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Reliability Basics | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Economical Life Model for Repairable
SystemsOne consideration
in reducing the cost of maintaining repairable systems is to establish an
overhaul policy that will minimize the total life cost of the system.
However, an overhaul policy only makes sense if the systems suffer from
wearout problems. In other words, the This article presents a methodology, implemented in RGA 6, for estimating the optimum overhaul time based on the Economical Life Model for Repairable Systems. Denote C as the replacement or
overhaul cost and _{2}C_{3}_{ }as the average cost
of scheduled maintenance. Scheduled maintenance is performed for every S
miles or time interval. In addition, let N_{1}_{ }be
the number of failures in [0,
t]
and let
N_{2}
be the number of replacements in
[0,
t].
Suppose that replacement or overhaul occurs at times
T,
2T,
3T.
The problem is to select the optimum overhaul time
T = T_{0}
so as to minimize the long term average system cost (unscheduled
maintenance, replacement cost and scheduled maintenance). Since β > 1,
the average system cost is minimized when the system is overhauled (or
replaced) at time
T_{0},
such that the instantaneous maintenance cost equals the average system cost.Total system cost between overhaul or replacement is:
So the average system cost is:
The instantaneous maintenance cost at time
The following equation holds at optimum
overhaul time
Therefore:
When there is no scheduled maintenance, Eqn. 4 becomes:
The
optimum overhaul time, In RGA 6, the Economical Life Model can be applied for repairable systems or fleet analysis, which are two types of analysis of fielded systems. ## Example
A sample of field data has been collected for
a fleet of systems which suffer from wearout problems. The start time for
each system is equal to zero and the end time for each system is 10,000
miles. Each system is scheduled to undergo an overhaul after a certain
number of miles. It has been determined that an overhaul is four times more
expensive than a repair. The data set is presented in the next table.
The data set is modeled using the Crow-AMSAA (NHPP) model and an increment length of 6000miles. The estimated parameters are shown in the next figure.
The QCP can be used to calculate the optimum overhaul interval, as shown next.
Note that in the QCP, you can enter either the actual repair and overhaul costs or a factor that describes the overhaul cost in comparison to the repair cost (as in this example). | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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