.