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 method for decreasing a failure rate of each asset of a set of assets comprising:
receiving, at a programmed hardware processor, 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, at said programmed hardware processor, a further input specifying a time horizon;
determining, at said programmed hardware processor, whether there is a need to replace said asset, and when a replacement of said asset is needed:
computing, at said programmed hardware processor, 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, using the programmed hardware processor, an optimal number of preventative maintenance actions K and time intervals t k for each asset independently by minimizing said 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; and
the programmed hardware processor device further storing said optimal number of preventative maintenance time intervals for each asset as data in a memory storage device operatively coupled with said processor device; and
the programmed hardware processor device generating a final maintenance schedule for the system of assets based on stored said optimal number of preventative maintenance time intervals by minimizing a deviation from the computed optimal PM time intervals subject to the labor and budget resource constraints.
2. The method 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.
3. The method of claim 2 , further comprising:
receiving, at said programmed hardware processor, an input specifying a time horizon;
determining, at said programmed hardware processor, by said processor device, whether there is a need to replace said asset, and with no replacement needed,
determining, at said programmed hardware processor, 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.
4. The method of claim 3 , wherein the first objective function of a total cost of the asset to be minimized is represented as f 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
)
d
t
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 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.
5. The method of claim 1 , wherein the objective function of a total cost of the asset to be minimized is represented as f 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
)
d
t
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.
6. The method of claim 1 , wherein computing a failure rate function h 0 (t) of an asset comprises:
receiving, at said programmed hardware processor, 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
computing, at said programmed hardware processor:
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.
7. The method of claim 1 , wherein said minimizing a deviation from the optimal PM time intervals subject to the labor and budget resource constraints comprises: solving, using parallel integer linear programming at said programmed hardware processor:
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 to 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; and x i k,n binary variable indicating whether the k-th PM or a replacement is conducted for the n-th asset 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.
8. The method of claim 7 further comprising:
comparing, at said programmed hardware processor, said impact weight w n against a threshold; and if the impact is bigger than said threshold:
fixing, using said programmed hardware processor, a maintenance schedule computed for the n-the asset; and
selecting, by said programmed hardware processor, values for said lower and upper bounds for PM intervals to reduce a size of integer linear programming problem.